11[anal add math cd]

1Additional Mathematics SPM Chapter 11

Penerbitan Pelangi Sdn. Bhd.

1. Index number of average temperature for the year 2005 based on the year 2000

= Temperature in the year 2005Temperature in the year 2000 100

= 3530 100= 116.7

2. Index number of books sold in the year 2006 based on the year 2005= Volume of books in the year 2006Volume of books in the year 2005 100

= 10.610.7 100= 99.1

3. Price index for the year 2000 based on the year 1900= Income for the year 2000Income for the year 1900 100

= 10 0006000 100= 166.7

4. (a) Index number in February based on January

= Volume of rain fall in FebruaryVolume of rain fall in January 100

= 1510 100

= 150(b) Index number in March based on January = Volume of rain fall in MarchVolume of rain fall in January 100

= 510 100 = 50

5. (a) Price index for the year 2007 based on the year 2000

= Price in the year 2007Price in the year 2000 100

= 2.001.20 100 = 166.7(b) Price index for the year 2005 based on the year

2007 = Price in the year 2005Price in the year 2007 100

= 1.502.00 100 = 75

6. Index number for the year 2006 based on the year 2005 = 120.5

Number of cars sold in the year 2006Number of cars sold in the year 2005

100 = 120.5

x10 000 100 = 120.5 x = 120.5 100 = 12 050

7. Price index for the year 2006 based on the year 2001 = 85Price in the year 2006Price in the year 2001 100 = 85

4y 100 = 85 y = 4 10085 = 4.71

8. Index number for houses sold in the year 2005 based on the year 2000 = 120Number of houses sold in the year 2005Number of houses sold in the year 2000 100

= 120

CHAPTER

11 Index Number

2 Additional Mathematics SPM Chapter 11


Number of houses sold in the year 2005= 120100 10 200= 12 240

9. Price index in the year 2003 based on the year 2000 = 130

Price in the year 2003Price in the year 2000 100 = 130

Price in the year 200312 100 = 130

Price in the year 2003 = 130 12100 = RM15.60

10. Price index in the year 2006 based on the year 2005 = 110


125Price in the year 2005 100 = 110


11. Composite index = wiIi wi

= (2 120) + (3 115) + (1 130)

+ (3 110) + (1 126)2 + 3 + 1 + 3 + 1 = 117.1

12. (a) Price index for A = 10080 100 = 125

Price index for B = 12094 100 = 127.7

Price index for C = 150130 100 = 115.4(b) Composite index in the year 2006 based on the

year 2005

= wiIi wi

= (2 125) + (3 127.7) + (1 115.4)2 + 3 + 1 = 124.8

13. Composite index = 103(4 110) + 90x + (6 120)4 + x + 6 = 103

440 + 90x + 720 = 103(10 + x) 1160 + 90x = 1030 + 103x 103x 90x = 1160 1030 13x = 130 x = 10

14. (a) Composite price index in the year 2002 based on the year 2005 = 122

(2 100) + 4x + (3 130) + (1 150)2 + 4 + 3 + 1 = 122

4x + 740 = 122(10) = 1220 4x = 480 x = 120(b) Price index of item C for the year 2002 based on

the year 2005 = 130 Price in the year 2002Price in the year 2005 100 = 130

2000Price in the year 2005 100 = 130


15. (a) Composite index for the year 2002 based on the year 2000

= (4 120) + (2 110) + (3 130) + (1 150)4 + 2 + 3 + 1 = 124(b) Price index for food in the year 2002 based on

