geometry in design

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6Geometry in Design

Why is knowledge of geometry important for so many activities Think

about a concert that you attended How did geometry influence

the band who wrote the music the craftspeople who made the

instruments the artists who decorated the concert hall the

architect who designed the hall the engineers who planned

the hallrsquos construction and the tradespeople whose skills andtalents made it all possible

In this chapter you will

identify real-world applications of geometric shapes andfigures through investigation in a variety of contextsand explain these applications

represent three-dimensional objects using concretematerials and design or drawing software in a varietyof ways

create nets plans and patterns from physical models arising from a variety ofreal-world applications by applying the metric and imperial systems and usingdesign or drawing software

solve design problems that satisfy given constraints using physical models ordrawings and state any assumptions made

Key Terms

constraint

golden ratio

golden rectangle

isometric perspectivedrawing

net

orthographic drawings

orthographic projection

pattern

plan

scale model

tessellation

Reasoning and Proving

Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating

2 MHR bull Chapter 6



Arqum studied graphic design at Fanshawe College and now creates

signs for companies selling a product or service He discusses each

project with his customers including size materials budget and

regulations and designs layouts for billboards and business signs

Arqum uses geometric shapes and scale when he creates his designs

on the computer

6 Geometry in Desgin bull MHR



Geometric Shapes

1 Identiy the two-dimensional geometric

shapes

a) b)

c) d)

2 Identiy the three-dimensional geometric

shapes

a) b)

c) d)

3 Identiy the polygons

a) b)

c) d)

e)

Perimeter and Area

Figure PerimeterCircumference Area

rectangle P = 2l + 2w A = lw

triangle P = a + b + c A = 1

_

2 bh

circle C = πd C = 2πr A = πr 2

4 Find the perimeter and the area o a

rectangular sports 1047297eld that measures

120 m by 100 m


school crest in the shape o an equilateral

triangle with a side length o 15 cm Teheight o the triangle is approximately

13 cm

6 Find the perimeter the and area o the

base o a circular wading pool with a

radius o 12 m

Surface Area and Volume

Figure Surface Area Volume

l w

h

SA = 2lw + 2wh + 2lh V = lwh

h

bl

c

a SA = al + bl + cl + bh V = 1

_

2 blh

h

r

SA = 2πrh + 2πr 2 V = πr 2h

Prerequisite Skills




Chapter Problem

Paul has secured a co-op position for one semester with

a firm of architects and designers The firm provides

customers with designs drawings scale models

plans patterns and cost estimates for a variety of

projects such as prefabricated outbuildings houses

and industrial products Paul will learn how to provide

customers with the services that the firm offers As he

works through the co-op position Paul will be given

design tasks that will require the knowledge and skills

that he has learned during his placement

7 Wilhelm built a closed room in his garage

to use as a paint shop Te room measured

8 m by 6 m by 25 m a) Wilhelm painted the interior walls and

ceiling Find the area that was painted

b) Wilhelm plans to install a blower to

pump resh air into the room Te size

o blower required depends on the

volume o the room Find the volume o

the room

8 Sunita built a wheelchair ramp in the

shape o a triangular prism as shown

Each surace o the ramp is to be paintedmdash

with the exception o the base Find the

surace area to be painted

09 m

06 m01 m

9 A cylindrical water tank a radius o 5 f

and a height o 12 f Te interior is to bepainted with waterproo paint Find the

area to be painted and the volume o wat

that the tank can hold

Angles in a Polygon

10 Te sum o the angles in a polygon with

n sides in degrees is given by the ormu

S = 180(n - 2) I the polygon is regular

the measure o each angle is given by the

sum divided by n Find the sum o the

angles and the measure o each angle o

a regular pentagon

Scale Factors

11 Anil is planning to grow vegetables in a

market garden measuring 24 m by 36 m

o plan the garden he will draw a diagra

using a scale o 1 cm to represent 2 m

Find the dimensions o the diagram

12 ed has made a scale model o a sailboat

that he is planning to build Te model

has a length o 10 in ed used a scale o1 in to represent 4 f What is the length

the sailboat

Get Ready bull MHR



What is the link between the cells that make up a cell phone network

and a tesselation pattern How are the Mona Lisa and the Great Pyramid

o Cheops in Egypt related What is the connection between music

and geometry

In this section you will investigate some o these relations and begin to

learn how to use geometric principles in art architecture and ashion

Investigate 1 The Mona Lisa

Tools copy of Leonardo

da Vincirsquos painting

Mona Lisa

ruleror

computer

The Geometerrsquos

Sketchpad reg

Uncover one o the secrets o the Mona Lisa

1 Draw a rectangle that encloses the ace o the

Mona Lisa

Method 1 Use Pencil and Paper

Use your ruler and pencil to draw the rectangle

Measure the length and width o the rectangle

Divide the length by the width

Method 2 Use The Geometerrsquos Sketchpad regTechnology TipIf the picture appears

too large or too small

you can resize it using

any drawing program

such as Microsoftreg

Paint

Open Te Geometerrsquos Sketchpad reg Search the Internet or a picture o

the Mona Lisa Right-click on the picture and select Copy Return to

Te Geometerrsquos Sketchpad reg Select Paste Picture rom the Edit menu

Draw a rectangle around the ace o the Mona Lisa Measure the

length and width o the rectangle Divide the length by the width

Investigate Geometric Shapesand Figures61




golden ratio

bull the ratio of two lengths

is approximately 16181

golden rectangle

bull a rectangle that is

pleasing to the eye

bull the ratio of the

length to the width isapproximately 16181

2 Te ratio o the length to the width on the actual painting is 16181

Tis is known as the golden ratio A rectangle that is drawn using

the golden ratio is known as a golden rectangle Te proportions

o golden rectangles are pleasing to the eye Te golden ratio is ofen

used in art and architecture

3 Re1047298ect Tink about windows that you have seen on buildings in you

neighbourhood Which windows appear to be golden rectangles

o learn more about the golden ratio in art and architecture go to

wwwmcgrawhillcalinksfoundations11 and ollow the links

Investigate 2 Tessellations

Tools centimetre grid paper

coloured pencils or

markers pattern block template

or pattern blocks

tessellation

bull a pattern that covers

a plane without

overlapping or leaving

gaps

bull also called a tiling

pattern

Certain shapes can be used to 1047297ll a plane

completely with no gaps Tis is known as

a tessellation or ldquotiling the planerdquo As you

can see rom a piece o grid paper a square isone o these shapes Clothing is ofen made

rom abrics with a checkerboard pattern I

colours are careully chosen and placed the

pattern becomes more attractive


1 Draw a square Ten draw additional squares identical to the 1047297rst

square such that they orm a tessellation Use at least our different

colours to make a pleasing pattern or clothing 2 riangles can also be used to orm tessellations Draw a triangle

Ten draw additional triangles identical to the 1047297rst triangle such

that they orm a tessellation Colour the triangles to create a

pleasing pattern

3 Re1047298ect Can you use any triangle to tile the plane ry several example

4 You can use a combination o triangles and rectangles to orm a

tessellation Find a combination o a rectangle and several triangles

that can be used to tile the plane Draw your tessellation Colour yopattern to create a pleasing design

5 You can also use other regular geometric shapes to construct

tessellations Pattern blocks include many different regular geometr

shapes Use the blocks to experiment with different shapes that can

tile the plane Examine a vertex that is common to several polygons

What is the measure o the angle around the vertex

61 Investigate Geometric Shapes and Figures bull MHR



Tools computer

The Geometerrsquos

Sketchpad reg

pattern block applet

Method 2 Use Computer Software

1 Open Te Geometerrsquos Sketchpad reg From the Graph menu choose

Show Grid Select both axes the origin and the unit point Choose

Hide Objects rom the Display menu

2 Start in the upper lef corner and draw our points to enclose one

o the squares Select the our points in order From the Construct menu choose Quadrilateral Interior Select the our points and the

interior From the Edit menu choose Copy and then Paste Drag the

image to another square

Technology TipOnce you have a basic

pattern you can select

all elements of the

pattern Then use the

Copy command from

the Edit menu andPaste it repeatedly This

is a fast way of tiling

the plane

3 Right-click on one o the interiors Choose Color and change the

colour o the square You can continue this process to tile the screen

with different coloured squares Use at least our different colours to

design a tessellation that would make a pleasing pattern or clothing

4 riangles can also be used to orm tessellations Start a new sketch

Draw a triangle Ten draw additional triangles identical to the 1047297rsttriangle such that they orm a tessellation Colour the triangles to

orm a pleasing pattern

5 Re1047298ect Can you use any triangle to tile the plane ry several

examples


tessellation Start with a grid o squares Find a combination o a

rectangle and several triangles that can be used to tile the plane Draw

your tesselation Colour your pattern to orm a pleasing design


tessellations Go to wwwmcgrawhillcalinksfoundations11 and

ollow the links to the Pattern Block Applet Use the applet to

experiment with different shapes that can tile the plane Examine a

vertex that is common to several polygons What is the measure o

the angle around the vertex

Te only regular polygons (triangle square pentagon and so on) that

can tile the plane are those whose interior angles divide evenly into 360degTese are the triangle (60deg) the square (90deg) and the hexagon (120deg)

