2.20 add math module 20 no indeks - penang free … papers add maths/index-number-pdf...the table...

INDEX

ADDITMATHE

MODU

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http://sahatmozac.blogspot.com

IONALMATICS

0

NUMBER

LE 20

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1

CHAPTER 11: INDEX NUMBER

CONTENTS PAGE

11.1 Conceptual Map 2

11.2 Calculate index number 3

11.3 Calculate price index 5

11.4 Calculate composite index 7

Past Year Question 9

Assessment 15

Answer 17

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2

11.1 CONCEPT MAP

Fill in the fomula in the blank boxes

APLICATION OF INDEXNUMBER

Price Index

Price index, I =

Where ,P1 = price of an item at aspecific timeP0 = price of an item at a basetime

Composite Index Number

Composite index number, I

I =

Where ,W = weightage of each itemI= Index number of each item



3

11.2 Calculate index number

Example 1:

Example 2:

The total sale of sun glasses in 2003 and 2004 are 80 and 96 pairs.Calculate the index in 2004 given that 2003 is the base year.

Base year, 03Q = 80

Specific year, 04Q = 96

I =03

04

Q

Qx 100 = 120

2. The index of Perodua Kancil in 1996 based on 1990 is 140 and the index number of

Perodua Kancil in 2000 based on 1996 is 105. Find the index number of the Perodua

Kancil in 2000 based on 1990.

1990 1996 2000

100=

105

x

x =100

140x 105

= 147

100 x

_ 100 105

Or x 100 = 140 x 100 = 105

90

96

P

P=

100

140

96

00

P

P=

100

105

Index number in 2000 based on 1990, I =90

00

P

Px 100

=96

00

P

Px

90

96

P

Px 100

=100

105x

100

140x 100

= 147



4

Exercise 11.2

1. The student population of a College MARA increased from 1000 students in year

2005 to 1380 students in year 2006. Calculate the index number to show change in the

student population of the school in year 2006 using year 2005 as the base year.

2. The price index of two items for the specific years are given in the following table.

Item 1995(1990=100)

1999(1990 = 100)

1999(1995=100)

P 125 140 xQ 135 y 120

Calculate the values of x and y



5

11.3 Calculate price index

Example 1

Exercise 11.3:

1. The price of a book was RM 0.90 in 1999. Its price became RM 1.35 in 2003.

Calculate the index price of the book in 2003 based on the year 1999

The price index of a packet of sugar weighing 1kg in year 2006 based on year

2004 was 115. If the price of a packet of the sugar in a year 2004 was RM 7.00,

find the price of a packet of sugar in year 2006.

Base year, 04P = RM 7.00

Specific year , 06P = ?

Price Index, I =04

06

P

Px 100

=00.706P

x 100

06P = x

= RM 8.05



6

2. The index number of the monthly house rental in Bertam Area in year 2004 based on

year 1999 was found to be 118. If the house rental in year 1999 was RM400 per month,

find the monthly house rental in year 2004.

3. The table shown the price per kg of good: A, B and C in the year 2005 and 2006.

Types of good Price Price index in 2006

(Base year = 2005)2005 2006

A RM 1.20 RM 1.60 z

B x RM 2.30 110

C RM 0.60 y 102

Find the value of x, y and z



7

11.4 Calculate Composite Index

Example:

The table below show the price indices of 3 types of thing to make a cake in a certainyear. Calculte the composite index.

1.Things Index WeightageP 100 4Q 120 2R 145 4

I =

W

IW

= 100(4) +120(2) + 145(4)4 + 2 +4

= 122

Exercise 11.4:

1. Calculate the composite index for each of the following data

Index number, I 120 110 105Weightage, W 3 4 3



8

2. Table below shows the prices index and the weightage of three items in 2000based on 1996.

Item Price Index WeightageA 125 5B x 3C 110 2

The composite index in 2000 is 116. Find the value of x.

3. Diagram shows a bar chart which represent the cost of three components, A, B, C

The composite index is 107. find the value of m

A B C Component

m

6

4

Cost



9

Past Year Question

2005 (Paper 2)1. Table 1 shows the prices and the price indices for the four ingredients P, Q, R and S used in

making biscuits of a particular kind. Diagram 1 is a pie chart which represent the relative amount

of the ingredients P, Q, R and S used in making these biscuits.

Ingredients Price per kg ( RM) Price index for the

year 2004 based on

the year 2001

Year 2001 Year 2004

P 0.80 1.00 x

Q 2.00 y 140

R 0.40 0.60 150

S z 0.40 80

Table 1

Diagram 1

a. Find the value x, y and z. [3 marks]

120O

60O

100O

QP

S

R



10

b. (i) Calculate the composite index for the cost of making these biscuits in the year2004 based on the year 2001

(ii) Hence, calculate the corresponding cost in the year 2001 if the cost in

the year 2004 was 2985 [ 5 marks]

c. The cost of making these biscuits is expected to increase by 50% from the year 2004

to the year 2007

Find the expected composite index for the year 2007 based on the year 2001

[2 marks]

Solution



11

2004 (Paper2)

2. Table 2 shows the price indices and percentage of usage of four items, P, Q, R and S, which are

the main ingredients in the production of a type of biscuit.