the year 2000 = 120


Price in the year 2002600 100 = 120 Price in the year 2002 = RM720

(c) Composite index for the year 2002 based on the year 2000 = 124

Average monthly expenditure

for the year 2002Average monthly expenditure for the year 2000

100 = 124

Average monthly expenditure

for the year 2002600 + 100 + 400 + 500 100 = 124



Average monthly expenditure for the year 2002 = 124100 1600 = RM1984

16. (a) Composite index number for the year 2001 based on the year 2000 = 115

7 + m + 2 + 43 + 4 + 5 + 8 100 = 115

13 + m = 115100 20 = 23 m = 10(b) Composite index for the year 2002 based on the

year 2000 = 12 + 5 + 6 + 43 + 4 + 5 + 8 100

= 2720 100 = 135

17. (a) Price index of A for the year 1995 based on the year 1990

= 125 110% = 137.5 Price index of B for the year 1995 based on the

year 1990 = 130 105% = 136.5 Price index of C for the year 1995 based on the

year 1990 = 160(b) The composite index for the year 1995 based on

the year 1990

= wiIi wi

= (2 137.5) + (1 136.5) + (3 160)2 + 1 + 3 = 148.6

18. Given I 2006, 2005 = 120

P2006 P2005 100 = 120

P2006 P2005 = 120100

I 2006, 2002 = 130P2006 P2002

100 = 130

P2006 P2002 = 130100

The composite index for the year 2005 based on the year 2002 = P2005 P2002

100

= P2005 P2006 P2006 P2002

100

= 100120 130100 100

= 108.3

1. (a) Index number of P in the year 2006 based on the year 2003 = 110

t12 100 = 110 t = 110 12100 = 13.20(b) Index number of Q in the year 2006 based on the

year 2003 = Index number of R in the year 2006 based on

the year 2003 10 yx 100 =

1510 100 10 = 140 yx =

140100 y = 75 x ......................1 Sum of Q for the years 2003 and 2006

= 12 x + y = 12 ..............................2 Substitute 1 into 2, x + 75 x = 12

12x5 = 12

x = 12 512 = 5 Substitute x = 5 into 2, 5 + y = 12 y = 7(c) (i) Given the composite index in the year 2006

based on the year 2003 = 130 Cost price in the year 2006Cost price in the year 2003 100 = 130

Cost price in the year 20061000 100 = 130 Cost price in the year 2006 = RM1300



(ii) Composite index for the year 2006 based on the year 2003 = 130

(2 110) + (n yx 100)

+ (1 1510 100)2 + n + 1 = 130

220 + 1n 75 1002 + 150 = 130(3 + n) 140n + 370 = 390 + 130n 10n = 390 370 n = 2

2. (a) x1.80 100 = 112 x = 112 1.80100 = 2.02

y = 3.002.40 100 = 125

1.50z 100 = 125 z = 1.50 100125 = 1.20(b) Composite index for the year 2002 based on the

year 2000

= wiIi wi

= (5 112) + (10 125) + (15 125)

+ (20 120)5 + 10 + 15 + 20 = 121.7

(c) Total monthly cost in the year 2002Total monthly cost in the year 2000

100 = 121.7

Total monthly cost in the year 2002 = 121.7 250 000100 = RM304 250

(d) Composite index for the year 2004 based on the year 2000

= 125% 121.7 = 152.1

3. (a) (i) I2010, 2000 = 140

P2010P2000 = 140100

I2009, 2000 = 120

P2009P2000 = 120100

\ I2010, 2009 = P2010P2009

100

= P2010P2000 P2000P2009

100

= 140100 100120 100

= 116.7

(ii) P2009P2000 100 = 120

8P2000 100 = 120

P2000 = 8 100120 = RM6.67 The price in the year 2000 is RM6.67. P2010P2009

100 = 116.7

P20108 100 = 116.7

P2010 = 8 116.7100 = RM9.34 The price in the year 2010 is RM9.34.

(b) (i) I2008, 2000 = 140

wiIi wi = 140

1 130 + 2 120 + 2y1 + 2 + 2 = 140 370 + 2y = 140 5 2y = 700 370 = 330 y = 165

(ii) I2008, 2000 = 140

P2008P2000 100 = 140

P200825 100 = 140

P2008 = 140 25100 = 35 The cost of the medicine made in the year

2008 is RM35.