A pentagon or example will not tile a plane because its interior angles

(108deg) do not divide evenly into 360deg

o learn more about tessellations go to wwwmcgrawhillcalinks

foundations11 and ollow the links




Investigate 3 Cell Phone Tower Networks

Cell phones are really small radios that

communicate with towers connected to

the telephone system Te towers in an

urban area must be placed close together

because cell phones are low-poweredtypically about 3 W and have a limited

range Also each tower only offers a

limited number o requencies (about

800) restricting the number o calls that

a tower can handle at one time

In an urban area towers are placed about 5 km apart Each tower is

thought o as the centre o a hexagonal cell as shown Consider an urba

area that measures 20 km on a side Draw a tessellation using hexagons

and show how many towers are needed to service the cell phone networ

Tools ruler

grid paper


1 Let 1 cm represent 1 km Draw a square to represent an area 20 km 20 km

2 Lightly draw a hexagon with a dot in the centre to represent the

tower Draw another hexagon next to the 1047297rst one leaving no gaps

Measure the distance between the two towers I it is not close to

5 cm adjust your hexagons Once you think you have the correct siz

o hexagon continue your diagram to cover the entire area

3 How many towers are required to service the urban area

4 Re1047298ect What are the similarities between tiling the plane withtriangles designing a pattern or clothing and ensuring that cell

phone users have good service




Tools computer

The Geometerrsquos

Sketchpad reg

Method 2 Use The Geometerrsquos Sketchpad reg


Show Grid Drag the unit point on the horizontal axis until you can

see +10 and -10 on your screen on both the horizontal and vertical

axes Use the Segment ool to draw a rectangle measuring 20 squares

by 20 squares Tis will represent an area 20 km by 20 km

Technology TipDo not worry if your

hexagons look a bit

irregular You will learn

how to draw regular

geometric shapes

accurately later in this

chapter

2 Use the Segment ool to construct a hexagon in the upper lef hand

corner o the 20 km by 20 km grid Draw a point in the centre o your

hexagon to represent the tower

3 Draw another hexagon next to the 1047297rst one leaving no gaps Determine

the distance between the two towers I it is not close to 5 km adjust

your hexagons by dragging vertices Once you think you have the

correct size o hexagon continue your diagram to cover the entire area


5 Re1047298ect What are the similarities between tiling the plane with

triangles designing a pattern or clothing and ensuring that cell


o learn more about cell phones and how they work go to


Example The Golden Ratio in Ancient Architecture

A cross-section o the Great Pyramid o Cheops on the Giza plateau in

Egypt is shown Find the ratio o the slant height s to hal o the base

Express your answer to three decimal places

s

146515 m

230363 m




Solution

Hal o the base = 230363 divide 2

115182

Use the Pythagorean theorem to 1047297nd the slant height

s2 (115182)2 + (146515)2

s2 34 733538 s radic

_________

34 733538

s 186369

Te slant height is approximately 186369 m

Slant heighthal o the base 186369115182

16181

The number given for

the golden ratio 1618

is an approximation

The exact value is

1 + radic __

5_

2 Use a

calculator to verify

that this expression

gives the correct

approximation

Math Connect

Te ratio in the Example is the golden ratio once again Te golden ratio

is a connection between the Mona Lisa and the Great Pyramid A triang

that has this property such as the cross-section o the Pyramid o Cheop

is known as an Egyptian triangle

o learn more about the Pyramids go to wwwmcgrawhillcalinks


Key Concepts

bull Geometric shapes are used in architecture art and fashion These shapeoften use the golden ratio which is approximately 16181 The golden

ratio is used in design because its proportions are pleasing to the eye

bull Some geometric shapes can be used to ldquotile a planerdquo such that there are

no spaces These tiling patterns are known as tessellations Some polygon

that tile a plane are squares rectangles equilateral triangles and regular

hexagons Combinations of regular polygons can also tile a plane

Discuss the Concepts

D1 How are geometric shapes used in the construction of your school

Make a list of the shapes that you notice and where they are usedD2 Can the shape shown be used to tile the plane Use a sketch to expla




Practise A 1 Which o these regular polygons cannot be used to tile a plane

A triangle B square

C hexagon D octagon

2 Sandor claims that the screen on his new HD television is a golden

rectangle It measures 32 in by 18 in Is he correct Justiy your answer

3 Look at the buildings in your neighbourhood Identiy geometric

shapes that you see in the construction o these buildings In

particular describe the use o shapes other than squares or rectangles

4 Tink about musical instruments that you have seen Geometric shapes

are present in the design o many musical instruments List several

instruments and identiy the geometric 1047297gures used in their design

5 Te old railroad station in Petrolia ON is now the public library

Identiy the different two-dimensional and three-dimensionalgeometric 1047297gures that were used in its design

Apply BLiteracy Connect 6 Uploading personal digital pictures to the Internet is a popular

activity I you do this and identiy people in your pictures thesofware that operates the posting site can ldquolearnrdquo to identiy aces

It uses measurements and ratios similar to those you ound or the

Mona Lisa in Investigate 1 Once a ace is in the database other users

can employ the sofware to identiy individuals in other pictures

Write a short paragraph discussing the advantages and disadvantages

o having such a sofware tool reely available on the Internet




For help with questions 7 and 8 refer to Investigate A

7 Sports such as soccer or lacrosse are ofen played on rectangular

1047297elds Investigate the dimensions o several o sports 1047297elds Find

the dimensions o an Olympic swimming pool Are any dimensions

close to a golden rectangle

Technology TipYou can search for

images directly using

most search engines

rather than searching

for web sites and then

looking for images

8 Use the Internet to 1047297nd a picture o each o these amous buildingsCopy each picture into Te Geometerrsquos Sketchpad reg and use the

sofware to identiy any golden rectangles that were used in the desi

a) Te Parthenon in Athens Greece Use a ront view

b) Te aj Mahal in Agra India Use a ront view taken down the

re1047298ecting pool

c) Te United Nations building in New York NY Use a view rom

the river

d) Te Buddhist emple in Niagara Falls ON Use a ront view

9 Te actor Drew Barrymore is considered as a classic example o aldquoround acerdquo while actor Fred Gwynne (who played a Frankenstein-

like character on a popular television show) is considered to be an

example o a ldquolong acerdquo Search or pictures o each actor Use penci

and paper or Te Geometerrsquos Sketchpad reg to determine how the acto

aces compare to the golden ratio

10 Te aces o some animals appear to have a greater width than heigh

One example is a house cat Use pencil and paper or Te Geometerrsquos

Sketchpad reg to determine the acial ratio o a typical cat




Chapter Problem 11 Paul has been reading about the history o architecture Ancient

Egyptian builders ofen needed to lay out large right angles or their

constructions Tey did this using a ldquo12-knot roperdquo Obtain a piece o

string about 1 m long ie 12 knots in the string such that the knots

are 5 cm apart ie the ends o the string together such that you have

12 equal sections Arrange the string to orm a triangle with sides o

3 4 and 5 sections a) Measure the angle opposite the longest side

b) Write a short explanation o the mathematics behind this method


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating

12 Where is the geometry in music Te 1047297rst ew bars o the classic

hard rock piece ldquoIn-A-Gadda-Da-Vidardquo by Iron Butter1047298y widely

acknowledged as the 1047297rst heavy metal band are shown

c

1

a) Notice the groupings o our notes Draw lines joining adjacent

notes in each group and then a single line returning to the 1047297rst

note Te 1047297rst triangle has been drawn or you Describe the kinds

o triangles that are ormed

b) riangles are ofen present in music composition Find two three-

note congruent triangles in this short excerpt rom the popular

holiday song ldquoO annenbaumrdquo

1

34

13 A stained glass panel contains several rectangles Which rectangles

are golden rectangles or close to being golden rectangles Explain

how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check

14 Anwar claims that a hexagon does not need to be regular to tile

the plane He says that any hexagon that has opposite sides equal

will work

a) Draw a hexagon with opposite sides equal Be sure to use three

different lengths in your drawing

b) Determine whether your hexagon can be used to tile the plane I

it can show how it can be done I it cannot explain why not

Extend C 15 An architect is designing a window using the golden ratio

a) Te longer side measures 25 m o the nearest tenth o a metre

what should be the length o the shorter side

b) Draw a sketch o the window Cut the window in hal using themidpoints o the lengths Compare the ratios o sides o one o th

smaller rectangles What do you notice

16 Many countries use international paper sizes such as ISO A4 A she

o A4 paper measures 297 cm by 210 cm Tis size is sold in Canad

at offi ce supply stores Obtain a piece o A4 paper or make one rom

a larger piece o paper

a) Find the ratio o the length to the width and record it

b) Fold the paper in hal across a line joining the midpoints o the

lengths Measure the length and width o the olded paper Findthe ratio o the length to the width

c) Fold the paper again Find the ratio o the length to the width o

the olded piece What do you notice

d) Te ratio o length to width or the ISO standard is always radic__

2 1

Use a calculator to compare this ratio to the ratios that you ound

17 Use pencil and paper or sofware such as Te Geometerrsquos Sketchpad

to design abric with a tessellation print Te abric should appeal to

person with a particular career or hobby such as a musician a gole

a pilot a nurse etc Be sure to use basic geometric shapes to orm amore complex shape Be creative in your selection o colours




Perspective and OrthographicDrawings62

scale model

bull a model that is an

enlargement of a small

object or a reduction of

a large object

Habitat 67 is an apartment complex in Montreal It was designed by

Canadian architect Moshe Sadie or Expo rsquo67 as an experiment in

building apartments that allowed urban dwellers to enjoy both privacy

and outdoor space A scale model was used to represent what the

complex would look like when 1047297nished


bull visual representation

of three-dimensional

objects in two

dimensions

orthographicprojection

bull a set of drawings that

show up to six views of

an object

bull usually front side and

top views are given

orthographic drawing

bull a drawing that

uses orthographic

projection

Another means o representing three-dimensional objects is an isometric

perspective drawing which creates the illusion o three dimensions on a

two-dimensional plane A third representation is a series o orthographic

projections which illustrate ront side and top views o the object

How could you draw the isometric perspective and the orthographic

representations o Habitat 67 How can drawing sofware be used to

create these representations

o learn more about Habitat 67 go to wwwmcgrawhillcalinks foundations11 and ollow the links




