Additional Mathematics Project 2013

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First and foremost, I would like to thank god that finally, I had succeeded

in finishing project work.

I would like to thank my beloved Additional Mathematics teacher, Mr. Ng

Seng Chew for all the assistance he has provided me during my job search. I appreciate the

information and advices he has given, as well as the connections he have shared with me. His

expertise and help have been invaluable during this process.

Also, thanks to my parents, Ahmad Hanit Mohd Jah and Rahemah Tan ,

for giving me full support in completing this project work. I sincerely appreciate their

generosity. 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 course work.

Last but not least, I would like to express my highest gratitude to all those

who gave me the possibility to complete this course work. I really appreciate all your helps.

Again, thank you so much.


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The aims of carrying out this project work are :

To apply and adapt a variety of problem-solving strategies to solve

problems.To improve thinking skills.

To develop mathematical knowledge through problem solving in way that

increase students interest and confidence.

To use the language of mathematical to express mathematical ideas

precisely.

To provide learning environment that stimulates and enhances effective

learning.

To develop positive attitude towards mathematics.


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Acknowledgement

Objective

Introduction

Part 1

Part 2

Part 3

Further Exploration

Conclusion

Reflection


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QUADRILATERAL

In Euclidean plane geometry, a quadrilateral is a polygon with four sides (or edges) and fourvertices or corners. Sometimes, the term quadrangle is used, by analogy with 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 (and planar) quadrilateral ABCD add up to 360 degrees of arc,

that is

This is a special case of the n-gon interior angle sum formula (n 2) 180. In a crossed

quadrilateral, the four interior angles on either side of the crossing add up to 720.[1]

All convex quadrilaterals tile the plane by repeated rotation around the midpoints of their

edges.

HISTORY OF QUADRILATERAL

Quadrilaterals 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.


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The Rectangle

means "right angle"

and show equal sides

Arectangleis a four-sided shape where every angle is aright angle(90).

Also opposite sidesareparalleland of equal length.

The Rhombus

Arhombusis a four-sided shape where all sides have equal length.

Also opposite sides are parallel andopposite angles are equal.

Another interesting thing is that the diagonals (dashed lines in second figure) meet in

the middle at a right angle. In other words they "bisect" (cut in half) each other at right

angles.

The Square

means "right angle"

show equal sides

Asquarehas equal sides and every angle is a right angle (90)

Also opposite sides are parallel.

A square also fits the definition of a rectangle(all angles are 90), and a rhombus(all

sides are equal length).
http://www.mathsisfun.com/geometry/rectangle.htmlhttp://www.mathsisfun.com/geometry/rectangle.htmlhttp://www.mathsisfun.com/geometry/rectangle.htmlhttp://www.mathsisfun.com/rightangle.htmlhttp://www.mathsisfun.com/rightangle.htmlhttp://www.mathsisfun.com/rightangle.htmlhttp://www.mathsisfun.com/geometry/parallel-lines.htmlhttp://www.mathsisfun.com/geometry/parallel-lines.htmlhttp://www.mathsisfun.com/geometry/parallel-lines.htmlhttp://www.mathsisfun.com/geometry/rhombus.htmlhttp://www.mathsisfun.com/geometry/rhombus.htmlhttp://www.mathsisfun.com/geometry/rhombus.htmlhttp://www.mathsisfun.com/geometry/square.htmlhttp://www.mathsisfun.com/geometry/square.htmlhttp://www.mathsisfun.com/geometry/square.htmlhttp://www.mathsisfun.com/geometry/square.htmlhttp://www.mathsisfun.com/geometry/rhombus.htmlhttp://www.mathsisfun.com/geometry/parallel-lines.htmlhttp://www.mathsisfun.com/rightangle.htmlhttp://www.mathsisfun.com/geometry/rectangle.html


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Example of the geometry in our daily lives

Rectangular swimming pool

Square design wallpaper.

Parallelogram design building.


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Rhombus design in an architecture college.

