Index Number: Additional Mathematics Tingkatan 4 questions

Section A: objective questions

10 marks

Choose the correct answer. Each question carries 1 mark.

The price of a cup of coffee was RM4.00 in 2018 and RM4.60 in 2020. What is the price index for 2020 based on 2018?

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I = 4.60 ÷ 4.00 × 100 = 115. Dividing the other way (87) uses 2020 as the base.

For the teacher: Remembering, low difficulty, standard 10.1.1

Textbook p. 274

The index number of the number of visitors this year based on last year is 92. This means that the number of visitors

decreased by 8%
increased by 92%
decreased by 92%
increased by 8%

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An index below 100 is a decrease. 100 − 92 = 8, so the decrease is 8%.

For the teacher: Understanding, low difficulty, standard 10.1.1

Textbook p. 274

The index of the number of students in 2019 based on 2014 is 125. If there were 300 students in 2019, how many were there in 2014?

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125 = 300 ÷ Q0 × 100, so Q0 = 300 × 100 ÷ 125 = 240. 375 multiplies by 1.25 instead.

For the teacher: Applying, low difficulty, standard 10.1.2

Textbook p. 274

The price index of an item in 2015 and 2020, both based on 2010, is 125 and 150 respectively. Find the price index in 2020 based on 2015.

275
120
25
187.5

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Both share the base year 2010, so divide: 150 ÷ 125 × 100 = 120.

For the teacher: Applying, low difficulty, standard 10.1.2

Textbook p. 275

The price indices of three items are 90, 120 and 150, with weightages 3, 5 and 2. The composite index is

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(90×3 + 120×5 + 150×2) ÷ 10 = 1 170 ÷ 10 = 117. 120 is the unweighted mean.

For the teacher: Applying, low difficulty, standard 10.2.1

Textbook p. 279

The price indices of four items are 120, 130, 140 and 150. No weightage is given. The composite index is

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With equal weightages: (120+130+140+150) ÷ 4 = 135.

For the teacher: Applying, low difficulty, standard 10.2.1

Textbook p. 280

The price index in 2016 based on 2015 is 130, and in 2015 based on 2012 is 120. Find the price index in 2016 based on 2012.

108.3
156
250
10

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I = 130 × 120 ÷ 100 = 156. Dividing (108.3) is for two indices that share a base year.

For the teacher: Analysing, medium difficulty, standard 10.1.2

Textbook p. 275

Two materials have price indices 120 and 160 in 2021 based on 2019, in the ratio of usage 3 : 1. What is the composite index?

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(120×3 + 160×1) ÷ 4 = 520 ÷ 4 = 130. The unweighted mean (140) ignores the 3 : 1 ratio.

For the teacher: Applying, low difficulty, standard 10.2.2

Textbook p. 283

The price indices of P, Q and R are 100, m and 120 with weightages 2, 3 and 5. The composite index is 113. Find m.

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(200 + 3m + 600) ÷ 10 = 113, so 3m = 330 and m = 110.

For the teacher: Analysing, medium difficulty, standard 10.2.2

Textbook p. 281

The composite index of production cost in 2020 based on 2012 is 140. If the cost in 2012 was RM85 000, what was the cost in 2020?

RM60 714
RM85 140
RM119 000
RM140 000

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Cost in 2020 = 85 000 × 140 ÷ 100 = RM119 000. Dividing gives RM60 714.

For the teacher: Applying, low difficulty, standard 10.2.2

Textbook p. 281

Section B: structured questions

30 marks

Answer all questions. Show your working.

The price per kg of three ingredients P, Q and R used in a biscuit in 2015 and 2019, and their weightages, are given below.

[3 marks] (a)P: RM4.00 to RM5.00 (weightage 5). Q: RM2.50 to RM2.00 (weightage 3). R: RM6.00 to RM7.80 (weightage 2). Calculate the price index of each ingredient in 2019 based on 2015.

