' I SN,I,ANtS6fr. ffiSti8*IION DEPARTMENT

ADDITIONAL MATHEMATICS PROJECT WORK II2OI2

PART 1

Polygons are evident in ,all architecture. They provide variation and charm in

buiidings. When applied to manufactured articles such as printed fabrics, wallpapers,

and tile flooring, polygons enhance the beauty of the structure itself.

(a) Collect six such pictures. You may use a camera to take the pictures or get

them from magazines, newspapers, internet or any other resources.

(b) Give the definition of polygon and write a brief history of it'

(c) There are various methods of finding the area of a triangle.State four different methods.

PART2 .r i : " r ' ; ' ' , ' ; ' ;1t '1 ' ; ' ; , l " r ' i ; :1 ' ! i l

A farmer wishes to build a herb garden on a piece of land. Diagram I shows the shapeof that garden, where one of its sides is 100 m in length. The garden has to be fencedwith a 300 m fence. The cost of fencing the garden is RM 20.00 per metre.(The diagram below'is not drawn to scale)

Diagram I

Calculate the cost needed to fence the herb garden.

Complete table 1 by using various values of p, the corresponding values of q

and 0.

p (m) a (m) 0 (degree) Area (nt')

Table 1

(a)

(b)

Additional Mathematics Project Work 1

PANITLA MATEMATIK TAMBAHANSMK JATAN EMPAT

BANDAR BARU BANGI

Selangor Education DePartment

Additional Mathematics Project Work 1

(c) Based on your findings in (b), state the dimension of the herb garden so that

the enclose d arca is maximum.

(d)(i) Only certain values ofp and of q arc applicable in this case' State the range of

values ofpandofq.

(tr) By comparing the lengths of p, q and the side, determine the relation

between them.

(fil) Make generalisation about the lengths of sides of a triangle. State the name of

the relevant theorem.

PART 3

If the length of the fence remains the same 300m, as stated inpartz:

(a) Explore and suggest at least 5 various other shapes of the garden that can be

constructed so that the enclosed area is maximum'

(b) 'Draw a conclusion from your exploration in (a) if:

(t) The demand of herbs in the market has been increasing nowadays.

Su$gest three types of local herbs with their scientific names that the

= f*nier r* ptant in the herb garden to meet the demand. Collect*

pictures and information of these herbs'

(ii) These herbs will be processed for marketing by a company' The design

of the packaging plays an important role in attracting customers. The

company wiitrei to design an innovative and creative logo for the

pa"t agirg. You are given the task of designing a logo to promote the

proOuit. bru* the logo on a piece of paper size 44. You must include

at least one polygon shape in the logo'

END OF PROJECT PAPER

PANITIA i4ATEMATI K TAIJI BAHANSMK JAI.AN EMPAT

8AI{TTAR BARU BANGI

Selangor Education DePartment

r Additional Mathematics Project Work 2

SELANGOR EDUCATION DEPARTMENT

ADDITIONAL MATHEMATICS PROJECT WORK 2I2OI2

PART 1

(a) Connecting a series of fwo points on straight lines which cross over each other can croate

abstract geometric patterns. Such attractive and sophisticated designs are also known as "string

art patterns". They can be produced and created using geometrical instruments. Diagram 1 shows

one of the designs which is created by drawing straight lines on the Cartesian plane.

Diagram I

Collect five such patterns from magazines, newspapers or internet. You can also design your

own patterns.

(b) Rene Descartes and Hero (or Heron) of Alexandria were two gteat mathematicians who had

made great contributions in mathematics. Conduct a research and write on the history of the two

mathematic ians and their important contributions -

PANITI,A MATEI'ATIK TAMBAHANSMK JALAN EMPAT

BANDAR BARU BANGI

Selangor Education DePartment Page 1.

Additional Mathematics Project Work Z

PART 2

Encik Ali owns a rectangular piece of land with a;dirnension of 3 km x 8 km. He wants to use

part of the land for rearing poultry.

(a) There is a small buildipg near the poultry farm. Find out the outline of the building by

$rawing all the lines and curve below on the same txes'

Name the type of the building.

1s3r= rs+L44,

8Y:3r+f iT,

3:r-7y*t :0,

s-ay;1*=0,

5r-?y+i38:0 *

Y=-Ar+l- ,*'\'

*p* y s3*: 0,

r * 5Y:14' : Do

3y = r* lfi"

2.r*3y:7,

r *Y :13,

r*5Y-f?:$:0

r*9:0,

s: -6.

r*1:0,

f f :3"

x :8,

-4<x{6

-1{r{7

ts{x{9

3{r4B

-6€r{-4

-4Ex{-1

' :6EYE7

*g.{'E { -1

-10q:r{-6

-t<yg?

7{x{9

-9Ex{?

-6{tsE3

-7 <1'E4

-851'1!3

-9<y<1

-6{yS3.5

PANITIA MATE MATIK TAM BAHANSMK JAI.AN EIdPAT

BANDAR BARU BANGI

Selangor Education Departrnent Page2

Additional Mathematics Project Work 2

(b) Diagram 2 shows the dimensions of the land, PprtS and the shaded triangle ABC as the part

of the land which he wants to dse for rearing poultry.