Trapezium bookshelves.

Kites.


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QUESTION A

Variables :

1. Length of the nylon string

2. Area of the brick

3. X = length of the trace area

4. Width of the trace area

5. Width of the brick

6. Shape of the trace

7. Length of each brick

8. Type of brick

Area of the trace area =


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2x + 2y = 7

2= 7 - 2

=

Area =( x )

=

QUESTION B

i. Differentiation

A= -

= =- 2

=

2

4


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A =

(

) (

)

=

= ( x , A )

= ( 1.75 , 3.0625 )

A = 3.0625 when x = 1.75 Thus, the maximum area of the trace area is 3.0625 .

ii. Graphical Method

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

X

m)

1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.80

A

3.06 3.0609 3.0616 3.0621 3.0624 3.0625 3.0624 3.0621 3.0616 3.0609 3.06


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QUESTION C

The perimeter of nylon string = 7.0 m

The length of a brick = 0.2 m

The minimum number of pieces =

=

= 35 bricks.

The minimum cost for making the trace area :

The minimum number of pieces x the cost = 355 x RM7

= RM245


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Therefore, the minimum cost to build the park site is RM245.


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= 0.7038 = 2.254

The radius of the ponds is 0.7038m and 2.254m

Since large fish pond has bigger radius, therefore the radius for the large fish pond is

2.254m

The diameter of the large fish pond = 2.254m + 2.254m

= 4.508m

Therefore the diameter of the large fish pond is 4.508m

QUESTION C

To minimise the cost of the construction of building a flower site, we must find its

maximum area of the flower site. There are many methods to find the maximum

area. In here, I will show two methods that is differentiation methodand

tabulation of data.

Differentiation method

Firstly, we use the quadratic equation we formed from the 3(a),

y= - 2x2+ (9-6x) + 138

We insert =22/7 into the formulae

y= -6.286x2-18.86x+138 + 28.29

y= -6.286x2

-18.86x + 166.89


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Now we differentiate the quadratic equation above

Since at the maximum point, it has a stationary value,

-12.572x18.86 = 0

-12.572x= 18.86

X =-1.500m2

Tabulation of data

x y = -6.286+ 18.857 x + 109.7141.0 122.285

1.1 122.850

1.2 123.290

1.3 123.604

1.4 123.793

1.5 123.856

1.6 123.793

1.7 123.604

1.8 123.290

1.9 123.850


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2.0 122.284


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1 ) CIRCLE

Area of circle ,


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Perimeter of circle ,

1 ) SQUARE

Area of square ,


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Perimeter of square ,

3) SEMI - CIRCLE

Area of semi-circle ,


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( )

Perimeter of regular pentagon ,

Therefore, circle is the best shape to build the garden as it gives the minimum perimeter than

other shapes.


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Area of circle ,

Perimeter of circle ,

As the conclusion to this project work , there are so many quadrilateral around us. Its

plays an important role in our design of building or an object . So, student should be more

aware about this.


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Plus, it is widely used in building of modern structures and designing of a gadget. The

triangle, for instance is often used in construction because its shape makes it comparatively

strong. The use of polygon shape reduces costs and maximizes profits in a business

environment . The rectangle is used in a number of applications, due to the fact our field of

vision broadly consist of a rectangle shape.

Without it, mans creativity will be limited. Therefore, we should be thankful of the

people who contribute in the idea of using quadrilateral.

While I am doing this Additional Mathematics project work, I have learned some

moral values. This project work had taught me to be responsible on the works that are given.


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I had learned on how to complete this project work by identifying and interpreting the

problems.

Moreover, this project work has also make me feel more confident to do all of the

work and to not give up easily when I found that it is hard to find the solution because, when

theres a will, there will always be a way.

Not just that, I am also enjoying doing this project. I spend more time with my

friends, thus it will tightened our friendship.

Last but not least, this project work has also increase my interest in learning

additional mathematics subject.


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Additional Mathematics Project 2013

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