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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.html8/13/2019 Additional Mathematics Project 2013
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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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