Investigate 1 Perspective Drawings of Cubes and Rectangular Prisms

Use a single linking cube or a model o a cube urn the cube until an

edge is acing you Ten tip the cube downwards as shown Tis is the

perspective that you will draw

Tools isometric dot paper

linking cubes or other

physical models ofcubes

ruler

coloured pencils


1 a) Inspect the isometric dot paper Find the lines o dots that are

vertical Draw a short vertical line segment in blue

b) Find the lines o dots that slope down to the right at 30deg Draw ashort line segment sloping down to the right at 30deg in red

c) Find the lines o dots that slope down to the lef at 30deg Draw a

short line segment sloping down to the lef at 30deg in green

d) Use the dot pattern to draw the isometric perspective as shown

2 Re1047298ect Compare the isometric perspective drawing with the view o

the cube On an isometric perspective drawing the lengths on the

drawing are the same as the lengths on the real cube Check that the

sides o the cube on the drawing are o equal length

The word ldquoisometricrdquocomes from the

Greek words ldquoisordquo

meaning ldquothe samerdquo

and ldquometricrdquo meaning

ldquomeasurerdquo

Math Connect 3 Use linking cubes to construct a model o a rectangular prism that

measures 1 cube by 2 cubes by 3 cubes Draw an isometric perspect

drawing o the prism

62 Perspective and Orthographic Drawings bull MHR



Tools computer

The Geometerrsquos

Sketchpad reg


1 Open Te Geometerrsquos Sketchpad reg Choose Open rom the File menu

Navigate to the directory that stores Te Geometerrsquos Sketchpad reg

1047297les on your computer Tis will likely be called Sketchpad and

be located in the Program Files directory Choose Samples then

Sketches and then Geometry Select and open the 1047297le Dot Papergsp

Select the button Isometric vertical

Technology TipYou can change the

spacing of the dots

using the slider marked

ldquodot spacingrdquo

2 Inspect the isometric vertical dot pattern Find the lines o dots that are

vertical Find the lines o dots that slope down to the right at 30deg Find

the lines o dots that slope down to the lef at 30deg Use the dot pattern

to create the isometric perspective drawing o the cube as shown





4 Use linking cubes to construct a model o a rectangular prism

that measures 1 cube by 2 cubes by 3 cubes Draw an isometric

perspective drawing o the prism




Investigate 2 Orthographic Drawings of Cubes and Rectangular Prism

Tools square dot paper


physical models of

cubes

ruler


1 Use a single linking cube or a model o the cube urn

Front Vithe cube until the ront is acing you Draw the ront

o the cube Label the drawing

2 urn the cube until the right side is acing you Draw and label the

side view Similarly draw and label the top view

3 Re1047298ect What do you notice about the three orthographic drawings

o the cube A cube is a simple shape However the same method

can be used to represent more complex shapes

4 Use linking cubes to construct a model o a rectangular prism that

measures 1 cube by 2 cubes by 3 cubes Create three orthographic

drawings o the prism ront view side view and top view

Tools computer

The Geometerrsquos

Sketchpad reg


1 Open Te Geometerrsquos Sketchpad reg Open the 1047297le Dot Papergsp

Select the button Square dot paper

2 Use a single linking cube or a model o a cube urn the cube until

the ront is acing you Draw the ront o the cube Label the drawin

3 urn the cube until the side is acing you Draw and label the side

view Similarly draw and label the top view Reer to the diagrams in

Method 1

4 Re1047298ect What do you notice about the three orthographic drawings o

the cube A cube is a simple shape However the same method can

used to represent more complex shapes




You have been using Te Geometerrsquos Sketchpad reg to draw perspective

diagrams echnical designers use more sophisticated programs such as AutoCADreg Te science-1047297ction television series Babylon 5 was created

using AutoCADreg to render three-dimensional spaceships space station

and even some aliens Amateur 1047297lmmakers ofen use commonly availab

drawing and design sofware to create inexpensive special effects or

their productions

o learn more about drawing sofware go to wwwmcgrawhillcalinks





Example 1 Modelling a Flight of Stairs

a) Use linking cubes to create a model or a 1047298ight o stairs Tere are

three steps Te steps are 30 cm deep and 120 cm wide Each riser

measures 30 cm Let the side o a cube represent 30 cm

b) Draw an isometric perspective drawing o the model

c) Sketch a set o orthographic drawings o the model

Solution

a) Te side o a cube represents 30 cm Te stairs will be 4 cubes wide

and 3 cubes deep at the bottom layer

b) Use isometric dot paper or Te Geometerrsquos Sketchpad reg to create the

isometric perspective drawing o the stairs




c) Use square dot paper or Te Geometerrsquos Sketchpad reg to draw the

orthographic drawings or the stairs

ront view

top view

side view

Example 2 Isometric Drawing of a Square-Based PyramidConstruct a model o a square-based pyramid using drinking straws

and masking tape or other materials Use isometric dot paper or Te

Geometerrsquos Sketchpad reg to sketch an isometric perspective drawing o

the pyramid

Solution

First draw the base Te base will appear as a diamond shape Select a

point in line with two opposite vertices to be the apex o the pyramid

Complete the pyramid by drawing the sides




Example 3 Isometric Drawings With Curved Edges

Consider a concrete model o a cylinder such as a juice or soup can

Use Te Geometerrsquos Sketchpad reg to sketch an isometric perspective

drawing o the can

SolutionCurved edges are represented by arcs o circles in isometric

perspective drawings

bull Open Te Geometerrsquos Sketchpad reg Open the 1047297le Dot Papergsp

Press the button Isometric vertical

bull Use the Point ool to draw three points just to the lef o three

o the points on the paper as shown

Technology Tip The dots in the

dot paper sketch

in The GeometerrsquosSketchpad reg are drawn

using transformations

If you try to draw an

arc through three of

these dots it will not

work Try it

bull Select the three points Select Arc Trough 3 Points rom the

Construct menu Drag the arc slightly to the right such that it alls

on three points on the dot paper In a similar manner construct

three more arcs Ten use the Segment tool to complete the sideso the cylinder as shown

Note You can also draw an isometric perspective drawing o a cylinder

on paper using a ruler and a compass




Key Concepts

bull A three-dimensional object can be represented in three ways

ndash as a scale model using concrete materials

ndash as an isometric perspective drawing

ndash as a set of orthographic drawings (usually the front view side view

and top view)


D1 Consider the isometric perspective drawing shown Indira claims

that all three orthographic drawings of this object will look the

same Laszlo says that only the front and the side will look the

same Soon-Tek says that all three will be different Who is correct

Give reasons

D2 Consider the isometric perspective drawing shown Discuss

whether the drawing could represent a real object Give reasons

for your answer




Practise A 1 Which o these representations is not suitable or representing a

three-dimensional object Explain why

A a scale model

B an isometric perspective drawing

C a blueprint showing ront and side views

D a set o orthographic drawings

2 Marcie is building a scale model o an offi ce building using linking

cubes Te building is a rectangular prism with a length o 49 m a

width o 35 m and a height o 56 m Suggest a suitable scale and

calculate the dimensions or the model

3 Farmer Jacques is building a new silo in the shape o a cylinder o

maximize the storage volume he is planning to make the diameter

the same as the height Which o these diagrams matches the side

view

A B C D

4 Ivanka is using linking cubes to make a scale model o the isometric

perspective drawing shown Describe the physical model in terms olength width and height




Apply BLiteracy Connect 5 Study the isometric perspective drawing shown Write a short

paragraph explaining why this drawing cannot represent a real obje

For help with question 6 refer to Example 1

6 Central courtyards are eatured in the architecture o many cultures

Te Romans ofen built their houses or villas with a central open

space surrounded by the rooms o the house a) Use linking cubes or other concrete materials to build a scale

model o a Roman villa Include a set o rooms surrounding a

central open space

b) Use isometric dot paper or Te Geometerrsquos Sketchpad reg to create

isometric perspective drawing o the model

c) Use isometric dot paper or Te Geometerrsquos Sketchpad reg to create

set o orthographic drawings or the model

For help with question 7 refer to Examples 2 and 3

7 Salvatore needs an isometric perspective drawing o a cone such tha

the height o the cone appears equal to the diameter

a) Use isometric dot paper or Te Geometerrsquos Sketchpad reg to create

an isometric perspective drawing o a cone that closely matches

Salvatorersquos requirements

b) Is it possible to match the height to the diameter exactly i

the diameter and the tip o the cone must land on one o the

dots Explain




8 Te artist M C Escher ofen used alse perspective in his drawings

to depict impossible situations Study the Escher work Convex

and Concave careully to see how the illusions work Consider the

ldquostairwayrdquo at the centre right o the drawing

a) Approximate the stairway with a triangle (ie do not show the

individual steps) Create a set o orthographic drawings in which

you see this as a stairway going up b) Create a set o orthographic drawings in which you see this as the

bottom support o an arch

c) Describe the triangles that occur in your orthographic drawings

Chapter Problem 9 Paul has been given a set

ront view top view side view

o orthographic drawings

or an inn to be built

near a tropical beach

Te design incorporates

open spaces throughoutthe building or air circulation Paulrsquos task is to create a scale model

and an isometric perspective drawing o the inn

a) Use the orthographic drawings to construct a scale model using

linking cubes or other concrete materials

b) Use isometric dot paper or Te Geometerrsquos Sketchpad reg to make an

isometric perspective drawing o the inn

Achievement Check

10 Sara used linking cubes to build the

structure shown in isometric perspective

Which drawing is a possible

orthographic projection o the top

view o the structure Explain

A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




Extend C 11 Use isometric dot paper or Te Geometerrsquos Sketchpad reg to create an

ldquoimpossiblerdquo isometric perspective drawing different rom the ones

in question D2 and question 5

12 In isometric perspective drawings the lengths in the drawing o a

cube match the side lengths o the real cube In real lie the apparen

size o an object decreases as the object moves arther away rom an

observer Artists use the concept o a ldquovanishing pointrdquo to achieve th

effect o perspective in their art

o see how this works draw a square using square dot paper or Te

Geometerrsquos Sketchpad reg Select a point ar away rom the square as

shown Join the vertices o the square to this ldquovanishing pointrdquo

Use these lines to draw the rest o the cube in perspective Ten hid

or erase the parts o the lines that extend outside o the cube

13 Advertisements or buildings that have not yet been constructed

ofen make use o two-point perspective In the example shown eac

street leads to a vanishing point Te lef side view o the building

uses the lef vanishing point while the right side view uses the right

vanishing point

Use square dot paper or Te Geometerrsquos Sketchpad reg to make a

two-point perspective drawing o the model in question 4




Create Nets Plans and Patterns63

Commercial products are packaged in various shapes o containers Tese

containers are ofen manuactured as a two-dimensional net and then

olded or bent into a three-dimensional shape One example is a cereal

box which is a rectangular prism

Other three-dimensional objects such as houses or items o urniture are

constructed rom a plan Plans are usually parts o nets drawn to scale

that give enough inormation to construct the three-dimensional objectClothing is made by using a pattern to cut the cloth Te cloth pieces are

then sewn together to make the clothing item A pattern is usually a net

that is drawn in separate pieces

Investigate 1 Design a Box

Tools empty cereal box

scissors

ruler

tape

Many products are packaged in rectangular prisms

1 Measure and record the dimensions Cereal

l w

ho the cereal box

net

bull a two-dimensional

diagram that can be cut

out and folded to form a

three-dimensional object

plan

bull a scale drawing of astructure or object

bull a design or arrangement

scheme

pattern

bull a form template or

model from which an

object can be created




The 1047297rst of the

modern packaged

cereals was toasted

corn 1047298akes introduced

in 1906 To learn more

about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links

Math Connect 2 Find the edge on the cereal box that was used to join the cardboard