4. (a) (i) Price of A in the year 2005Price of A in the year 2000 100 = 150

500Price of A in the year 2000 100 = 150

Price of A in the year 2000 = 500 100150 = RM333.33 (ii) Price index of B in the year 2005 based on

the year 2003 = P2005 P2003

100

= P2005 P2000 P2000 P2003

100

= 1 130100 2 1100120 2 100

= 108.3

(b) (i) Composite index for the year 2005 based on the year 2000

= wiIi wi = 130

(2 150) + (2 130) + (1 m)

+ (5 125)2 + 2 + 1 + 5 = 130 1185 + m = 1300 m = 1300 1185 = 115

(ii) Price of bread in the

year 2005Price of bread in the year 2000

100 = 130

Price of bread in the year 2005 = 130 5100 = RM6.50

1. (a) x20 100 = 120 x = 20100 120 = 24

13y 100 = 130

y = 13 100130 = 10

z = 1812 100 = 150

(b) Price for D in the year 2005Price for D in the year 2000 100 = 200

3000Price for D in the year 2000 100 = 200

Price for D in the year 2000 = 3000 100200 = RM1500

(c) (i) Composite index for the year 2005 based on the year 2000

= wiIi wi

= (2 120) + (4 130) + (1 150)

+ (3 200)2 + 4 + 1 + 3 = 151

(ii) Composite index for the year 2006 based on the year 2000

= 151 110% = 166.1

2. (a) The composite index for the year 2006 based on the year 2000 = 120

wiIi wi = 120

(2 110) + (2 115) + (m + 1) 120

+ (2 125) + m 1302 + 2 + (m + 1) + 2 + m = 120

820 + 250m7 + 2m = 120 820 + 250m = 120(7 + 2m) = 840 + 240m 250m 240m = 840 820 10m = 20 m = 2

(b) Price for A in the year 2006Price for A in the year 2000 100 = 110

Price for A in the year 2006 = 110 200100 = RM220(c) Price index for B in the year 2000 based on the

year 2006 = Price in the year 2000Price in the year 2006 100

= 100115 100 = 86.96



3. (a) Price index for item A in the year 2005 based on the year 2000

= 2010 100 = 200 Price index for item B in the year 2005 based on

the year 2000 = 3020 100 = 150 Price index for item C in the year 2005 based on

the year 2000 = 1010 100 = 100(b) (i) Composite index for the year 2005 based on

the year 2000

= wiIi wi

= (1 200) + (2 150) + (3 100)1 + 2 + 3 = 133.3

(ii) Price in the year 2005Price in the year 2000 100 = 150

30Price in the year 2000 100 = 150

Price in the year 2000 = 30 100150 = RM20

4. (a) (i) Expenditure for the

year 2003Expenditure for the year 2000

100 = 120

Expenditure on item A for the year 2003 = 120 1300100 = RM1560

(ii) Expenditure for the

year 2003Expenditure for the year 2000

100 = 135

1500Expenditure for the year 2000

100 = 135

Expenditure on item C for the year 2000 = 1500 100135 = RM1111.11

(b) (i) Composite index for the year 2003 based on the year 2000

= wiIi wi

= 116

(2 120) + 3x + (1 135)

+ (4 110)2 + 3 + 1 + 4 = 116 815 + 3x = 1160 3x = 345 x = 115

(ii) Total expenditure for

the year 2003Total expenditure forthe year 2000

100 = 116

Total expenditure for the year 2003 = 116 8000100 = RM9280(c) The composite index for the year 2005 based on

the year 2000 = 120% 116 = 139.2

5. (a) x1.10 100 = 130 x = 130 1.10100 = 1.43

1.80y 100 = 125 y = 1.80 100125 = 1.44(b) Price index for item Q in the year 2004 based on

the year 2001 = 1.200.80 100 = 150 Price index for item S in the year 2004 based on

the year 2001 = 1.401.20 100 = 116.7(c) Composite price index for the year 2004 based

