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WJEC GCSE Maths

Topic questions Pure mathematics Indices

Indices

46 questions · 171 marks · about 4 hours

Indices questions

Unit 1: Non-calculator June 2025 Foundation tier, Question 12 3 marks

(a)

Calculate 7² × 2³.

[2]

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(b)

Write down the next two numbers in the following sequence.

$Question 12, shown as an image$

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Unit 1: Non-calculator June 2025 Higher tier, Question 15 5 marks

(a)

(a)(i)

$Question 15, shown as an image$

$Question 15, shown as an image$

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(a)(ii)

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(b)

Figure for question 15

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Unit 1: Non-calculator November 2024 Higher tier, Question 14 3 marks

$Question 14, shown as an image$

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Unit 2: Calculator-allowed November 2024 Higher tier, Question 17 1 mark

Figure for question 17

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Unit 1: Non-calculator June 2024 Intermediate tier, Question 16, also on the Higher paper 3 marks

(a)

Express 0·0057 in standard form.

[1]

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$Question 16, shown as an image$

Give your answer in standard form.

[2]

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Unit 2: Calculator-allowed June 2024 Intermediate tier, Question 11 4 marks

(a)

$Question 11, shown as an image$

[2]

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(b)

What is the greatest integer value of n if 2n < 17?

[1]

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(c)

What is the least integer value of n if 2ⁿ > 125?

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Unit 1: Non-calculator June 2024 Higher tier, Question 7, also on the Intermediate paper 3 marks

(a)

Express 0·0057 in standard form.

[1]

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$Question 7, shown as an image$

Give your answer in standard form.

[2]

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Unit 2: Calculator-allowed June 2024 Higher tier, Question 11 1 mark

$Question 11, shown as an image$

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Unit 1: Non-calculator November 2023 Higher tier, Question 16 7 marks

(a)

Circle the correct answer for each of the following statements.

(a)(i)

$Question 16, shown as an image$

$Question 16, shown as an image$

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(a)(ii)

$Question 16, shown as an image$

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(b)

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(c)

Figure for question 16

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(d)

Give an example of an irrational number that lies between 6 and 7.

My example of an irrational number is_........

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Unit 2: Calculator-allowed November 2023 Higher tier, Question 13 1 mark

Figure for question 13

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Unit 1: Non-calculator June 2023 Foundation tier, Question 19 6 marks

(a)

Express 48 as a percentage of 400.

[2]

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(b)

Share £45 in the ratio 8: 1.

£_........ and £_........

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(c)

Express 1 maths symbol $fraction$ as a single fraction in the form $fraction$ , where a and b are integers.

[2]

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Unit 1: Non-calculator June 2023 Intermediate tier, Question 19 4 marks

(a)

Express 0·0076 in standard form.

[1]

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(b)

Calculate the value of (3 × 10¹⁷) × (2 × 10⁻¹²).

Give your answer in standard form.

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(c)

Calculate the value of (2·3 × 10⁴) + (5 × 10³).

Give your answer in standard form.

[2]

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Unit 2: Calculator-allowed June 2023 Intermediate tier, Question 2 4 marks

(a)

Which one of the following fractions can be written as a recurring decimal?

Circle your answer.

$Question 2, shown as an image$

[1]

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(b)

Which three numbers from the list below are prime numbers?

27 31 35 39 43 47 51 55

The three prime numbers are:

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(c)

Figure for question 2

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Unit 1: Non-calculator June 2023 Higher tier, Question 17 5 marks

(a)

$Question 17, shown as an image$

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(b)

(b)(i)

Figure for question 17

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(b)(ii)

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(b)(iii)

Write down an integer value of x that is greater than 5, for which $fraction$ and $fraction$

are both rational.

[1]

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Unit 1: Non-calculator November 2022 Intermediate tier, Question 20 4 marks

(a)

$Question 20, shown as an image$

[2]

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Unit 1: Non-calculator November 2022 Higher tier, Question 7 4 marks

(a)

$Question 7, shown as an image$

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Unit 1: Non-calculator November 2022 Higher tier, Question 15 4 marks

(a)

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$Question 15, shown as an image$

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Unit 1: Non-calculator June 2022 Intermediate tier, Question 17, also on the Higher paper 2 marks

Circle the correct answer for each of the following statements.

(a)

7·2 m³ is equal to

720 cm³ 72 000 cm³ 7·2 maths symbol 10⁵cm³ 7·2 10³cm³ 7·2 10⁶cm³

[1]

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$Question 17, shown as an image$

$Question 17, shown as an image$

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Unit 1: Non-calculator June 2022 Higher tier, Question 7, also on the Intermediate paper 2 marks

Circle the correct answer for each of the following statements.