Cut along this edge Cut any other joins that you 1047297nd

3 Unold the cereal box to orm a net Measure the edges o the net

Identiy each edge as one o the dimensions o the box

4 Re1047298ect Compare the measures o the net to the measures o the cere

box How are the dimensions o the net ound to produce a box o thdesired shape and size

5 Sketch a net or a box that will measure 4 cm by 3 cm by 2 cm Labe

the edges est your net by cutting it out and olding it into a box

ape the box together Measure the dimensions to check that the

box matches the dimensions given Suggest a product that would be

suitable or a package o this size

Investigate 2 Design a CylinderTools empty tissue roll

ruler

tape

Some products are packaged in cylindrical containers

1 Measure and record the height and diameter o the tissue rolld

h

2 Cut the roll along its height and spread it into a rectangle race

the rectangle onto a piece o paper Measure the dimensions o the

rectangle Which dimension is equal to the height o the roll What is

the name o the other dimension in relation to the cylinder Divide th

other dimension by the diameter o the tissue roll What do you notic

3 o draw two congruent circles or the top and bottom o the cylinde

what dimension do you need to consider Draw two circles or the

top and bottom using this dimension Cut out the net and bend it t

orm a cylinder with a top and a bottom

4 Re1047298ect Compare the measures o the net to the measures o the

cylinder How are the dimensions o the net related to the height an

diameter o the cylinder

5 Sketch a net that can be bent into a cylinder with a diameter o 6 cm

and a height o 10 cm est your net by cutting it out and bending it in

a cylinder with a top and a bottom ape the model together

63 Create Nets Plans and Patterns bull MHR



Investigate 3 Patterns

Tools simple item of clothing

(old T-shirt etc)

scissors

newsprint

Patterns or clothing are nets that are used to cut cloth Te pieces o cloth

are sewn to orm the three-dimensional garment

1 Identiy the seams on the article o clothing

Use scissors to careully cut the threads along

each seam Lay out the pieces

2 Sketch the pattern on newsprint

3 Re1047298ect How can clothing manuacturers use a pattern to cut out

hundreds o pieces at one time Research clothing manuacturing

on the Internet to help you explain

4 Sketch a pattern that could be used to

cut out the pieces or a bucket hat

Example Cabin Plan

a) Draw a 1047298oor plan or a vacation cabin Te cabin will measure 8 m

along the side by 6 m across the ront Tere will be two congruent

square bunkrooms at the back with side length 3 m Tere will be a

bathroom measuring 2 m by 3 m along the ront wall Te remainingspace will be living area Label the measurements on your plan

b) Te cabin will be o the A-rame type measuring 5 m tall

Sketch orthographic drawings o the cabin Label all measurements




Solution

a) Select a suitable scale For example let 1 cm represent 1 m Draw a

rectangle to represent the 1047298oor o the cabin Draw walls or the two

bunkrooms and the bathroom Label all dimensions

6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m

b) Draw the ront side and top views o the cabin

6 m 6 m 6 m

8 m

5 m5 m


Key Concepts

bull A three-dimensional object can be constructed by folding or bending

a two-dimensional net

bull Parts of a net drawn to scale can be used as a plan to construct a


bull A net can be separated into pieces to form a pattern The pattern

can be used to make pieces of a three-dimensional object which

can be assembled into the object

Discuss the ConceptsD1 Sketch a net for a cube Explain how it must be folded to make

the cube

D2 A hobby club builds and 1047298ies model airplanes To make such an

airplane would you use a net a plan or a pattern Discuss the

advantages and disadvantages of each representation




Practise A 1 Consider the net shown Te distance

between two dots represents 5 cm When

olded what three-dimensional object

will the net make

A an open box 5 cm high with a square

base with side length 15 cm

B a closed box 5 cm high with a square


C an open box 15 cm high with a square


2 Draw a net that can be used to make a cube-shaped box with an

open top

3 Sketch a pattern that could be

used to make a mitten

4 Woodworking magazines ofen include diagrams in their articles

about building urniture I you were writing an article about building

a bookcase would you include a net a plan or a pattern Explain

Apply B

For help with question 5 refer to Investigate 1Literacy Connect 5 Neela submitted an alternative net or a cube as shown

a) Write a short paragraph explaining why Neelarsquos net will not work

b) Explain how the net can be modi1047297ed so it will work




For help with question 6 refer to Investigate 2

6 A bakery needs a new cylindrical package or their oatmeal cookies

Each cookie is 1 cm thick and has a diameter o 8 cm Each package

should hold a dozen cookies

a) Draw a net that can be used to make a model o the package

b) Cut out your net and bend it to orm the package ape the mod

together

c) Check the dimensions o the model by measuring Do they meet

the requirements

7 An imported cheese is sold in the

4 cm

4 cm

4

12 cm

shape o a triangular prism Te ends

o the prism are congruent equilateral

triangles Each triangle has a side

length o 4 cm and the prism is

12 cm long

a) Draw a net that can be used to make

a model o the package

b) Cut out your net and bend it to

orm the model ape the model together


the requirements

Chapter Problem 8 Paulrsquos company has been asked to design a grain storage shed that

will be exported to developing countries Te shed will be made o

galvanized sheet metal with our congruent square walls with side

length 3 m Te roo will be our congruent equilateral triangles wit

side length 3 m Te bottom will be lef open so that the shed can be

attached to a poured concrete base Te sheds will be shipped as net

to conserve shipping space Paulrsquos task is to design the net or the

shed and to estimate the cost o the metal required

3 m

3 m

3 m3 m

a) Draw a net that can be used to make a model o the shed

b) Find the total area o sheet metal required

c) Sheet metal costs $650m2 Find the cost o the metal or the she




9 Te owner o a garden centre needs a pedestal or displaying a prize-

winning 1047298owering plant Te pedestal is to be made o painted sheet

metal with dimensions as shown Te bottom o the pedestal will be

lef open Draw a net that could be used to make the pedestal Show

all measurements

20 cm

10 cm

10 cm

Achievement Check

10 Reer to question 9 Te pedestal will be modi1047297ed Now the top

will have a circular hole to accommodate a 10-cm diameter metal

cylinder Te height o the cylinder will be 30 cm Draw the net

or the modi1047297ed pedestal and the net or the cylinder Show

all measurements

Extend C 11 A regular tetrahedron is a three-dimensional shape with our

congruent equilateral triangular aces Consider a tetrahedron

made o equilateral triangles with side length 3 cm

a) Draw a net that can be used to make the tetrahedron

b) Cut out your net and old it into a tetrahedron ape thetetrahedron together

12 Lydia made a square shape using eight linking

cubes leaving the centre space empty Draw a

net that could be used to make a paper model

o the shape I you think it is not possible to

make a net explain why

13 A regular octahedron has eight congruent

equilateral triangular aces It looks like twosquare-based pyramids glued together at their

bases Draw a net that can be used to make a regular

octahedron Cut out your net and old it into an

octahedron ape the octohedron together




Use The Geometerrsquos Sketchpadreg to Draw Plans WithDynamic Measurements

Tools computer

The Geometerrsquos

Sketchpad reg

Use Te Geometerrsquos Sketchpad reg to draw a scale 1047298oor plan or the vacatiocabin in Example 1 o section 63 Te cabin will measure 8 m along

the side by 6 m across the ront Tere will be two congruent square

bunk rooms at the back with side length 3 m Tere will be a bathroom

measuring 2 m by 3 m along the ront wall Te remaining space will be

living area

1 Start by constructing the 1047297xed boundaries o the cabin Open Te

Geometerrsquos Sketchpad reg Choose Preferences rom the Edit menu a

then the Units tab Choose Show Grid rom the Graph menu Drag

the origin to the lower lef area o the workspace I necessary adjus

the unit point until you can see at least 10 gridlines horizontally and8 gridlines vertically

2 Choose Plot Points rom the Graph menu Plot the point (8 6) In the

same way plot the points (0 6) and (8 0) Select the origin and the thr

plotted points moving clockwise Choose Segments rom the Constr

menu You now have a rectangle that represents the boundaries o the

cabin ry to move one o the corners What happens

3 Use the Segment ool to sketch the bunk rooms and the bathroom

Select the endpoints o the width o a bunk room Choose Coordin

Distance rom the Graph menu Move the measurement to a

convenient location Measure and label dimensions or remaining th

rooms Include the outside dimensions o the cabin Hide the axes a

the grid

Use Technology

Use Technology bull MHR



4 Re1047298ect Select the line segment that orms the wall between

the bunk rooms Move it up and down Note how the measurements

change as you move the line segment ry changing the dimensions othe other rooms

5 Calculate the area o each room Choose Calculate rom the Measure

menu A calculator will appear Select the length o one bunk room

Press the button Select the width o the bunk room Move the area

measurement to a convenient location Change the label to Bunk

Room 1 Measure the areas o the other rooms o 1047297nd the living

area calculate the area o the entire cabin and subtract the areas o

the rooms

6 Re1047298ect Change the dimensions o one room by dragging a wallNotice how the measurements including the areas change




Scale Models64

A scale model o a building a piece o urniture or an item o clothing

is useul in the planning stages o construction or manuacturing Te

model can highlight problems that are not obvious in a two-dimensiona

representation Te model can also demonstrate improvements to a plan

Fixing the plan beore production can save materials resources and tim

Example 1 Design a Cylindrical Tank

An engineer is designing a cylindrical tank or a tanker truck that will

hold about 800 f3 o liquid Te length o the cylinder should be twice

the diameter and should be a whole number o eet

a) Use the ormula or the volume o a cylinder to determine the

dimensions o the tank required

b) Select a suitable scale and draw a net or a paper model o the tank

c) Cut out your net and bend it into the cylindrical shape ape the

model together

64 Scale Models bull MHR



Solution

a) Te ormula or the volume o a cylinder is V = πr 2h In this case h is

twice the diameter or our times the radius

Te volume ormula becomes

V = πr 2(4r )

= 4

πr

3

ry different values or the radius

Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708

A radius o 4 f gives a volume o just over 800 f3 Using a radius o

4 f the diameter is 2 times 4 f or 8 f and the length is 2 times 8 f or 16 f

b) One dimension o the rectangle or the net is the length o the

cylinder or 16 f Te other dimension is the circumerence o

the cylinder

C = πd

= π(8)

