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Mathematics questions, chapter 1
Nama / NameKelas / ClassTarikh / Date

Indices

44 marks. Use Practice to check each answer as you go, or Exam to answer everything first. Show your working for Section B.

Section A: objective questions

12 marks
Choose the correct answer. Each question carries 1 mark.
1

Question 1

In (−3)5, the index is ______
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C
In an, a is the base and n the index, so the index is 5 and the base is −3. −15 would be (−3) × 5.
For the teacher: Remembering, low difficulty, standard 1.1.1
Textbook p. 2
2

Question 2

Which is the index form of 0.3 × 0.3 × 0.3 × 0.3 × 0.3?
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B
Five factors of 0.3 give base 0.3 and index 5. 0.3 × 5 is a multiplication, not a repeated one.
For the teacher: Understanding, low difficulty, standard 1.1.1
Textbook p. 2
3

Question 3

Given 81 = 9m and 81 = 3n. What is the value of m + n?
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D
81 = 92 so m = 2 and 81 = 34 so n = 4, giving m + n = 6. 8 comes from 2 × 4.
For the teacher: Applying, medium difficulty, standard 1.1.2
Textbook p. 4
4

Question 4

Simplify 2k2 × 4k3.
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A
Multiply the coefficients 2 × 4 = 8 and add the indices 2 + 3 = 5. Multiplying the indices (6) or adding the coefficients (6) are common slips.
For the teacher: Applying, low difficulty, standard 1.2.1
Textbook p. 7
5

Question 5

Simplify 25x2y3 ÷ 5xy.
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D
25 ÷ 5 = 5, x2−1 = x, y3−1 = y2. 20 comes from subtracting the coefficients.
For the teacher: Applying, low difficulty, standard 1.2.2
Textbook p. 10
6

Question 6

Simplify (2x3)4.
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B
Every factor in the bracket is raised to the power 4: 24 = 16 and x3×4 = x12. 8 is 2 × 4; x7 adds the indices.
For the teacher: Applying, low difficulty, standard 1.2.3
Textbook p. 11
7

Question 7

2a−4 is written in positive index form as ______
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C
Only a has the negative index, so a−4 = 1/a4 and the 2 stays on top. 1/(2a4) wrongly moves the 2 as well.
For the teacher: Understanding, low difficulty, standard 1.2.5
Textbook p. 15
8

Question 8

Calculate 163/4.
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A
163/4 = (4√16)3 = 23 = 8. 12 is 16 × 3/4.
For the teacher: Applying, low difficulty, standard 1.2.6
Textbook p. 17
9

Question 9

Find the value of 50 + 2−3.
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C
50 = 1 and 2−3 = 1/8, so the sum is 1 + 1/8 = 9/8. 50 is not 0, and 2−3 is not −6 or −8.
For the teacher: Applying, low difficulty, standard 1.2.5
Textbook p. 14
10

Question 10

Find x if 2x × 4x+1 = 211.
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D
4x+1 = 22x+2, so x + 2x + 2 = 11 and x = 3. Without changing the base the indices cannot be added.
For the teacher: Analysing, high difficulty, standard 1.2.9
Textbook p. 22
11

Question 11

Which statement is true?
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B
The cube root of 8 is 2. 23 × 22 = 25 (the base does not change), (32)3 = 36, and 5−2 = 1/25.
For the teacher: Evaluating, low difficulty, standard 1.2.4
Textbook p. 11
12

Question 12

Calculate 32−2/5.
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A
321/5 = 2, so 32−2/5 = 1/22 = 1/4. 1/16 comes from using the 5th root as the power 4.
For the teacher: Applying, medium difficulty, standard 1.2.6
Textbook p. 18

Section B: structured questions

32 marks
Answer all questions. Show your working.
13

Question 13

Simplify each expression.
[1 mark] (a)m3n2 × m4n5
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Tick each point you got.
[2 marks] (b)18x5y3 ÷ 6x2y
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Tick each point you got.
[2 marks] (c)(3m2n3)3 ÷ 6m3n
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Tick each point you got.
For the teacher: Applying, low difficulty, standard 1.2.1
Textbook p. 9
14

Question 14

Write in positive index form, then give the value.
[1 mark] (a)3m−4 (positive index form only)
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Tick each point you got.
[2 marks] (b)(25)−3
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Tick each point you got.
[2 marks] (c)32 × 34 ÷ 38
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Tick each point you got.
For the teacher: Understanding, low difficulty, standard 1.2.5
Textbook p. 15
15

Question 15

Calculate without a calculator.
[1 mark] (a)1251/3
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Tick each point you got.
[2 marks] (b)163/4
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Tick each point you got.
[2 marks] (c)27−2/3
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Tick each point you got.
For the teacher: Applying, low difficulty, standard 1.2.6
Textbook p. 17
16

Question 16

Simplify. Give each answer in positive indices.
[2 marks] (a)(8a6)1/3 × a−2
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Tick each point you got.
[3 marks] (b)(4x3y−2)2 ÷ (2x2y)3
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Tick each point you got.
For the teacher: Applying, medium difficulty, standard 1.2.7
Textbook p. 20
17

Question 17

Given the equation 3x × 9x−1 ÷ 34 = 1.
[3 marks] (a)Write all terms with base 3 and find the value of x.
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Tick each point you got.
[1 mark] (b)Show that your value satisfies the equation.
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Tick each point you got.
For the teacher: Analysing, medium difficulty, standard 1.2.9
Textbook p. 22
18

Question 18

Calculate the possible values of x for the equation 2x2 × 23x = 210.
[4 marks] (a)Form an equation in x and solve it.
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Tick each point you got.
For the teacher: Analysing, high difficulty, standard 1.2.9
Textbook p. 23
19

Question 19

A machine bought for RM60 000 loses value. Its value after n years is RM60 000 × (45)n.
[2 marks] (a)Calculate its value after 3 years.
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Tick each point you got.
[2 marks] (b)Calculate its value after 5 years, to the nearest RM.
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Tick each point you got.
For the teacher: Applying, medium difficulty, standard 1.2.9
Textbook p. 26