add math ain

7/30/2019 Add Math Ain

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PART 1Question a)

Brief history :

In Euclidean plane geometry, a quadrilateral is a polygon with four sides (or edges)and four vertices or corners. Sometimes, the term quadrangle is used, by analogywith triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on.

The origin of the word "quadrilateral" is the two Latin words quadri, a variant of four,

and latus, meaning "side."

Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting), also

called crossed. Simple quadrilaterals are either convex or concave.

The interior angles of a simple quadrilateral ABCD add up to 360 degrees of arc.

Pictures :

i. Parallelogram

ii.

Square
http://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/Polygonhttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Pentagonhttp://en.wikipedia.org/wiki/Hexagonhttp://en.wikipedia.org/wiki/Simple_polygonhttp://en.wikipedia.org/wiki/Complex_polygonhttp://en.wikipedia.org/wiki/Convex_polygonhttp://en.wikipedia.org/wiki/Concave_polygonhttp://en.wikipedia.org/wiki/Internal_and_external_anglehttp://en.wikipedia.org/wiki/Degrees_of_archttp://en.wikipedia.org/wiki/Degrees_of_archttp://en.wikipedia.org/wiki/Internal_and_external_anglehttp://en.wikipedia.org/wiki/Concave_polygonhttp://en.wikipedia.org/wiki/Convex_polygonhttp://en.wikipedia.org/wiki/Complex_polygonhttp://en.wikipedia.org/wiki/Simple_polygonhttp://en.wikipedia.org/wiki/Hexagonhttp://en.wikipedia.org/wiki/Pentagonhttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Polygonhttp://en.wikipedia.org/wiki/Euclidean_geometry


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iii. Scalene Trapeziod

iv. Rectangle

v. Isosceles Trapeziod


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vi. Right-angled Trapeziod


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Question b)Pictures and their characteristics :

1.

A rectangle is a four-sided shape

every angle is a right angle (90)

opposite sides are paralleland of equal length

2.

A square has equal sides and every angle is a right angle (90)

opposite sides are parallel.

A square also fits the definition of a rectangle(all angles are 90), anda rhombus(all sides are equal length)
http://www.mathsisfun.com/rightangle.htmlhttp://www.mathsisfun.com/geometry/parallel-lines.htmlhttp://www.mathsisfun.com/geometry/square.htmlhttp://www.mathsisfun.com/geometry/square.htmlhttp://www.mathsisfun.com/geometry/parallel-lines.htmlhttp://www.mathsisfun.com/rightangle.html


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3.

A rhombus is a four-sided shape where all sides have equal length

opposite sides are parallel and opposite angles are equal

the diagonals of a rhombus bisect each other at right angle

4.

A trapezium is a four-sided shape.

Has two equal sides.

Has two parallel sides. (same direction)
http://www.mathsisfun.com/geometry/rhombus.htmlhttp://www.mathsisfun.com/geometry/rhombus.html


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REFLECTION :

If people do not believe that additional mathematics is simple, it is only because they do not

realize how complicated life is.


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Appreciation :First and foremost, I would like to thank Allah, The All Mighty that finally, I had succeeded in

finishing this project work.

Also, thanks to my mom, Pn. Zuraidah Bt. Yaakub and my dad, En. Mohd Alayudin B. Che

Hasan for giving me fully support in completing this project work and permission to use their

computer and internet for further research in completing this project work. Isincerely appreciate

their generosity.

Not to forget, all my beloved Additional Mathematic Teachers, Pn. Munzarina, Pn. Mimie and

Pn. Fadhillah for all the assistances they has provided me during my job search. I appreciate

the information and advices they have given, as well as the connections they have shared with

me. Their expertise and help have been invaluable during this process.

I would like to give my special thanks to my fellow friends who had given me extra information

on the project work and study group that we had done. Thank you for spending time with me to

discuss about the coursework.

Last but not least, I would like to express my highest gratitude to all those who gave me the

possibility to complete this coursework. I really appreciate all your helps. Again, thank you so

much. May Allah bless us.