251

Te circumerence is approximately 251 f

Select a suitable scale (or example

1 in represents 4 f) Draw therectangle or the with a net Add

two circles each diameter o

2 in or the ends

c)




Example 2 Design a Pentagonal House

An architect has designed a house in the shape o a regular pentagonal

prism Te 1047298oor orms a pentagon with a side length o 6 m Te 1047297ve

walls are congruent squares Te peaked roo is made o 1047297ve congruent

equilateral triangles Select a suitable scale Draw a net that can be used

make a scale model o this house Ten cut out your net and old it intomodel o the house ape the model together

Solution


bull Choose an appropriate scale For example 1 cm represents 1 m Draw

a regular pentagon A regular pentagon consists o 1047297ve congruent

isosceles triangles whose apexes meet at the centre o the pentagon

Te apex angle or each triangle is 360deg divide 5 = 72deg Draw a dot or the

centre and a horizontal line segment to the 1047297rst vertex Draw an angle

o 72deg rom the horizontal line segment Use compasses to help you

create an isosceles triangle that includes the second vertex Continue

this process until you have 5 vertices Join the vertices

bull Use a ruler and compasses to draw a square on each side o the

pentagon Ten draw an equilateral triangle on each square

bull Use your net to make a

scale model o the house


bull Draw the pentagonal base urn on automatic labelling o points Sket

a horizontal line segment AB Select point A and choose Mark Cente

rom the ransform menu Select the segment and point B ChooseRotate rom the ransform menu Change the 1047297xed angle to 72deg

Select Rotate Continue until you have 1047297ve vertices Join the vertices

bull Draw the square walls Select one endpoint o a side Choose Mark

Center rom the ransform menu Select the segment and the other

endpoint Choose Rotate rom the ransform menu Change the 1047297xe

angle to 90deg Select Rotate Repeat or each side Ten use the other




s

t

1 m

1 m

1 m

3 m

endpoint o the side as the centre and rotate through an angle o 270deg

Complete the 1047297ve squares

bull Draw the triangular roo aces Select one outside corner o a square

Choose Mark Center rom the ransform menu Select the outside

segment and the other endpoint Choose Rotate rom the ransform

menu Change the 1047297xed angle to 60deg Select Rotate Repeat or the other

squares Complete the 1047297ve triangles Hide the points and labelsbull Print your net and use it to make a scale model o the house

Example 3 Design a Tent

An out1047297tting company plans to manuacture a new tent Orthographic

drawings or the tent are shown Te distance between pairs o horizontal

or vertical dots represents 1 m

s

t


Use paper or drinking straws and masking tape to construct a scale model

o the tent Select a suitable scale Make any necessary calculations

SolutionLet s represent the slant length o the side o the tent and t represent the

slant length o the roo Use the Pythagorean theorem to 1047297nd the lengths

o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14

Te side slant length is Te top slant length is

approximately 32 m approximately 14 m

Select a scale that is suitable or your materials For example let 4 cm

represent 1 m Te base o the model will measure 4 times 4 cm or 16 cm

Te side slant length will measure 4 times 32 cm or 128 cm Te top slant

length will measure 4 times 14 cm or 56 cm




Key Concepts

bull Scale models can be constructed using nets orthographic drawings

or isometric perspective drawings

bull Models are useful in the planning stages of a project

bull Models can identify problems in a plan or suggest improvements


D1 Can a model of any three-dimensional object be constructed

using a net Explain

D2 To obtain a building permit for a house the owner must submit a

set of orthographic drawings known as elevations Suggest reasons

why orthographic drawing are required rather than a scale model

or an isometric perspective drawing

Practise A 1 Maria is building a scale model o a garden shed She will let 1 in

represent 2 f I the base o the shed measures 10 f by 12 f what

measurements will Maria need or the model

2 Te most amous Canadian-designed and -built aircraf was the Av

CF-105 Arrow A number o 1 _

8 scale models were made or testing i

a wind tunnel Te length o the model was 10 f 8 in What was the

length o the ull-size aircraf

3 Te town o Port Colborne is planning to construct a new

recreational centre including a skating arena and a swimming pool

Suggest reasons why an architect bidding on the contract wouldprovide a scale model in addition to drawings

4 Freda is planning a new silo or her arm made o a cylinder topped

with a hemisphere Te height o the cylinder will orm a golden rat

with its diameter Freda would like to make a scale model o the silo

to see i her design works Describe a procedure and suggest materi

that Freda could use to make the scale model




5 Suleiman plans to construct a

ldquominimalistrdquo chair as shown in

the isometric perspective drawing

He will use three pieces o

1 in-thick plywood Te distance

between a pair o dots represents

1 f Draw plans that show the pieces owood required with measurements

Apply BLiteracy Connect 6 A standard gol ball has a diameter o 168 in You have been

contracted to design a package to hold 12 gol balls Sketch a set

o orthographic drawings or your chosen package Write a brieexplanation o why you selected this design

7 Draw an isometric perspective drawing or the tent in Example 3

8 A local artist wants to include a rectangular prism in her newest

sculpture Te prism should have a length o 1 m a width o 2 m

and a height o 3 m

a) Select a suitable scale Use pencil and paper or Te Geometerrsquos

Sketchpad reg to draw a net that can be used to make a scale model

o the prism

b) Cut out your net and old it to make the model ape the model

together

c) Te artist has decided to paint all o the sides o the prism except

one which will be placed on the ground She has not however

decided which side will be placed on the ground I paint costs

$2m2 what are the possible costs or painting the prism


9 A new soup can must hold at least 500 mL o soup Its height must

be equal to its diameter Te height and the diameter must be wholenumbers o centimetres

a) Determine the minimum height and width o the can

b) Select a suitable scale Draw a net that can be used to make a scale

model o the can

c) Cut out your net and bend it to make a scale model o the can

ape the model together




For help with question 9 refer to Example 2Reasoning and Proving

Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating

10 A band council has decided to commission a new community centr

to be used or various events such as the annual pow-wow Te cent

will be in the shape o a regular hexagon with each side measuring

10 m Each congruent rectangular wall will be 3 m high Te buildin

will have a 1047298at roo

a) Select a suitable scale Choose measurements that ensure youhave a regular hexagon Use pencil and paper or Te Geometerrsquos

Sketchpad reg to draw a net that can be used to make a scale mode

o the centre


together

c) Te base o the centre will be poured concrete 10 cm thick ake

measurements rom your net to 1047297nd the area o the hexagonal

base Multiply the area by the thickness to determine how many

cubic metres o concrete will be needed d) Concrete costs $75m3 delivered to the site Estimate the cost o

the concrete or the base

11 Afer studying the scale model in question 10 the band council

decided to change the 1047298at roo to one made o six congruent isoscel

triangles Tis will ensure that snow and rain will not accumulate on

the roo It will also make the building more attractive Te central

peak o the roo will be 5 m above the 1047298oor

a) How will this change affect your net Explain

b) How will this change affect the cost o concrete or the base Explai

Chapter Problem 12 A customer has seen the post offi ce in Gorrie ON and would like

a similar building or his business He has supplied Paulrsquos company

with sample orthographic drawings as shown Te distance betwee

pairs o horizontal or vertical dots represents 2 m

a) Draw a net that can be used to make a scale model o the buildin

b) Cut out the net and construct the model ape the model togeth

c) Te cost o the building is estimated to be $1200m2 o 1047298oor area

Estimate the cost o the building




Achievement Check

13 A propane storage tank is to be built rom the orthographic drawings

shown Te distance between pairs o horizontal or vertical dots

represents 1 m

Which description best 1047297ts the propane tank Explain

A A cylinder 11 m long with a hemisphere o radius 2 m at

each end

B A cylinder 7 m long with a hemisphere o radius 2 m at each end C A cylinder 11 m long with a hemisphere o radius 4 m at

each end

D A cylinder 7 m long with a hemisphere o radius 4 m at each end

Extend C 14 How can you make a net or a cone Roll a piece o notebook paper

to orm a horn Cut the horn to orm a cone Continue cutting until

you have the minimum amount o paper necessary to orm the cone

Unroll the paper and sketch the net

15 Use trial and error to make a net or a cone with a radius o 5 cm

and a height o 3 cm Cut out your net and use it to make the cone

Measure the dimensions to check that they are correct




Solve Problems With GivenConstraints65

constraint

bull a condition that limits

the acceptable range

of values for a variable

Designers such as architects engineers or ashion designers ofen must

ensure their designs satisy given constraints Examples o constraints

include a maximum cost a minimum or maximum size or regulations

governing saety energy effi ciency or perormance

Example 1 Modular House

Orthographic drawings or a modular house are shown

s

tu


Te distance between pairs o vertical or horizontal dots represents

5 f Te house will be built in two sections and then transported to the

building site or assembly Highway traffi c rules limit the width o each

section to 15 f or less Te centre wall will be located 15 f rom the lef

ront wall It will be doubly thick so that each hal o the house will hav

our walls during transport

65 Solve Problems With Given Constraints bull MHR



a) Select a suitable scale Draw a net or each section o the house

b) Cut out your nets and make scale models or the two sections o the

house ape your models together Ensure that the models 1047297t together

properly or assembly

Solution

a) From the orthographic drawings the centre wall is 175 f high Usethe Pythagorean theorem to determine the slant lengths o the roo

s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50

s 168 t 56 u 71 Slant length s is Slant length t is Slant length u is

approximately 168 f approximately 56 f approximately 71 f

Let the distance between pair o horizontal or vertical dots represent

5 f Calculate the measures or the scale drawing by dividing each

actual measure by 5

Te net or the lef side o the house

168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f




Te net or the right side o the house

175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f

b) Use the nets to make scale models o the two halves o the house

o learn more about modular homes go to wwwmcgrawhillcalink


Example 2 Oil Tank

Sometimes basic saety considerations depend on understanding nets

and volumes Consider an engineer who needs to design a square-based

berm a shallow container to prevent the spread o oil rom a leaking oil

tank Te cylindrical oil tank is 20 m in diameter and has a height o

20 m Te berm must have a height o 5 m




a) Make appropriate calculations and 1047297nd the minimum dimensions

o the berm

b) Select a suitable scale Draw a net or the berm and a net or the oil

tank Use your nets to construct a scale model o the arrangement

required

Solution a) Start by calculating the maximum volume o oil that must be

contained i the tank is ull

V = πr 2h

= π times 102 times 20

6283

A square-based

berm has the

shortest side

lengths requiredto contain a

given volume

Minimizing the

bermrsquos perimeter

cuts down on the

cost of materials

Math Connect Te berm must be able to hold 6283 m3 o oil

Let the side length o the square base o the berm be represented by s

Volume o berm = area o base times height

= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354

It is saer to overestimate Round 354 m up to 40 m Suitable

dimensions or the berm would be 40 m by 40 m by 5 m b) Draw a net or the berm Let the space between pairs o horizontal or

