Addmaths 2012

7/31/2019 Addmaths 2012

1/12

Table of contents

1.Appreciation.2

2.Part 1.3

3.Part 2.5

4.Part 3.6

5.Further Exploration..11

7/31/2019 Addmaths 2012

2/12

Additional Maths Project 2012

1

ACKNOWLEDGEMENT

Initially, I would like to thank my Additional Mathematics subject

teacher Ms. Lim Siew Feei as she had guided me throughout the project

and has been a very supportive figure for me to finalize the project.

Besides that, I would also like to thank all my friends for lending me a

helping hand in the process of finalizing this project. Without their help

and assistance, this project might not be completed.

Last but not least, I would like to express my gratitude towards my

beloved parents for providing me the equipment and knowledge to

complete this project. They were both very supportive and this gives a big

boost for me to complete this project.

7/31/2019 Addmaths 2012

3/12


2

PART1

A)

B) Polygon is defined as a closed, 2-dimensional shape made up of three or more

straight line segments connected end to end to end. Polygons have been known since

ancient times which started with the ancient Greeks. The pentagram, a non-convex

regular polygon (star polygon), appears on the vase of Aristophonus, Caere, dated to

the 7th century B.C.Non-convex polygons in general were not systematically studied

until during the 14th century where it was studied by Thomas Bredwardine. In 1952,

Shephard generalized the idea of polygons to the complex plane, where each real

dimension is accompanied by an imaginary one, to create complex polygons.

7/31/2019 Addmaths 2012

4/12


3

C) The four different methods of finding the area of a triangle are stated below:

Method 1:

h

b

Method 2:

a

b

Method 3: |

|

Method4: Area = (mx1 + c) dx + (mx2 + c) dx - (mx3 + c) dx

7/31/2019 Addmaths 2012

5/12


4

Part 2

A) Cost needed to fence the herb garden = RM20.00 per metre x 300m

= RM6000.00B)

p (m) q (m) cos degree area (m2)

50 150 1.0000 0.00 0.00

55 145 0.8809 28.25 1887.46

60 140 0.7857 38.21 2598.08

65 135 0.7094 44.81 3092.33

70 130 0.6484 49.58 3464.10

75 125 0.6000 53.13 3750.0080 120 0.5625 55.77 3968.63

85 115 0.5345 57.69 4130.68

90 110 0.5152 58.99 4242.64

95 105 0.5038 59.75 4308.42

100 100 0.5000 60.00 4330.13

105 95 0.5038 59.75 4308.42

110 90 0.5152 58.99 4242.64

115 85 0.5345 57.69 4130.68

120 80 0.5625 55.77 3968.63125 75 0.6000 53.13 3750.00

130 70 0.6484 49.58 3464.10

135 65 0.7094 44.81 3092.33

140 60 0.7857 38.21 2598.08

145 55 0.8809 28.25 1887.46

150 50 1.0000 0.00 0.00

C) In order for the enclosed area to be maximum, the shape of the triangle must be

equilateral. Therefore, the length of both p and q must be 100m.

D) (i) 50

7/31/2019 Addmaths 2012

6/12


5

Part 3

A) Suggestion 1 (Quadrilateral)

y x Area (cm^2)0 150 0

20 130 2600

40 110 4400

60 90 5400

75 75 5625

80 70 5600

100 50 5000

120 30 3600140 10 1400

150 0 0

2 + 2 300 + 150

x

y

The area of a quadrilateral will be

at the maximum when both sides

are of equal length.

7/31/2019 Addmaths 2012

7/12


6

B) Suggestion 2 (Circle)

23002 150

150

Area = 7 161.97

The area of the circle will increase as the value of r increases. Due

to the limit of the circumference, the r value of the circle is

constant and the maximum area achievable is 7 161.97 .

However, among all the other shapes, the circle has the highest

area for 300m of fencing.

The weakness of a circle is the land area that you would need to

accommodate the circle must be larger than the circle itself. Unless

the farmer has a large land but only can afford 300m of fence, then

a circle will be a practical option.

r

7/31/2019 Addmaths 2012

8/12


7

C) Suggestion 3 (Pentagon)

300 60 72 54

ta54 30 41.29

T

12 605 6193.71

The pentagon is a polygon of 5 triangles arranged around

an axis of rotation. Its maximised area is . when it is limited by the perimeter of 300m.

The weakness of this polygon is that it requires an area

larger than the shape for this polygon to fit in. Therefore,

this polygon is not suitable.

7/31/2019 Addmaths 2012

9/12


8

C) Suggestion 4(Semicircle)

+ 2300

+ 2

58.35 12

.

The semi-circle is half of a complete circle. Like a circle its area

increases with the value of r. Due to the constant circumference of

300m, the r value is constant. Hence the maximum area achievable

is. .However, it has the same weakness as the circle. An area larger than

the semi-circle is required to fit in the shape. Therefore, it is not so

practical on a small plot of land.

7/31/2019 Addmaths 2012

10/12


9

D) Suggestion 5 (Hexagon)

Therefore, the most suitable shape is the quadrilateral as it has a largemaximum area and can be fenced on the minimal area of land.

60 60ta60 25 43.3

Perimeter=300m

One side=50m Area12 50 6

.

The hexagon is basically an arrangement of 6 triangles around

an axis of rotation. Its maximised area is.

when itis limited by the perimeter of 300m.

The weakness of this polygon is that it requires an area larger

than the shape for this polygon to fit in. Therefore, this polygon

is not the most suitable to be used for the herb garden.

T

7/31/2019 Addmaths 2012

11/12


10

Further Exploration

(A) Suggest 3 types of herb

(i)serai wangi (Cymbopogon nardus)

(ii)kecubung (Datura fastuosa)

(iii)ganda suli (Hedychium coronarium)

Origin: South India

Family:PoaceaeFunction:

-mosquito repellent

-anti-bacteria cleansing agent

Origin: IndiaFamily: Solanaceae

Function:

-cures baldness-helps with cardiac problems

-helps relieve asthma

Origin: India

Family: Solanaceae

Function:

-cures baldness

-helps with cardiac problems

-helps relieve asthma

7/31/2019 Addmaths 2012

12/12


11

(B) Logo

Addmaths 2012

Documents

Transcript of Addmaths 2012