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Add Math Project Work Answer Perak - Janjang
T10, T11, T12, T13, T14, T15,………
(b) For the number sequence that you have generated, find the values of
Express each answer as a decimal.
(c) Determine the value of
correct to four significant figures.
Add Math Project Work Answer Perak - Janjang
Additional Mathematics Project Work 2014
Source: Sektor Pengurusan Akademik, Jabatan Pelajaran Negeri (JPN) Perak
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 progression
2. 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. 1
For the same job specifications, two companies offer a different salary scale:
Company A: Starting monthly pay = RM900.00
Company B: Starting monthly pay = RM750.00
Monthly 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. 2
Two companies, C and D, offer a different salary scale for the same post:
Company C: Starting monthly pay = RM500.00
Thereafter, the monthly salary for a particular month is 10% more than the monthly salary for the preceding month
Company D: Starting monthly pay = RM300.00
Thereafter, 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
|
7
|
Total 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
|
7
|
Monthly salary (RM)
|
1003.52
|
1123.94
|
1258.82
|
1409.87
|
1579.06
|
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
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.
(b) For the number sequence that you have generated, find the values of
Express each answer as a decimal.
Based on your answers, form a conjecture. Prove it.
(c) Determine the value of
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.
Determine whether such rectangles are golden rectangles.
(iii) The width of a golden rectangle is 8 cm.
Find its length. Use two methods.
Use two methods in each case.
(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.
REFLECTION
‘Additional Mathematics is awesome. ....... patterns, sequences, ............ everywhere.'
Reflect creatively.
Reflect creatively.