pakuranga college year 10 mathematics...2012 eoy year 10 sincos page 1 edited by: kim smith name:...

2012 EOY Year 10 SINCOS Page 1 Edited by: Kim Smith

NAME:

TEACHER:

Pakuranga College

Year 10 Mathematics

2012 Examination

Time: 2 hours

DC 2rA

hbaA )(

2

1

bhA

2

1

Volume =

base area x

height

bhA

bhA

Answer ALL questions in the spaces provided in this booklet. Show ALL working.

Sections Page number Result

1 Algebra 2

2 Graphs 4

3 Measurement 6

4 Probability 8


Section 1 Algebra ==========================================================================

QUESTION ONE In each of these equations, n stands for a

number. Write what number it stands for.

Where indicated, show your working.

(a) 4 + n = 15 n = __________

(b) 5n = 20 n = __________

(c) 24 – n = 14 n = __________

(d) 4n + 3 = 27

___________________________________

n = __________

(e) 6n – 5 = 3 ___________________________________

n = __________

(f) n + 2 = 3n - 4

___________________________________

___________________________________

n = __________

QUESTION TWO

Expand (and simplify where possible)

(a) 4(n + 2) _________________________

(b) 5(x + y) _________________________

(c) 2x(4 – 3x) _________________________

___________________________

(d) (5+ p)(p – 2) _________________________

___________________________

QUESTION THREE

Simplify the following expressions:

(a) 5 x p __________________

(b) k x k x k x k __________________

(c) 5n + 6 – 7n + 8 __________________

___________________

(d) 7

2

6

xx

_________________

_________________

___________________

QUESTION FOUR

(a) Write and simplify an expression for the

perimeter of this trapezium.

___________________________________

___________________________________

(b) One such trapezium has a perimeter of 17. Calculate the value of x.

___________________________________

___________________________________

QUESTION FIVE

The area of a trapezium is given by the formula

A = ½(a+b) x h

(a) Find the area of a trapezium where a = 3, b = 7 and h = 4.

___________________________________

___________________________________

(b) If a trapezium has an area of 42 cm2, h = 8 and b = 6, the formula can be rewritten

as 42 = 4(a + 6). Find the length of side a

___________________________________

___________________________________


QUESTION SIX

Samara wants to throw a large party for her

birthday. She needs to budget $15 per person for

snack food and drinks and have $120 left over

for decorations and other incidentals. She has

$900 put aside for the party.

(a) Write an equation that could be used to work out the number of people Samara can

afford to invite.

___________________________________

(b) Solve your equation. Show all working. ___________________________________

___________________________________

QUESTION SEVEN

(a) Write and simplify an expression for the

area of this triangle. (Recall that the area

of a triangle = ½ base x height). ___________________________________

___________________________________

(b) If the area of this triangle is 16 cm2, what is the value of x? Show your working.

___________________________________

___________________________________

___________________________________

___________________________________

___________________________________

___________________________________

(c) Recall Pythagoras’ theorem

a2 + b

2 = c

2

where a and b are the two shorter sides and c

is the hypotenuse (longest side).

Write an expression for the length of the

third side of this triangle in terms of x.

___________________________________

___________________________________

___________________________________

QUESTION EIGHT

Sita wishes to build a chicken coop with 30 m of

chicken wire fencing. She wishes to have a main

enclosure that is 5m long with a smaller square

enclosure on the side. The dimensions of the

square enclosure will depend on the amount of

fencing wire available. Fencing is not needed in

the two 1.5 m gaps that are left for gates.

(a) Write and solve an equation that could be used to calculate the length of the square

enclosure (x).

___________________________________

___________________________________

___________________________________

___________________________________

___________________________________

(b) Calculate the total area of the two enclosures.

___________________________________

___________________________________

___________________________________

___________________________________

___________________________________


Section 2 Graphs ==========================================================================

QUESTION ONE

Plot the following points on the graph in order

and join (like a “dot to dot”)

(0,-2), (2, -1), (2, 3), (1, 2), (-1, 2), (-2, 3),

(-2, -1), (0, -2)

QUESTION TWO

a) Write down the y-intercepts of the lines Line A ________________

Line B _________________

b) Write down the gradients of the lines Line A __________________

Line B __________________

QUESTION THREE

Give the equations of these three lines

(a) _______________________________

(b) _______________________________

(c) _______________________________

QUESTION FOUR

This graph shows the charges of two taxi

companies, where x = number of minutes and y

= charge in $.

The two equations are Company A: y = 2x and

Company B: y = x + 10.

(a) Which company has a fixed charge as well as a charge based on how long you travel?

How is this shown on the graph?

_______________________________________

Line B

Line A


(b) What is the price per minute charge for each company? How is this shown on the graph?