vertical dots represents 5 m Te base o the berm measures 8 dots by

8 dots and the height measures 1 dot




Draw a net or the oil tank Te net consists o two circles o

diameter 20 m or the top and bottom plus a rectangle or the wall

o the cylinder One dimension o the rectangle is the same as the

height o the tank or 20 m Te other dimension is the same as the

circumerence o the tank

C = πd

= π times 20

63

Te circumerence is approximately 63 m

Use the nets to construct the scale models or the berm and the

oil tank




Key Concepts

bull Design problems are often subject to constraints or conditions

bull Constraints may include cost considerations safety regulations

maximum or minimum sizes or performance requirements


D1 A fashion designer is to design a new line of sunglasses to

complement a clothing line Discuss some of the constraints

that she might face during the design stage

D2 The highest mountain in Africa is

Mt Kilimanjaro in Tanzania On the

Marangu hiking route to the top

climbers spend the night in huts

designed by Norwegian architects

There is no road The trail is the

only route to the huts Discuss some of the constraints that the architects faced when

designing the huts

Practise A 1 A new laundry detergent will be sold in a cubical box Te box holds

1 L o detergent Find the side length o the box

2 A actory temporarily stores liquid wastes in a circular cement-lined

pond that has a base area o 500 m2 Find the length o berm needed

to enclose the pond

3 Santorsquos Pizzeria is introducing a new giant-size pizza with a diameter

o 24 in Give possible reasons why the pizza will be packaged in an

octagonal box rather than a square box

4 Preabricated housing or developing countries with warm climates is

ofen made o galvanized sheet metal Discuss some o the constraints

that might affect the designers o this type o housing




Apply B 5 A one-story bungalow is to be designed or a small lot Te 1047298oor pla

o the house must 1047297t into a rectangle measuring 30 f by 40 f Te

buyer has made the ollowing speci1047297cations

Room Minimum Floor Area (ft2)

bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300

Tere must be a clear path to all rooms Use pencil and paper or

drawing sofware to design such a house Design ip Lay out the

rooms such that you minimize the area required or hallways

6 A 1047298exible 1047298oating pipe is used to contain an oil spill Te pipe can

contain a depth o 50 cm o oil It is placed around a leaking tanker

carrying 200 000 m3 o oil Te pipe is laid such that it orms a circle

around the leaking tanker What length o pipe is needed to contain

all o the oil

7 Build a boat using one piece o water-resistant cardboard or plastic

the same size as notebook paper up to six popsicle sticks glue as

required and enough tape to join the edges Te boat must hold the

maximum load possible without sinking est the boat using standa

weights coins or other materials Record your plan

Many bridges use

triangles in their

construction Triangles

are rigid and add to

the strength of the

bridge

Math Connect 8 Build a bridge using 12 plastic drinking straws one sheet o notebo

paper and duct tape to join the straws Te bridge must span 15 cm

and hold the maximum load possible Note Te duct tape may be

used only to join the straws It may not be used to reinorce the bridg

Place the bridge over a gap o 15 cm and test it with standard weights

coins or other materials Record your plan




9 Farmer Macdonald sketched an isometric perspective drawing o

a new chicken coop that he would like to build Te space between

pairs o dots represents 1 m

a) Draw a set o orthographic drawings or the coop b) Draw a net that can be used to make a scale model o the coop

Cut out the net and construct the model ape the model

together

c) All sides o the coop except the 1047298oor will be made o sheet metal

which sells or $15m2 Estimate the cost o buying the sheet metal

or the coop

Chapter Problem 10 Te uranium uel or a nuclear reactor is placed in a cylinder Te

cylinder lies horizontally on its side with a diameter o 8 m and a

length o 6 m It must be surrounded by a containment building in theshape o a vertical cylinder Paul has been given the task o designing

the building and estimating the cost o the buildings concrete exterior

a) Use pencil and paper or drawing sofware to determine the

minimum dimensions o the containment building required

b) Find the area o the walls and roo o the building Te concrete

exterior must be 80 cm thick Multiply the area by the thickness

to determine the approximate volume o concrete required in

cubic metres

c) Concrete can be delivered to the site and poured or $90m3

Estimate the cost o the concrete or the building




Achievement Check

11 Reer to the oil tank problem rom Example 2 Hartmut suggests

using a circular berm that is also 5 m high He says that the circular

berm would be smaller than the square berm Is he correct Show

calculations to support your answer

Extend C 12 Te inside o a new high-pressure scuba tank has a volume o 1 f3

Te walls top and bottom must be 05 in thick to withstand the

pressure Te ratio o height to diameter will be 31 Model the tank

using a cylinder Determine the dimensions required inside and

outside Prepare a set o orthographic drawings or the tank

13 An electric urnace can produce a maximum o 12 000 W o heat A

concrete building requires a heat source o 10 Wm2 on its exterior

walls and roo

a) Design a small offi ce building in the shape o a rectangular prism

that could be heated by this urnace running at maximum Note

For multiple storeys the building code requires that each storey

a minimum o 3 m in height

b) Construct a scale model o your building

14 Te layout or a new terminal at the international airport will use

the ldquosnow1047298akerdquo design Passengers will arrive through one ace

o a square-based reception building Once they have checked in

they will ollow a passageway through one o the other aces to ahexagonal ldquosnow1047298akerdquo gate cluster Five o the aces will be gates or

aircraf while the sixth will house the passageway Te aircraf usin

these gates need a clear square area with a side length o at least 50

in ront o the gate

Use pencil and paper or drawing sofware to design the terminal Te

passageways should be kept as short as possible to minimize the distan

that passengers need to walk to get rom one ldquosnow1047298akerdquo to another

Entrance

Check-in

Area

To Gates

Snow1047298akeGateCluster

To Gates




Use The Geometerrsquos Sketchpadreg to Create TessellationsUsing Rotations

Tools computer

The Geometerrsquos

Sketchpad reg

Use Te Geometerrsquos Sketchpad reg to draw a complex tessellation using

rotations Begin with a regular hexagon Ten alter the interior o the

hexagon using the ransform menu

1 Open Te Geometerrsquos Sketchpad reg Use the method shown in Section

64 Example 2 Method 2 to draw a regular hexagon All the angles

in each triangle will be 60deg Draw a point approximately in the centre

o one o the triangles that make up the hexagon Select this point as

well as the centre and a vertex o the hexagon as shown Choose Arc

Trough 3 Points rom the Construct menu

2 Select the centre o the hexagon Choose Mark Center rom the

ransform menu Select the arc Choose Rotate rom the ransform

menu Adjust the angle o rotation to 60deg Repeat the rotation until

you have six arcs one in each triangle

3 Select the six vertices o the hexagon Choose Hexagon Interior rom

the Construct menu You can change the colour by choosing Color

rom the Display menu Select one o the arcs Choose Arc Interior

rom the Construct menu Ten choose Arc Segment While the arc

interior is selected change the colour by choosing Color rom the

Display menu Repeat this procedure until you have six arc segments

o different colours

Use Technology




4 Hide the lines the points and the arcs

5 Select the hexagonal pattern and then choose Copy rom the Edit

menu Choose Paste rom the Edit menu Move the copy beside the

original pattern Continue pasting copies until you have ormed a

tessellation

6 Re1047298ect Tink o other ways to use rotations For example you can

use a polygon in place o an arc Consider other colour variations

What other regular polygons can be used or tessellations What

combinations o polygons can be used




61 Investigate Geometric Shapes

and Figures pages XXndashXX 1 Afer using the ldquo12-knot roperdquo to lay

out a square or rectangle on the ground

ancient builders then measured the two

diagonals Why did they do this Why

does this method work

2 Basiruddin has sewn a blanket or his

sisterrsquos new baby It measures 130 cm by

80 cm Basiruddin claims that the blanket

is a golden rectangle and that i it isolded in hal the hal-rectangle is also

a golden rectangle Use calculations to

check his claims

62 Perspective and OrthographicDrawings pages XXndashXX

3 Shawna is designing

an unusual seven-room

house or a client Each

room will have the

shape o a cube Shawna

has represented the

basic plan as an

isometric perspective

drawing as shown

a) Use linking cubes or other materials to

build a scale model o the house

b) Draw a set o orthographic drawings

or the house

4 Jorge drew orthographic drawings o

his amily home in Spain as shown Tedistance between horizontal or vertical

pairs o dots represents 2 m Draw

an isometric perspective drawing o

the house


63 Create Nets Plans and Patternspages XXndashXX

5 You are designing a rondaval a circular

hut Te hut will have a diameter o 24 f

In the centre will be a square washroom

block with side length 8 f Te hutrsquos

diameter will divide the washroom block

and the hut into two units each witha washroom and a bedroom Select a

suitable scale and draw a 1047298oor plan or

the rondaval Include all measurements

6 A new line o bath crystals will be

marketed in a decorative cylindrical

container with a diameter o 6 cm and a

height o 18 cm A cork will be used to

seal the container so no top is required

Review 6




Draw a net that could be used to make a

model o the container Cut out your netand construct the container Check the

dimensions o the model by measuring

7 David is building an airplane Te rame

is made o welded steel tubing and will

be covered with abric Each wing is in

the shape o a rectangle measuring 5 m

long by 1 m wide with a semicircle at

one end Te wing will be covered with

abric Sketch a pattern that could beused to sew an envelope to slip over the

wing rame Show all measurements

64 Scale Models pages XXndashXX

8 Model airplane kits are commonly sold

in1 _

72 scale A Boeing 777 airliner has a

wingspan o 609 m and a length o

739 m Find the wingspan and length o

a 1 _ 72

model o the Boeing 777

9 Quonset huts are ofen used or storage

o arm machinery aircraf or other

large machines

5 m

10 m

10 m

Sandrine is planning to build a Quonse

hut to shelter the ultralight aircraf thatshe is building It will have a square 1047298oo