3km

Diagram 2

Find the length of fence needed to fence up the poultry farm. Give your answer correct to the

nearest km.

(c) His friend, Encik Muthu, suggested that he should set up the poultry farm in the shape

of a right-angled triangle. Encik Ali has agreed and decided to fence up the new triangle, ABD,

with a right angle at B such that the area of triangle ABD must be equal to that of triangle ABC.

By using two different methods, determine the position of D.

(d) Encik Ali found that usually three chickens will lay three eggs in one and a half day. Howmany eggs will nine chickens lay in ten days?

PANITIA MATEMATI K TAMBAHANSMK JAI,.AN EMPAT

BAT'IDAR EARU BANGI

t 'II

I3.5 km

II+

R

k

N

IIB

5km

III

dlP

<-1.5km------+

s

1km

1I

3kmt

I+

Selangor Education Department Page 3

Additional Mathematics Project Work 2

PART 3

In order to increase his income, Encik Ali has decided to build a nursery on another part of his

land. He bought 100 meters of fencing to fence another triangular area. He prefers to fence an

isosceles triangle with the values of the measurement of area and length of sides, in integer.

(a) Using calculator or ICT, help Encik Ali to explore the dimensions and area of the

different isosceles triangles that can be formed by completing the table below. Hence, state the

dimensions of the fourlsosceles triangles with areas and length of sides, in integer. (You may

use Heron's formula to find the area of a triangle.)

fHeron's Formula: Area of AIBC :1rffi, where "

:

-ll

and a'

b and c are the sides of L ABq

a b c Area

(b) Using calculus, show that the area of the triangle ABC with a perimeter of 100 meters is

maximum when the triangle is an equilateral triangle. Hence, find the maximum area of the

triangle ABC.

FURTHER EXPLORATION

Heron's Formula can be used to find the area of a triangle when the lenglhs of the three sides are

known. There are many proofs of Heron's Formula. Most can be categorized as algebraic,

geometric, or trigonometric. Conduct a research using the internet to find out one proof of the

Heron's Formula in any one of the list categories'

PAN IT"IA |},?\ IEfu'IA,I I K TAM EAI.IAN$MK JAL,AN EMFI,ET

BA},!DAR BARU BAI.IGI

Selangor Education Department Page 4

Additional Mathematics Proiect Work 2

REFLECTION

While you were conducting the project, what have you learnt? What moral values did you

practice? Represent V""r .if"i"ns or feelings creatively through usage of symbols' illustrations'

drawings or even in a song.

END OF PROJECT PAPER

PAN ITIA II'ATEMATI K TAM BAHANSMK JATAH"EMPAT

BAHDAR BARU BANGI

Selangor Education DePartmentPage 5

RTJBRIC F'OR ADDITIONAL MATHEMATICS PROJECT WORK 2012

Namg: . , . . . . . r . . . r . . . . r r r . . r r I r r r r . r r r . . I l l . r { . r r r I r | . . | . r . t FOrm 5.. ' r r r . . . ! . r | | t r . r r r r r . t

Range ofmarks

MarksAwarded

Subtotal

i{ ?.fI

Al. General Aspect(60/ol

Appropriate title. tContent pdge. I

S ystemati c prssentati on. r -2Creativity. t*2

A2.Introduction(10%)

Comprehensive introduction - may include historyo valuesand other information relevant to the task includingpictures and captions.

5 -7

Sati sfactory i ntroducti on, t -4Relating given task to real-life situations. I -3

Bl. Specify the task

{s%}Identify and state all given information and required resultsin effective mathematical statements,

4-5

{l=

Identiff and state given information and required resultsincompletely.

1-3

Cl. Procedurs(3s %)

In-depth understanding of the questions.Use very effi cient problem-solving strategies.Answer all questions g_Ql{ectlY.

3l -35

Understand the questions.

$r* strategies that lead to solutions of the problems.Answer all questions cotrectly_.

15 - 30

partially understand the question. Use strategies that arepartially useful. Do not answer allqqes{qns correctly,

5-14

C2. Communication& Reasoning

(1s%)

Communicate precisely and efficiently using mathematicalrepresentations such as symbol s/graphs/tabl es/di agrams.Refined and complex reasoning.

13 -- 15

Communicate effectively using mathemati calrepressntations such as symbo I s/graphsltables/diagrams.Use effective mathematical reaqqnlng' -

10 - 12

eommunicate ineffectively. Limited use of mathematicalrepresentations such as symbol s/graphs/tables/di agrams .

Sorne evidence of mathematical rofls9nllg.5-9

C3. Making andsupportingconjecture

(6%l

Evidence of making and supporting coqiectures. 6

Making conjecture only.3

Dl. FurtherInvestigation

(15%)

10 - l5

Some exploration. s-9

D2. Conclusion /Generalisation

(3%)State relevant conclusi on/generalisation, 1-3

El. Reflection(5%)

Comprehensive refl ection. 4*5lncomplete reflection. 1-3

Total score (Al + L2 + Bl + Cl + CZ + C3 + D1+I)2+ EU

PANITIA TIATEMATIK TAMBAHAN$[IK JALAH Ei'PAT

BANDAR BARU BANGT