Item Price Index for the year 1995

based on the year 1993

Percentage of usage

(%)

P 135 40

Q x 30

R 105 10

S 130 20

Table 2

(a) Calculate

(i) the prices of S in the year 1993 if its price in the year 1995 is RM 37.70,

(ii) the price index of P in the year 1995 based on the year 1991 if its price index

in the year 1993 based on the year 1991 is 120. [5 marks]



12

(b) The composite index number of the cost of biscuit production for the year 1995 based

on the year 1993 is 128. Calculate

(i) The value of x

(ii) The price of a box of biscuit in the year 1993 if the corresponding price in the

year 1995 is RM 32. [5 marks]

Solution

2003( Paper 2)

3. Diagram 2 is a bar chart indicating the weekly cost of the items P, Q, R, S and T for the year

1990. Table 3 shows the prices and the price indices for the items

Weekly Cost ( RM)

12

15

24

30

33

P Q R S T Items



13

Diagram 2

Items Price in 1990 Price in 1995 Price Index in 1995

based on 1990

P x RM0.70 175

Q RM2.00 RM2.50 125

R RM4.00 RM5.50 y

S RM6.00 RM9.00 150

T RM2.50 z 120

Table 3

(a) Find the value of

(i) x

(ii) y

(iii) z [3 marks]

(b) Calculate the composite index for the items in the year 1995 based on the year 1990.

[2 marks]



14

(c) The total monthly cost of the items in the year 1990 is RM456. Calculate the

corresponding total monthly cost for the year 1995 [2 marks]

(d) The cost of the items increase by 20% from the year 1995 to the year 2000. Find the

composite index for the year 2000 based on the year 1990. [3 marks]



15

ASSESSMENT

(30 MINUTES)

1. Price indices of a Korean car in the year 2000 and 2002 based on the year 1998 are 116 and 125

respectively. Calculate the price indices for the year 1998 and 2000 if the year 2002 is used as the

base year.

Solution

2. The table below shows the price indices and percentage of usage of four items, J, K, L and M,

which are the the main ingredients in the production of a type of cheese cake.

Items Price index for the year

2004 based on the year 2002

Percentage of usage (%)

J 130 30

K y 20

L 102 40

M 145 10

(a) Calculate

(i) the price of M in the year 2002 if its price in the year 2004 is RM28.13



16

(ii) the price index of J in the year 2004 based on the year 2000 if its price index

in the year 2002 based on the year 2000 is 110.

(b) The composite index number of the cost of choclate cake production for the year 2004 based on

the year 2002 is 126. Calculate

(i) the value of y

(ii) the price of a box of cheese cake in the year 2002 if the corresponding price in the year

2004 is RM24



17

2. (a) Table 4 shows the price index and the weightage of four types of electrical

components in television items in 2000 based on 1996.

Electrical component Price Index Weightage

Capasitor 110 2

Diode 105 m

Resistor 120 4

Transistor 125 n

Table 4

Find the values of m and n given the composite index is 118 and the total weightage

is 10

(b) Table 5 shows the prices of four types of electrical components in television items in 1998 and

2000. Diagram 3 shows the pie chart that reflects the proportion of expenditure of Samsung

Factory in 1998.



Component Price

1998 2000

J RM6.00 RM7.20

K RM5.00 RM5.50

L RM4.00 RM5.20

M RM7.00 RM9.10

Table 5

Dia

(i) Find the comp

(ii) The expenditu

expenditure fo

K


J

gram

osite

re fo

r Sam

120o

80o

18

3

index for the four types of electrical component.

r Samsung Factory in 1998 is RM1200. Find the corresponding

sung Factory in 2000

L70o

K


19

ANSWER

Exercise 11.2

1. 138

2. x = 112, y = 162

Exercise 11.3

1. 150

2. 472

3. x = RM2.09 , y = RM0.61 , z = 133.33

Exercise 11.4

1. 111.5

2. x = 105

3. m = 10

Past Year Question

1. a. x = 125 , y = 2.80 , z = 0.50

b. (i) 129.44 (ii) 2306.94

c. 150

2. a. (i) RM129 (ii) 162

b. (i) x = 125 (ii) RM25

3. a. (i) x = RM0.40 (ii) y = 137.5 (iii) z = RM3.00

b. 140.9

c. RM642.5

d. 169.1

ASSESSMENT

1. 80, 92.8

2. a. (i) RM19.40 (ii) 143

b. (i) y = 158.5 (ii) RM19.05

3. a. m = 1 , n = 3 b. (i) 121.67 (ii) RM1460



20

PANEL OF ADDITIONAL MATHEMATICS MODULESPROGRAM DIDIK CEMERLANG AKADEMIKJABATAN PELAJARAN PULAU PINANG

NO TEACHER’S NAME SCHOOL’S NAME TOPICS1 SUHAIMI BIN MOHD

TABIEESMKA AL-IRSHAD Functions

2 MOHD AMRAN BINWAHAB

SMK SERI BALIK PULAU Functions

3 SABARIAH BINTI DAHLAN SMK SERI MUDA Quadratic Equations4 HANISAH BT ABDUL

RAHIMSMK TAMAN INDERAWASIH Quadratic Functions

5 SHUKOR BIN MD NOOR SMK BAKTI Simultaneous Equations6 NORA BT ROSDIN SMK PAYA KELADI Indices and Logarithms7 ZAWEYAH BT SULAIMAN SMK PTG TOK JAYA Coordinate Geometry8 WANISMAWATI BT

OTHMANSMK AIR ITAM Coordinate Geometry

9 MUMINAH BT ABDULRAHMAN

SMK(P) ST GEORGE Statistics

10 AZIZAH BT ABDULRAHMAN

SMK POKOK SENA Statistics

11 MIMI SHUHAIDA BTPAWAN TEH

SMS TUN SYED SHEHSHAHABUDIN

Circular Measure

12 AZIZAH BT ISMAIL SMK PENANTI Differentiations13 DASIMAH BT AHMAD SMK SERI BALIK PULAU Differentiations14 ZURAINI BT ABDULLAH SMK PTG TOK JAYA Solution of Triangles

15 SITI AISHAH BT ABDULAZIZ

SMK DATUK HJ AHMADBADAWI

Index Number



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