with side length 10 m Te curved roo

will have a maximum height o 5 m

Draw a net that can be used to make a

scale model o the Quonset hut Cut ou

your net and construct the scale model

10 A new offi ce building will have a square

base with side length 40 m It will be

60 m high A revolving restaurant in thshape o a cylinder with a diameter o

80 m and a height o 4 m will be built

on top Draw nets that can be used to

make scale models o the building and

the restaurant Cut out your nets and

construct the models

65 Solve Problems With GivenConstraints pages XXndashXX

11 Martin is designing a hexagonalbunkhouse containing six triangular

rooms that meet at the centre Te base

o the bunkhouse will be poured concre

10 cm thick Concrete can be delivered

to the site or $75m3 Te budget or th

concrete base is a maximum o $600 T

walls will be congruent squares and the

roo will be 1047298at Te cost o wood or th

walls and the roo is $20m2

a) Design the base such that the

hexagon is as large as possible witho

exceeding the cost constraint

b) Continue the design or the walls

and roo Estimate the total cost o

materials or the base walls

and roo

Chapter 6 Review bull MHR



1 Which rectangle A

D

E

G

B

C

F His closest tobeing a golden

rectangle

A ABCD B AEGD

C EBHF D FHCG

2 Te measures o the interior angles o

several regular polygons are shown

Which o these polygons can be used to

tile the plane A 108deg pentagon B 120deg hexagon

C 135deg octagon D all o them

3 An ornament is a square-based pyramid

with a sphere on top Te pyramid has a

base o side length 4 cm and a height o

6 cm Te diameter o the sphere is 5 cm

Which o these represents the top view o

the ornament

A B

C D

4 A new specialty ruit and nut bar is

being made Te bar has a diamondcross-section made up o two congruent

equilateral triangles with side length

12 cm Te bar is 24 cm long Draw a

set o orthographic drawings or the bar

Include all measurements

12 cm

12 cm

12 cm

24 cm

12 cm

12 cm

5 Select a suitable scale and draw a net

that could be used to make a scale model

o a package or the ruit and nut bar in

question 4

6 Yasmini received a pet budgie in acylindrical cage with a diameter o 60 cm

and a height o 50 cm Yasmini needs

a night cover or the cage Te cover

requires a top and sides but no bottom

Select a suitable scale and draw a pattern

that could be used to cut the pieces o

cloth needed to make the cover

Practice Test6




7 An isometric perspective drawing or

a new building is shown Te distance

between pairs o dots represents 5 m

Draw orthographic drawings or thebuilding

8 A gif box or a travel mug will have a

square base with side length 4 in and a

square lid with side length 6 in Te box

must be 5 in high Select a scale andsketch nets that can be used to make a

model o the box and the lid Show all

measurements on the net

9 A new tomato juice can is being designe

such that the ratio o the height to the

diameter is equal to the golden ratio T

diameter will be 12 cm

a) Select a scale and draw a net that

could be used to make a scale model

o the can

b) Determine the volume o tomato juic

that the can will hold

Chapter Problem Wrap-Up

Paul has learned a lot about geometry and

architecture during his coop placement Choose

a design project of your own similar to the projects

you have worked on throughout this chapter It

could be a building or structure a package or an

item of clothing

a) Write a plan for your project Include at least four

geometric elements in the design Describe the

constraints on your project and how you can meet them

b) Draw an isometric perspective drawing or a set of orthographic drawings

for your project

c) Calculate the projectrsquos dimensions Draw a pattern or a net Build a scale

model of your projectd) Write a summary of your project Include your drawings and model Show all

your calculations and measurements

Chapter 6 Practice Test bull MHR



Chapter 4 Quadratic Relations I

1 a) Which o these relations are quadraticExplain your reasoning

i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2

b) Check your predictions by graphing

each relation

2 Describe the graph o each parabola

relative to the graph o y = x 2

a) y = (x + 4)2 b) y = ndash(x ndash 1)2

c) y = ndash03(x + 7)2 d) y = 2(x + 9)2

e) y = 09(x + 32)2 f) y = ndash4(x ndash 18)2

3 For each relation

i) identiy the coordinates o the vertex

ii) determine i the parabola opens

upward or downward

iii) determine i the parabola is vertically

stretched or vertically compressed

iv) sketch the graph

a) y = (x ndash 1)2 + 9 b) y = ndash2(x + 8)2 ndash 5

c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13

4 A 1047298are is sent up as a distress signal

Te path is modelled by the relationh = ndash49(t ndash 6)2 + 1774 where h is the

1047298arersquos distance above the water in metres

and t is the time in seconds

a) How long will the 1047298are take to reach

its maximum height What is the

maximum height

b) A typical 1047298are will stay lit or 7 s How

high above the water will the 1047298are be

7 s afer it is launched c) Graph this relation

d) Afer how many seconds will the 1047298are

hit the water

Chapter 5 Quadratic Relations II

5 Expand and simpliy

a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)

c) (12x ndash 8)(2x + 05) d) (6 + 2x )(6 ndash 2x )

6 a) Write an expression in simpli1047297ed

orm or the area o an apartment

with dimensions s ndash 1 by 4s ndash 7

b) I s = 15 m 1047297nd the actual area o the

apartment

7 Write each relation in standard orm

a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27

d) y = ndash32(x ndash 4)2 ndash 08

8 Determine the y -intercept or

y = (7 ndash 3x )(2x ndash 6)

Review Chapters 4 to 6




9 Factor each trinomial

a) x 2 + 11x + 24 b) x 2 + x ndash 30 c) x 2 ndash 8x + 7 d) x 2 + 8x + 16

e) 3x 2 + 39x + 108 f) ndash10x 2 ndash 110x ndash 100

10 Which pairs contain equivalent

expressions How do you know

a) x 2 + 4x ndash 5 (5 + x )(x ndash 1)

b) x 2 + 35x + 3 (x ndash 2)(x ndash 15)

c) x 2 + x ndash 2 (x ndash 1)(x + 2)

11 Find the zeros by actoring Check by

substituting your answers or x

a) y = x 2 ndash x ndash 20

b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315

12 Te height o a rectangular prism is

16 cm more than the length o the base

Te width o the base i hal the length

a) Sketch and label a diagram to

represent the rectangular prism

b) Write an expression or the surace

area o the prism

c) What is the surace area o the prism i

the width o the base is 5 cm

d) What are the dimensions o the prism

i the surace area is 640 cm

2

14 a) Use linking cubes to model the capit

letter ldquoLrdquo Te base o the L should be10 cm and the height should be 20 cm

Te letter should be 10 cm thick Let

the side o a cube represent 5 cm

b) Use the model to help you draw an

isometric perspective drawing

c) Use the model to help you sketch a s


15 A car dealership has ordered a platorm

to display their newest car models Anisometric perspective drawing or the

display platorm is shown Te distance

between pairs o vertical or horizontal

dots represents 2 m

a) Draw a set o orthographic drawings

or the platorm

b) Draw a net that can be used to make

a scale model or the platorm Te

rectangles that will become the slope

part o the platorm should have a

length o 3 units and a width o

225 units Cut out the net and



Arqum studied graphic design at Fanshawe College and now creates

signs for companies selling a product or service He discusses each

project with his customers including size materials budget and

regulations and designs layouts for billboards and business signs

Arqum uses geometric shapes and scale when he creates his designs

on the computer

6 Geometry in Desgin bull MHR



Geometric Shapes


shapes

a) b)

c) d)


shapes

a) b)

c) d)


a) b)

c) d)

e)

Perimeter and Area




_

2 bh




120 m by 100 m




13 cm



radius o 12 m



l w

h


h

bl

c


_

2 blh

h

r


Prerequisite Skills




Chapter Problem



















the room






09 m

06 m01 m





Angles in a Polygon







a regular pentagon

Scale Factors









the sailboat

Get Ready bull MHR






and geometry






Mona Lisa

ruleror

computer

The Geometerrsquos

Sketchpad reg



Mona Lisa








any drawing program


Paint










golden ratio



golden rectangle


pleasing to the eye














coloured pencils or


or pattern blocks

tessellation


a plane without


gaps


pattern














pleasing pattern













Tools computer

The Geometerrsquos

Sketchpad reg












all elements of the


Copy command from



the plane









examples


































Tools ruler

grid paper














Tools computer

The Geometerrsquos

Sketchpad reg








hexagons look a bit


how to draw regular

geometric shapes


chapter


















s

146515 m

230363 m




Solution


115182


s2 (115182)2 + (146515)2

s2 34 733538 s radic

_________

34 733538

s 186369



16181



is an approximation

The exact value is

1 + radic __

5_

2 Use a



gives the correct

approximation

Math Connect







Key Concepts














A triangle B square

C hexagon D octagon




























most search engines



looking for images







the river






















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Geometric Shapes


shapes

a) b)

c) d)


shapes

a) b)

c) d)


a) b)

c) d)

e)