_______________________________________

_______________________________________

(c) For what lengths of trip would Company B be the cheaper option? How is this shown on

the graph?

_______________________________________

_______________________________________

QUESTION FIVE

Jamie loves cappuccino and has 2 cappuccinos

per week with his friends. This costs him $5

each time. He is considering buying a

cappuccino maker. After the machine, which

costs $300, is paid for, it will only cost him $1

for each cappuccino (the cost of the milk and

coffee beans).

This graph shows his costs for x weeks after his

purchase of the cappuccino maker.

Add another line to the graph to show his costs

for the same time period if he does not buy a

cappuccino maker.

Calculate the number of weeks that it will take

for the cappuccino maker to be his cheaper

option.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

Investigate and comment on the difference it

would make if his local coffee shop puts the

price of cappuccino up to $6.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________


Section 3 Measurement (formula sheet on front page) ========================================================================

QUESTION ONE Below is a “life size” picture of a cellphone

(a) Use your ruler to measure the: Length = ___________________

Width = ___________________

(b) Calculate the area of the cellphone. Show your working.

____________________________________

____________________________________

(c) The cellphone comes packaged in a box with these dimensions:

(i) Calculate the volume of the box

____________________________________

____________________________________

(ii) How many boxes of cellphones could be

packaged in a carton that is cube-shaped,

60 cm in length, width and height?

____________________________________

____________________________________

____________________________________

QUESTION TWO

Give the area and perimeter of the shape drawn

on the grid. (Assume the grid shows square

centimetres). Colour or shade the diagram to

show how it can be divided into rectangles.

____________________________________

____________________________________

____________________________________

____________________________________

Area = ________________ cm²

Perimeter = ____________ cm

QUESTION THREE

(a) What approximate temperature does this

thermometer show

(i) in oCelsius?

___________________

(ii) in oFahrenheit?

___________________

(b) Roughly what temperature in oFahrenheit is equivalent

to -5

oCelsius?

________________


Tuesday Channel 11 Listings

06.40 Wake up NZ

08.10 Terry the Turtle

08.30 Playtime

09.00 First News

09.50 Mellow Drama

10.30 Infomercials

12.10 Talkline

13.25 Squirly Squirrel

QUESTION FOUR

Here is an excerpt from a Television Channel’s

programme guide:

(a) Give Squirly

Squirrel’s start

time as a 12-hour

clock time:

________________

________________

(b) How long does Mellow Drama

run for?

_________________

(c) Which item runs for the longest, and how long is it?

____________________________________

QUESTION FIVE

Fill the gaps with an appropriate unit (e.g. mL)

(a) An adult male might weigh 78 _____

(b) A 2-storey building might be 520 _____ high

(c) A teaspoon of sugar might weigh 10 ____

(d) The distance between cities is usually

measured in _____

QUESTION SIX

A building contains an internal roofless courtyard

that can only be accessed from inside the

building. A basic floor plan is shown above.

(a) Calculate the area of the floor space (shaded). ____________________________________

____________________________________

____________________________________

(b) Calculate the perimeter of the internal courtyard.

____________________________________

____________________________________

QUESTION SEVEN

A cylinder of gold (shown below) is melted down

and moulded into a cube. What is the surface

area of the cube?

The formula for volume of a cylinder is V = πr2h

QUESTION EIGHT A biology teacher uses a 15L chillybin to bring

cows’ eyeballs to school for her students to

dissect. The inside of the chillybin is a cuboid

with a base that is 30 cm long and 25 cm wide.

The eyeballs are roughly spherical and 5 cm in

diameter. Calculate the maximum number of

eyeballs that could fit in the chillybin if a square

grid stacking arrangement is used. What volume

of crushed ice could theoretically be fit around

them? Hint: you may need to work out the height

of the chillybin.

The formula for volume of a sphere is V = 4/3 πr

3

2cm

9.8cm


Section 9 Probability ==========================================================================

QUESTION ONE Draw a dot on the scale to show how likely each

event is.

(a) You take a plane trip to another New Zealand town and find a snake in the seat pocket in

front of you.

(b) You roll a die (one “dice”) 4 times and get a

6 every time.

(c) Someone who sunbathes for 3 hours without

sunscreen on a hot day gets sunburn.

(d) A couple who have two children have one

boy and one girl.

QUESTION TWO

Sandra invents a board game where you have a

choice of rolling a die or spinning this wheel.

(a) If you choose to spin the wheel, what is the

probability of getting something bad?

______________________________________

(b) What is the probability that you will be asked to roll the die if you land on white?

______________________________________

(c) If you spin the wheel, what is the probability that you will get to move 6? Hint: consider

the die roll but not the “2 turns” option.

______________________________________

______________________________________

QUESTION THREE

Simone made this table to show the results of the

friend requests she received on Facebook in one

year. She noted down whether the people asking

to be friends had any mutual friends with her,

and whether she accepted their friend request.