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ADDITIONAL M ATHEMATICS

Name : Ain Sajda Bt. Mohd Alayudin

I/C No : 950811-10-6546

Registration No :

Teachers Name :


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OBJECTIVEa) Apply mathematics to everyday situations and appreciate the importance and the beauty of

mathematics in everyday lives.

b) Improve problem-solving skills, thinking skills, reasoning and mathematical communication.

c) Develop positive attitude and personalities and intrinsic mathematical values such as

accuracy, confidence and systematic reasoning.

d) Stimulate learning environment that enhances effective learning, inquiry-based and team

work.

e) Develop mathematical knowledge in a way which increases students interest and

confidence.


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INTRODUCTIONAll Form 5 students who takes additional mathematics as an elective is required to carry out a

project. This year, the Curriculum Development Division, Ministry of Education has prepared

some task for us. We have to complete the task based on the methods. Through this project,

we are able to :

1. To wider our knowledge.

2. Apply and adapt a variety of problem.

3. Experience a classroom environment which is challenging and meaningful, thus, improving

thinking skills.

4. Experience a classroom environment where knowledge and skills are applied in showing real

life problems.

5. Experience a classroom environment where expressing ones mathematical thinking is highly

encouraged.

6. Experience a classroom environment that stimulate and enhance effective learning.

7. Acquire effective learning mathematical communications through oral and writing and to use

the language of mathematics to express idea correctly and precisely.


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Something about QuadrilateralsQuadrilaterals were invented by the Ancient Greeks. It is said

that Pythagoras was the first to draw one. In those days quadrilaterals had

three sides and their properties were only dimly understood. It was the genius

of the Romans to add a fourth side and they were the first to make a list of the

different kinds of quadrilaterals but it wasn't until 1813 that an English

mathematician, J.P. Smith, discovered the trapezium. Quadrilaterals remain a

rich source of investigations for researchers, the best known unsolved problem

being to find a general formula for the number of interior angles.

Types of quadrilaterals :

Parallelogram:A four-sided polygon with two pairs of parallel and equal sides. The following is a

parallelogram.

Rectangle:A rectangle is a parallelogram with 4 right angles. The following is a rectangle.

Square: A square is a rectangle with 4 equal sides.The following is square


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Rhombus:Arhombus is a parallelogram with 4 equal sides. The following is a rhombus.

Trapezoid:A trapezoid is a quadrilateral with only one pair of parallel sides. The following

are trapezoids.

Scalene trapezoid:A scalene trapezoid is a trapezoid with no equal sides.The following is a

scalene trapezoid

Right-angled trapezoid:A right-angled is a trapezoid with two right angles. The following is

a right-angle trapezoid.

Isosceles trapezoid:In an isosceles trapezoid, non-parallel sides are equal. The following is

an isosceles trapezoid.


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PART 2Question a)

Variables :

1. Length of the nylon string

2. Area of the plywood

3. X = length of the trace area

4. Width of the trace area

5. Width of the plywood

6. Shape of the trace

7.

Length of each plywood

8. Area of rectangular shape

Area of the trace area = xy

2x + 2y = 5

2y = 5-2x

y =

y =

-x

Area = x (

-x)

=

-x


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Question b)

i. Differentiation

A =

x - x

=

=

2x

=

2x = 0

2x =

4x = 5

X =

A =

(

)

(

)

=

= (x,A)

= (1.25,1.5625)

A = 1.5625 m when x = 1.25 m

Thus, the maximum area of the trace area is 1.5625m


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i. Graphical method

Plot graph A against x. Based on the table of values of x and A

X (m) 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30

A

(m)

1.56

00

1.560

9

1.561

6

1.562

1

1.562

4

1.562

5

1.562

4

1.562

1

1.561

6

1.560

9

1.560

0

A = 1.5625 m when x=1.25 m

Thus, the maximum area of the trace area is 1.5625 m

1.5595

1.56

1.5605

1.561

1.5615

1.562

1.5625

1.563

1.18 1.2 1.22 1.24 1.26 1.28 1.3 1.32

A (m)

A (m)


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Question C)

The perimeter of nylon string = 5.0 m

The length of 1 piece of plywood = 0.5 m

The minimum number of pieces =

=

= 10 plywoods

The minimum cost for making the trace area = the minimum number of

plywood x the cost

= 10 x RM 14.00

= RM 140.00

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