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P: 5.00 ÷ 4.00 × 100 = 125 [1]1
Q: 2.00 ÷ 2.50 × 100 = 80 [1]1
R: 7.80 ÷ 6.00 × 100 = 130 [1]1

Tick each point you got.

[3 marks] (b)Find the composite index and interpret it.

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(125×5 + 80×3 + 130×2) ÷ 10 [1]1
= 112.5 [1]1
Overall cost increased by 12.5% from 2015 to 2019 [1]1

Tick each point you got.

[2 marks] (c)The cost of the biscuit ingredients in 2015 was RM240. Find the cost in 2019.

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240 × 112.5 ÷ 100 [1]1
= RM270 [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 10.2.2

Textbook p. 281

The price index of an item in 2016 based on 2012 is 120. The price index in 2020 based on 2016 is 110. The price of the item in 2020 was RM52.80.

[2 marks] (a)Find the price index in 2020 based on 2012.

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120 × 110 ÷ 100 [1]1
= 132 [1]1

Tick each point you got.

[2 marks] (b)Find the price of the item in 2012.

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52.80 ÷ 132 × 100 [1]1
= RM40 [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 10.1.2

Textbook p. 275

The student entry indices of three subjects in a college in 2019 based on 2015 are given below, with their weightages.

[3 marks] (a)Subject A: index 130, weightage 3. Subject B: index m, weightage 5. Subject C: index 115, weightage 2. The composite index is 118. Find m.

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(390 + 5m + 230) ÷ 10 = 118 [1]1
5m = 1 180 − 620 [1]1
m = 112 [1]1

Tick each point you got.

[1 mark] (b)State what the weightage tells you.

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How important each subject is in the composite index [1]1

Tick each point you got.

For the teacher: Analysing, high difficulty, standard 10.2.2

Textbook p. 281

A park had 2.5 million visitors in 2015. The number rose by 20% from 2015 to 2018. The rate of increase from 2018 to 2020 was the same.

[2 marks] (a)Find the number of visitors in 2018.

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2.5 × 120 ÷ 100 [1]1
= 3.0 million [1]1

Tick each point you got.

[2 marks] (b)Find the number of visitors in 2020.

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3.0 × 120 ÷ 100 [1]1
= 3.6 million [1]1

Tick each point you got.

[1 mark] (c)Find the index for 2020 based on 2015.

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3.6 ÷ 2.5 × 100 = 144 [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 10.1.3

Textbook p. 276

Two materials A and B are used to make a cleaner in the ratio 3 : 2. Their price indices in 2021 based on 2019 are 125 and 140. From 2021 to 2023, the price of A falls by 20% and the price of B rises by 10%, so the index of each is changed by that percentage.

[2 marks] (a)Find the composite index in 2021 based on 2019.

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(125×3 + 140×2) ÷ 5 [1]1
= 131 [1]1

Tick each point you got.

[3 marks] (b)Find the composite index in 2023 based on 2019.

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Index of A = 125 × 0.8 = 100 [1]1
Index of B = 140 × 1.1 = 154 [1]1
(100×3 + 154×2) ÷ 5 = 121.6 [1]1

Tick each point you got.

[2 marks] (c)The cost in 2019 was RM12.50. Find the cost in 2023.

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12.50 × 121.6 ÷ 100 [1]1
= RM15.20 [1]1

Tick each point you got.

For the teacher: Evaluating, medium difficulty, standard 10.2.2

Textbook p. 284

The price of a bicycle was RM400 in 2018 and RM460 in 2021.

[1 mark] (a)Find the index for 2021 based on 2018.

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460 ÷ 400 × 100 = 115 [1]1

Tick each point you got.

[1 mark] (b)Interpret your answer.

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The price rose by 15% [1]1

Tick each point you got.

For the teacher: Understanding, low difficulty, standard 10.1.1

Textbook p. 274

Section A: objective questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Section B: structured questions

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16