Accepted Declined Totals

Has mutual

friends 34 2

No mutual

friends 12 15

Totals

(a) Fill in the missing totals on the table. Use these to help answer the following questions.

(b) If we pick one of the friend requests at random, what is the probability that Simone

accepted it? _________________________________________

(c) If we pick one of the requests from people with mutual friends at random, what is the

probability that their request was declined?

______________________________________

(d) If we pick a declined request at random, what is the probability that they had no mutual

friends with Simone?

______________________________________

QUESTION FOUR

Babies born in the “breech” position have their

bottom or legs emerge first instead of their head.

Only 3% of full term babies are born breech.

Roughly 88% of babies are born full term.

(a) What is the probability of a baby being born full term and breech?

______________________________________

______________________________________

(b) If 250 babies are born in a city on a given day, how many would we expect to be full

term and not breech?

______________________________________

______________________________________

SINCOS Publications Page 9 Year 10 Examination 2011

QUESTION FIVE

The game “Pass the Pigs” involves people

throwing small pig figurines instead of dice.

While most of the scoring is based on the

position two pigs land in, some positions gain

points if even one pig lands that way.

(a) How do the points relate to the likelihood of each position occurring?

______________________________________

______________________________________

(b) What is the probability of the double snouter (both pigs in the snouter position)?

______________________________________

(c) When the two pigs are lying on opposite sides (one dot up and one dot down) only one

point is gained. What is the probability of

this combination?

______________________________________

______________________________________

(d) Which do you think should earn the most points: a double trotter, a double snouter or a

combination where one pig is razorback and

one is leaning jowler. Justify your answer.

QUESTION SIX

Three jars have ten marbles each in them. A

child randomly draws a marble from each jar.

(a) What is the probability that the marble from

jar B is a black one?___________________

(b) What is the probability that all three marbles are white?

______________________________________

______________________________________

(c) What is the probability that two of the marbles are striped?

______________________________________

______________________________________

(d) Find the probability that the three marbles are all different. You may find that a tree

diagram helps you with this.

Position Frequency Score

Side (no dot) 35% -

Side (dot) 30% -

Razorback (on its back) 22% 5 points

Trotter (on its feet) 9% 5 points

Snouter

(balanced on its nose and two

front feet)

3%

10 points

Leaning Jowler

(balanced on an ear, snout

and one foot)

1%

15 points

SINCOS Publications Page 10 Year 10 Examination 2011

QUESTION SEVEN

This diagram shows a game played by one

person with a coin. The player starts with a

counter in the centre. They move left if the coin

lands heads and right if it lands tails.

(a) A coin is flipped up to 4 times. Work out the likelihood of each of the 5 positions on the

gameboard being the end location (if win or

lose is reached earlier, no more coin tosses

occur).

(b) A player plays 100 consecutive games. 54 of them are lost. Comment on whether the coin

is likely to be a fair coin.

Produced by SINCOS Schedule Page 1 2012 EOY Year 10 (102)

Year 10 Mathematics

2012 Examination Schedules

Topics

Algebra Page 2

Patterns and Graphs Page 4

Measurement Page 5

Probability Page 6


Algebra

Q Evidence Code Judgement Sufficiency

1a

1b

1c

1d

1e

1f

2a

2b

2c

3a

3b

3c

11

4

10

4n=24, n=6

6n=8, n=4/3

6 = 2n , n=3

4n + 8

5x + 5y

8x - 6 x2

5p

k^4

-2n + 14

A

A

A

A

A

A

A

A

A

A

A

A

No alternative

Achievement

7 out of 12

code A

2d

3d

4a

4b

5a

5b

6a

6b

7a

5p – 10 + p² - 2p= p² + 3p = 10

7x + 12x = 19x

42 42

x + 1 + x – 1 + x + x + 3

=4x + 3

4x + 3 = 17, x = 3.5

½(3 + 7) × 4= 20

42 = 4a + 24

18 = 4a

4.4 = a

15p + 120 = 900

p = 52

½(x + 6) × 2x

x² + 6x

M

M

M

M

M

M

M

M

M

Award A for any partly

correct factorising

consistent with answer in

6a

Merit:

Achievement

plus

5/9 of Code M

or

(Any M or E can replace

A but can only be used

once)


7b

7c

8a

8b

x² + 6x – 16 = 0

(x – 2)(x + 8)=0

x= 2 or -8. Length can’t be –ve

so 2

c2 = (x+6)

2 + (2x)

2

= x2 + 12x + 36 + 4x

2

=5x2 + 12x + 36

c = 36125 2 xx

10 + 5x – 2(1.5) = 30

5x + 7 = 30

5x = 23, x = 4.6 m

44.16 m2

E

E

E

E

Must have equation for E.