on the year 2001

= wiIi wi

= (1 130) + (4 150) + (3 125) + (2 116.7)1 + 4 + 3 + 2 = 133.8



(d) Total cost of production

in the year 2004Total cost of production in the year 2001

100 = 133.8

Total cost of production in the year 2004 = 133.8 1.2100 = RM1.606 millions(e) The composite index for the year 2005 based on

the year 2001 = 130% 133.8 = 173.9

6. (a) Composite index for A and B = 3403 100x + 120yx + y =

3403 300x + 360y = 340(x + y) = 340x + 340y 40x = 20y y = 2x x : y = 1 : 2

Composite index for A and C = 1652 100x + 80zx + z =

1652 200x + 160z = 165x + 165z 35x = 5z z = 7x x : z = 1 : 7 Therefore, x : y : z = 1 : 2 : 7.(b) Composite index in the year 2006 based on the

year 2001 = (1 100) + (2 120) + (7 80)1 + 2 + 7 = 90

(c) Price of B in the year 2006Price of B in the year 2001 100 = 120

450Price of B in the year 2001 100 = 120

Price of B in the year 2001 = 450 100120 = RM375(d) Composite index for the year 2007 based on the

year 2001 = 110% 90 = 99


Price in the year 2006Price in the year 2007


Price in the year 200612 000 99100 100 = 90

Price in the year 2006 = 90 12 00099 = RM10 909.09

1. (a) (i) 10 + 2 + x + 44 + 5 + 3 + 8 100 = 115

16 + x20 100 = 115

16 + x = 115 20100 = 23 x = 7

(ii) 5 + 6 + 12 + 44 + 5 + 3 + 8 100 = 2720 100

= 135

(b)

CommodityPrice index for the year 2001 based on the

year 1999Weightage

A 54 100 = 125 1

B 65 100 = 120 2

C 123 100 = 400 3

D 48 100 = 50 4

Composite index

= (125 1) + (120 2) + (400 3)

+ (50 4)1 + 2 + 3 + 4 = 176.5



2. (a)

Brand of computers

Price index for the year 1998 based on

the year 1995Weightage

A 50004000 100 = 125 2

B 60005000 100 = 120 3

C 40002500 100 = 160 1

Composite price index = (125 2) + (120 3) + (160 1)2 + 3 + 1 = 128.3

(b) 60005000 + 6000 + 4000 360 = 144

(c) x4000 100 = 50004000 100

x = 5000 Therefore, the selling price for brand A for the

year 2000 is RM5000.

3. (a) x 66 = 21x 44 2

x 66 = x 42

2x 12 = 6x 24 4x = 12 x = 3(b) 64 100 = 150

4. (a) Substained for others at the pie chart = 80 The percentage for others = 80360 100% = 22.22%(b) x500 100 = 105

x = 105 500100 = 525 Therefore, the expenditure for house rental in the

year 1995 is RM525.

(c) Composite price index = 110 160 + 105 80 + 120 40 + 115 80360 = 111.1

5. (a) Composite index for 2001 based on 1999

= 112 2 + 110 1 + 108 1 + 120 2

+ 114 2 + 118 32 + 1 + 1 + 2 + 2 + 3 = 114.9

(b) For electricity:

P2000P1999

100 = 110

1020P1999 100 = 110

P1999 = 1020 100110

= 927.3

P2001P1999

100 = 112

P2001927.3 100 = 112

P2001 = 112 927.3100

= 1038.58 Therefore, the electricity bill for the year 2001 is

RM1038.58.(c) For others:

P2001P1999

100 = 118

10 050P1999 100 = 118

P1999 = 10 050 100118

= 8516.95

P2000P1999

100 = 112

P20008516.95 100 = 112

P2000 = 112 8516.95100

= 9538.98 The increase from the year 2000 to 2001 = 10 050 9538.98 = RM511.02



6. (a) P1992 = RM50 P1993 = 110% 50 = RM55 Price index for the year 1993 based on 1992 = 5550 100 = 110

(b) Price index for the year 1992 based on 1993 = 5055 100 = 90.91

(c) Price for 1994 = 55 110% = RM60.50

11[anal add math cd]

Documents