add maths project work 20141

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SEKTOR PENGURUSAN AKADEMIKJABATAN PELAJARAN NEGERI PERAK

SMK METHODIST (ACS), PARIT BUNTAR, PERAK

ADDITIONAL MATHEMATICSProject Work 2014

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Additional Mathematics Project Work 2014

The charm of Mathematics lies in the surprising nature of its number patterns. Words are not required to demonstrate its charm. It is obvious from the pattern attained. Arithmetic progressions and geometric progressions are just two amazing examples that immediately come to our mind. Look, enjoy and be amazed……….. This project will make you love number patterns more! Try it wholeheartedly to experience its sensation!!

PART A

Create an A4-size poster on any local theme that exhibits the following number patterns creatively:1. Arithmetic progression2. Geometric progression

PART B

You are a Form 5 Additional Mathematics student of a school in Malaysia. As part of the syllabus requirement, you need to complete four assignments.

Assignment No. 1For the same job specifications, two companies offer a different salary scale:

Company A : Starting monthly pay = RM900.00Monthly increment = RM50.00

Company B: Starting monthly pay = RM750.00Monthly increment = RM60.00

(a) In January 2014, Ali starts to work in Company A and Ahmad in Company B.When will the monthly salary of Ali and Ahmad be the same?Use three methods. Include the use of ICT.

(b) Which salary scale is the better deal? Justify.

Assignment No. 2Two companies, C and D, offer a different salary scale for the same post:

Sektor Pengurusan Akademik JPN PERAK

An amazing journey begins …………………..3, 2, 1, 0

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Company C: Starting monthly pay = RM500.00Thereafter, the monthly salary for a particular month is 10% more than the monthly salary for the preceding month

Company D: Starting monthly pay = RM300.00Thereafter, the monthly salary for a particular month is 15% more than the monthly salary for the preceding month

(a) Azrin and Aidil start to work for company C and D respectively in the same month.After how many months will Aidil’s monthly salary be more than Azrin’s monthly salary?Use two methods.

(b) Which salary scale is the better deal? Justify.

Assignment No. 3(a) A company offers a lucrative yearly salary increment. Table 1 shows the total salary a

worker received after working for n years.

Number of years , n 3 4 5 6 7Total salary received (RM) 28 080 39 360 51 600 64 800 78 960

Table 1

Based on Table 1, write a suitable conjecture about the salary scale.By using a suitable graphical method, verify your conjecture. Describe completely the salary scale.

(b) Table 2 shows the monthly salary a worker received in the nth year.

n 3 4 5 6 7Monthly salary (RM) 1 003.52 1 123.94 1 258.82 1 409.87 1 579.06

Table 2

Based on Table 2, write a suitable conjecture about the salary scale.By using a suitable graphical method, verify your conjecture. Describe completely the salary scale.

Assignment No. 4


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For the last part of this amazing journey, you are going to explore a fantastic number sequence……….

FURTHER EXPLORATION(a) Count the number of petals in each of the following flowers to generate the first 9

terms of a fantastic number sequence. Observe the number pattern carefully to generate the next 6 terms of the sequence.


T1 T2

T4 T5 T6

T7 T9

T10, T11, T12, T13, T14, T15,………………………………………………………………………………………

T8

T3

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(b) For the number sequence that you have generated, find the values of and .

Express each answer as a decimal.Based on your answers, form a conjecture. Prove it.

(c) Determine the value of correct to four significant figures.

Your answer for part (c) above is known as the golden ratio. The Greeks observed that this is a pleasing dimension for a building or any structure. Thus, if a rectangle of

length y cm and width x cm, where y > x, is such that , then it

is a golden rectangle with a pleasing dimension.

(d) Identify 5 different types of products with rectangular surfaces. For each type of product, collect a few items with different sizes. Based on the products that you have collected, determine whether product marketing nowadays exhibits the golden ratio. Tabulate your findings.

(e) (i) You are given the following information:

Determine whether such rectangles are golden rectangles.

(ii) You are now given a general case:


1 cm

x cm

is such that Rectangle

x cm

y cm

is such that Rectangle

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Determine whether such rectangles are golden rectangles.

(iii) The width of a golden rectangle is 8 cm. Find its length. Use two methods.

(iv) You are given two pieces of wire, each 20 cm long. One piece is to be bent to form the biggest possible rectangle and the other piece to form a golden rectangle. Determine the length and width of each rectangle. Use two methods in each case.

REFLECTION‘ Additional Mathematics is awesome. ....... patterns, sequences, ............ everywhere.’Reflect creatively.


add maths project work 20141

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