(no guess & check!)

consistent from 8a

Excellence:

Merit PLUS

2E

OR 4 E’s

Any E can be used for M,

but can only be used once


Graphs

Q Evidence Marks Judgement

1a

2a

2 b

Line A: yin = -3

Line B: yin = 2

Line A: grad = 2

Line B: grad = 2/3

7A

A

A

A

A

Achieved = 6/11A’s

3a

3b

3c

4a

4b

y = 3x + 2

x = 4

y = -2/3 x + 5

Company B, shown by y intercept.

Company A $2/minute, Company B

$1/minute, shown by gradient.

M

M

M

M

M

Merit = Achieved plus 3/ 5 M’s

if they get only m or only CORRECT, can

…count for achieved

5 300 + 2x = 10x

The cappuccino maker is cheaper in

the 38th

week.

$6 per cappuccino puts that option up

to $12 per week. Cappuccino maker

would be cheaper after 30 weeks

E

E

Excellence = Merit + one E


Measurement


1a

1b

1c i

1c ii

2

3a i

3a ii

3b

4a

4b

4c

5a

5d

8.8cm and 4.3cm

49.49cm²

216 cm³

***1000 (if they just divided volume

by cell box volume)*** see M

21 cm², 22 cm

15°C 60°F 24°F 1:25pm

40 minutes

Infomercials, 1hr 40 minutes

kg

Km

AA

AA

AA

AA

AA

A

A

A

A

A

AA

A

A


one for answer consistent with values they got

in 1a, the other for correct units

‘’

A for correct volume of container box

A for answer consistent with dividing by 1c i

1c ii

5b

5c

6a

6b

60 ÷ 3=20

60 ÷ 12 = 5

60 ÷ 6 = 10

20 × 5 × 10 = 1000

cm

g

Whole floor area – courtyard area

= 120 – 16 = 104 m²

20m

M

M

M

M

M


7

8

Cyl. V = (π(2)² × 9.8) =123.15cm³

Cube side=³ √123.15 = 4.98cm SA = 6(4.98)²=148.8cm²

V eyeball=65.45cm³

square grids: 125cm³

No. Eyeballs=15000÷125=120

Space=(125-65.45)×120

=7146 cm³

(M)

E

E

Excellence = Merit + one E

must show logical steps, and have correct units.

Allow a minor error

must show logical steps, and have correct units.

Allow a minor error


Probability


1a

1b

1c i

1c ii

2a

2b

3a

3b

3c

3d

5a

6a

At or near impossible

Well below 50/50 but above

impossible.

At or near certain

At 50-50

1/3

1/3

37/51

2/36 = 1/18

12/14 = 6/7

Positions that are less likely gain higher

points

4/10 0r 0.4

Accepted Declined Totals

Has

mutual

friends

34 2 36

No

mutual

friends

3 12 15

Totals 37 14 51

A

A

A

A

A

A

AAA

A

A

A

A

A


Do not need to simplify fractions for achieved

1A for each of 2 and an extra if all correct

2c

4a

4b

5b

5c

5d

Factors in the 1/6 chance that the die

roll gives a 6. 1/6 + 1/6 + 1/36 = 13/36

0.88 × 0.03 = 0.0264 or 2.64%

0.88×0.97×250 = 213.4 (213 or 214)

0.03 × 0.03 = 0.0009

2(0.35×0.3) = 0.21

Probability of double trotter = 0.09 x

0.09 = 0.0081

Probability of double snouter =

0.00009

Probability of one razorback and one

leaning jowler = 2(0.22 x 0.01) =

0.0044

The least likely is the double snouter, it

M

M

M

M

M

M

M

M

M



6b

should have the highest number of

points (it does).

0.5 x 0.2 x 0.5 = 0.05

M

6c

6d

7a

7b

Ways this can happen:

Striped, striped, not (0.096)

Striped, not, striped (0.036)

Not, striped, striped (0.056)

Total probability = 0.188

Relevant combinations are

BWS (0.2 x 0.2 x 0.2) = 0.008

BSW (0.2 x 0.4 x 0.5) = 0.04

WSB (0.5 x 0.4 x 0.3) = 0.06

WBS (0.5 x 0.4 x 0.2) = 0.04

SWB (0.3 x 0.2 x 0.3) = 0.012

SBW (0.3 x 0.4 x 0.5) = 0.06

Probability is 0.22

6/16 chance of losing, 6/16 chance of

winning and 4/16 chance of winning

(3/8, 1/4, 3/8).

It is possible that the coin is fair, but

we would expect closer to 37 or 38

losses.

E

E

E

E

Excellence = Merit + 2 E

Any method is fine, can use tree or groups as

shown

pakuranga college year 10 mathematics...2012 eoy year 10 sincos page 1 edited by: kim smith name:...

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