Perimeter and Area




_

2 bh




120 m by 100 m




13 cm



radius o 12 m



l w

h


h

bl

c


_

2 blh

h

r


Prerequisite Skills




Chapter Problem



















the room






09 m

06 m01 m





Angles in a Polygon







a regular pentagon

Scale Factors









the sailboat

Get Ready bull MHR






and geometry






Mona Lisa

ruleror

computer

The Geometerrsquos

Sketchpad reg



Mona Lisa








any drawing program


Paint










golden ratio



golden rectangle


pleasing to the eye














coloured pencils or


or pattern blocks

tessellation


a plane without


gaps


pattern














pleasing pattern













Tools computer

The Geometerrsquos

Sketchpad reg












all elements of the


Copy command from



the plane









examples


































Tools ruler

grid paper














Tools computer

The Geometerrsquos

Sketchpad reg








hexagons look a bit


how to draw regular

geometric shapes


chapter


















s

146515 m

230363 m




Solution


115182


s2 (115182)2 + (146515)2

s2 34 733538 s radic

_________

34 733538

s 186369



16181



is an approximation

The exact value is

1 + radic __

5_

2 Use a



gives the correct

approximation

Math Connect







Key Concepts














A triangle B square

C hexagon D octagon




























most search engines



looking for images







the river






















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Chapter Problem



















the room






09 m

06 m01 m





Angles in a Polygon







a regular pentagon

Scale Factors









the sailboat

Get Ready bull MHR






and geometry






Mona Lisa

ruleror

computer

The Geometerrsquos

Sketchpad reg



Mona Lisa








any drawing program


Paint










golden ratio



golden rectangle


pleasing to the eye














coloured pencils or


or pattern blocks

tessellation


a plane without


gaps


pattern














pleasing pattern













Tools computer

The Geometerrsquos

Sketchpad reg












all elements of the


Copy command from



the plane









examples


































Tools ruler

grid paper














Tools computer

The Geometerrsquos

Sketchpad reg








hexagons look a bit


how to draw regular

geometric shapes


chapter


















s

146515 m

230363 m




Solution


115182


s2 (115182)2 + (146515)2

s2 34 733538 s radic

_________

34 733538

s 186369



16181



is an approximation

The exact value is

1 + radic __

5_

2 Use a



gives the correct

approximation

Math Connect







Key Concepts














A triangle B square

C hexagon D octagon




























most search engines



looking for images







the river






















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm












and geometry






Mona Lisa

ruleror

computer

The Geometerrsquos

Sketchpad reg



Mona Lisa








any drawing program


Paint










golden ratio



golden rectangle


pleasing to the eye














coloured pencils or


or pattern blocks

tessellation


a plane without


gaps


pattern














pleasing pattern













Tools computer

The Geometerrsquos

Sketchpad reg












all elements of the


Copy command from



the plane









examples


































Tools ruler

grid paper














Tools computer

The Geometerrsquos

Sketchpad reg








hexagons look a bit


how to draw regular

geometric shapes


chapter


















s

146515 m

230363 m




Solution


115182


s2 (115182)2 + (146515)2

s2 34 733538 s radic

_________

34 733538

s 186369



16181



is an approximation

The exact value is

1 + radic __

5_

2 Use a



gives the correct

approximation

Math Connect







Key Concepts














A triangle B square

C hexagon D octagon




























most search engines



looking for images







the river






















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









golden ratio



golden rectangle


pleasing to the eye














coloured pencils or


or pattern blocks

tessellation


a plane without


gaps


pattern














pleasing pattern













Tools computer

The Geometerrsquos

Sketchpad reg












all elements of the


Copy command from



the plane









examples


































Tools ruler

grid paper














Tools computer

The Geometerrsquos

Sketchpad reg








hexagons look a bit


how to draw regular

geometric shapes


chapter


















s

146515 m

230363 m




Solution


115182


s2 (115182)2 + (146515)2

s2 34 733538 s radic

_________

34 733538

s 186369



16181



is an approximation

The exact value is

1 + radic __

5_

2 Use a



gives the correct

approximation

Math Connect







Key Concepts














A triangle B square

C hexagon D octagon




























most search engines



looking for images







the river






















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Tools computer

The Geometerrsquos

Sketchpad reg












all elements of the


Copy command from



the plane









examples


































Tools ruler

grid paper














Tools computer

The Geometerrsquos

Sketchpad reg








hexagons look a bit


how to draw regular

geometric shapes


chapter


















s

146515 m

230363 m




Solution


115182


s2 (115182)2 + (146515)2

s2 34 733538 s radic

_________

34 733538

s 186369



16181



is an approximation

The exact value is

1 + radic __

5_

2 Use a



gives the correct

approximation

Math Connect







Key Concepts














A triangle B square

C hexagon D octagon




























most search engines



looking for images







the river






















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm























Tools ruler

grid paper














Tools computer

The Geometerrsquos

Sketchpad reg








hexagons look a bit


how to draw regular

geometric shapes


chapter


















s

146515 m

230363 m




Solution


115182


s2 (115182)2 + (146515)2

s2 34 733538 s radic

_________

34 733538

s 186369



16181



is an approximation

The exact value is

1 + radic __

5_

2 Use a



gives the correct

approximation

Math Connect







Key Concepts














A triangle B square

C hexagon D octagon




























most search engines



looking for images







the river






















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Tools computer

The Geometerrsquos

Sketchpad reg








hexagons look a bit


how to draw regular

geometric shapes


chapter


















s

146515 m

230363 m




Solution


115182


s2 (115182)2 + (146515)2

s2 34 733538 s radic

_________

34 733538

s 186369



16181



is an approximation

The exact value is

1 + radic __

5_

2 Use a



gives the correct

approximation

Math Connect







Key Concepts














A triangle B square

C hexagon D octagon




























most search engines



looking for images







the river






















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Solution


115182


s2 (115182)2 + (146515)2

s2 34 733538 s radic

_________

34 733538

s 186369



16181



is an approximation

The exact value is

1 + radic __

5_

2 Use a



gives the correct

approximation

Math Connect







Key Concepts














A triangle B square

C hexagon D octagon




























most search engines



looking for images







the river






















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm










A triangle B square

C hexagon D octagon




























most search engines



looking for images







the river






















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm
















most search engines



looking for images







the river






















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm


















Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating




c

1








1

34



how you know

40 mm160 mm

68 mm

42 mm

64 mm

32 mm

32 mm200 mm




Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Achievement Check



will work




















2 1










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm










scale model




a large object









objects in two

dimensions




an object


top views are given


bull a drawing that

uses orthographic

projection



















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm
















ruler

coloured pencils
















ldquomeasurerdquo



drawing o the prism




Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Tools computer

The Geometerrsquos

Sketchpad reg









spacing of the dots




















physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm












physical models of

cubes

ruler













Tools computer

The Geometerrsquos

Sketchpad reg








Method 1












their productions












Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm















Solution










ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm











ront view

top view

side view




the pyramid

Solution










drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm












drawing o the can








dot paper sketch






work Try it










Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Key Concepts





and top view)






Give reasons



for your answer






A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm











A a scale model











view

A B C D













central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm
















central open space













dots Explain

























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm






























Achievement Check






A B

C D


Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating





















vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm


























vanishing point


















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm





















scissors

ruler

tape



l w

ho the cereal box

net





plan



scheme

pattern


model from which an






modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm










modern packaged

cereals was toasted



about packaging

go to httpwww

mcgrawhillcalinks

foundations11 and

follow the links













ruler

tape



h





















(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm











(old T-shirt etc)

scissors

newsprint












Example Cabin Plan










Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Solution




6 m

3 m

3 m8 m

5 m

2 m

3 m

3 m

3 m

Bunk RoomBathroom

Bunk Room

3 m


6 m 6 m 6 m

8 m

5 m5 m


Key Concepts









the cube










will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm












will the net make








open top






Apply B













together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm















together


the requirements


4 cm

4 cm

4

12 cm





12 cm long






the requirements









3 m

3 m

3 m3 m











all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm













all measurements

20 cm

10 cm

10 cm

Achievement Check





all measurements




















Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm










Tools computer

The Geometerrsquos

Sketchpad reg





living area
















the grid

Use Technology













the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm


















the rooms





Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Scale Models64














model together




Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Solution




V = πr 2(4r )

= 4

πr

3


Radius (f)

1

2

3

4

5

Volume (f3)

126

1005

3393

8042

15708





the cylinder

C = πd

= π(8)

251





2 in or the ends

c)










Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm















Solution


























s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









s

t

1 m

1 m

1 m

3 m












s

t






o s and t

s2 = 32 + 12 t 2 = 12 + 12

s2 = 10 t 2 = 2

s = radic ___

10 t = radic __

2

s 32 t 14










Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Key Concepts







using a net Explain





































and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm






















and a height o 3 m



o the prism


together










model o the can







Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm










Re1047298ecting

Selecting Tools

Connecting

Representing

Problem Solving

Communicating








o the centre


together
























Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Achievement Check



represents 1 m



each end


each end













constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm










constraint










s

tu















Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm













Solution


s

t u

15 f 5 f 5 f

25 f

75 f5 f

s2 = 152 + 752 t 2 = 52 + 252 u2 = 52 + 52

s2 = 28125 t 2 = 3125 u2 = 50





actual measure by 5


168 f 10 f

10 f

10 f

175 f

175 f

175 f

40 f

15 f





175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm










175 f

175 f

175 f

40 f

10 f 15 f

15 f

15 f

71 f

71 f

71 f

56 f

56 f

56 f




Example 2 Oil Tank










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm










o the berm



required



V = πr 2h


6283

A square-based

berm has the

shortest side


given volume

Minimizing the


cuts down on the

cost of materials




= s2 times 5

= 5s2

5s2 = 6283

s2 = 6283

_

5

s2 = 12566

s = radic ______

12566

s 354













C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm














C = πd

= π times 20

63



oil tank




Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Key Concepts















designing the huts





to enclose the pond














bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm













bedroom 1 200

bedroom 2 150

bedroom 3 100

bathroom 100

eat-in kitchen 200

living room 300








all o the oil






Many bridges use

triangles in their



the strength of the

bridge















together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm














together



or the coop










cubic metres






Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









Achievement Check












walls and roo












in ront o the gate




Entrance

Check-in

Area

To Gates


To Gates





Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm










Tools computer

The Geometerrsquos

Sketchpad reg




















o different colours

Use Technology








tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm













tessellation



















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm




















check his claims





room will have the


has represented the

basic plan as an


drawing as shown




or the house





the house
















Review 6

















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm






















in1 _




a 1 _ 72




large machines

5 m

10 m

10 m
































and roo




1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm









1 Which rectangle A

D

E

G

B

C


rectangle

A ABCD B AEGD

C EBHF D FHCG











the ornament

A B

C D







12 cm

12 cm

12 cm

24 cm

12 cm

12 cm




question 4








Practice Test6




















o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm

























o the can









item of clothing





for your project









i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm











i) x y

0 17

1 13

2 9

3 5

4 1

5 -3

6 -7

ii) x y

1 0

3 1

5 3

7 6

9 10

11 15

13 21

iii) y = 2x + 1 iv) y = 12 ndash 2x 2


each relation




c) y = ndash03(x + 7)2 d) y = 2(x + 9)2


3 For each relation



upward or downward





c) y = 01x 2 ndash 1 d) y = 91x 2

e) y = 05(x ndash 2)2 + 2 f) y = 8(x + 1)2 + 13







maximum height





hit the water



a) (3x + 4)(10x + 1) b) (x ndash 2)(4x + 15)






apartment


a) y = (x ndash 4)2 + 05

b) y = (x + 10)2 ndash 3

c) y = 8(x + 2)2 + 27



















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm




















b) y = 10x 2 ndash 360

c) y = ndash2x 2 + 4x + 70

d) y = 35x 2 + 21x + 315







area o the prism





2













dots represents 2 m


or the platorm







geometry in design

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