(a)

7·2 m³ is equal to

720 cm³ 72 000 cm³ 7·2 maths symbol 10⁵cm³ 7·2 10³cm³ 7·2 10⁶cm³

[1]

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$Question 7, shown as an image$

$Question 7, shown as an image$

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Unit 1: Non-calculator June 2022 Higher tier, Question 14 2 marks

$Question 14, shown as an image$

Simplify your answer.

[2]

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Unit 1: Non-calculator November 2021 Intermediate tier, Question 15, also on the Higher paper 3 marks

(a)

Express 0·0058 in standard form.

[1]

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$Question 15, shown as an image$

Give your answer in standard form.

[2]

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Unit 1: Non-calculator November 2021 Higher tier, Question 6, also on the Intermediate paper 3 marks

(a)

Express 0·0058 in standard form.

[1]

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$Question 6, shown as an image$

Give your answer in standard form.

[2]

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Unit 1: Non-calculator November 2021 Higher tier, Question 14 5 marks

(a)

$Question 14, shown as an image$

[2]

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$Question 14, shown as an image$

Express your answer as a fraction.

[3]

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Unit 1: Non-calculator November 2020 Foundation tier, Question 15 5 marks

Calculate each of the following.

(a)

3³ × 10²

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(b)

0·4 × 0·2

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$Question 15, shown as an image$

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Unit 1: Non-calculator November 2020 Higher tier, Question 11 2 marks

(a)

Figure for question 11

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(b)

Figure for question 11

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Unit 2: Calculator-allowed November 2020 Higher tier, Question 11 2 marks

Write 16¹⁰⁰ in the form 2ⁿ.

[2]

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Unit 1: Non-calculator November 2019 Intermediate tier, Question 15, also on the Higher paper 3 marks

Circle the correct answer for each of the following.

(a)

81 =

$Question 15, shown as an image$

[1]

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(b)

2·1⁵ =

32·5 10·5 40·84101 30·84101 32·1

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$Question 15, shown as an image$

6·48 3·6 4·32 3·3 2·16

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Unit 1: Non-calculator November 2019 Higher tier, Question 4, also on the Intermediate paper 3 marks

Circle the correct answer for each of the following.

(a)

81 =

$Question 4, shown as an image$

[1]

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(b)

2·1⁵ =

32·5 10·5 40·84101 30·84101 32·1

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$Question 4, shown as an image$

6·48 3·6 4·32 3·3 2·16

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Unit 1: Non-calculator November 2019 Higher tier, Question 14 3 marks

(a)

[2]

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(b)

Circle the correct answer for the following statement.

$Question 14, shown as an image$

$Question 14, shown as an image$

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Unit 1: Non-calculator June 2019 Higher tier, Question 13 4 marks

(a)

Figure for question 13

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$Question 13, shown as an image$

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Unit 1: Non-calculator November 2018 Intermediate tier, Question 15, also on the Higher paper 6 marks

(a)

Circle the correct answer for each of the following statements.

(a)(i)

$Question 15, shown as an image$

$Question 15, shown as an image$

[1]

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(a)(ii)

Figure for question 15

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(a)(iii)

$Question 15, shown as an image$

35² 15² 15 35 15⁴

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(a)(iv)

3^{– 4} is equal to

$Question 15, shown as an image$

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Unit 1: Non-calculator November 2018 Higher tier, Question 6, also on the Intermediate paper 6 marks

(a)

Circle the correct answer for each of the following statements.

(a)(i)

$Question 6, shown as an image$

$Question 6, shown as an image$

[1]

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(a)(ii)

Figure for question 6

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(a)(iii)

$Question 6, shown as an image$

35² 15² 15 35 15⁴

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(a)(iv)

3^{– 4} is equal to

$Question 6, shown as an image$

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$Question 6, shown as an image$

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Unit 1: Non-calculator November 2018 Higher tier, Question 15 8 marks

(a)

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(b)

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$Question 15, shown as an image$

$Question 15, shown as an image$

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Unit 1: Non-calculator June 2018 Intermediate tier, Question 14, also on the Higher paper 4 marks

(a)

$Question 14, shown as an image$

[2]

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$Question 14, shown as an image$

Give your answer in standard form.

[2]

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Unit 1: Non-calculator June 2018 Higher tier, Question 5, also on the Intermediate paper 4 marks

(a)

$Question 5, shown as an image$

[2]

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$Question 5, shown as an image$

Give your answer in standard form.

[2]

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Unit 1: Non-calculator June 2018 Higher tier, Question 14 2 marks

Circle the correct answer for each of the following statements.

$Question 14, shown as an image$

$Question 14, shown as an image$

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$Question 14, shown as an image$

$Question 14, shown as an image$

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Unit 1: Non-calculator November 2017 Intermediate tier, Question 1 7 marks

Calculate each of the following.

(a)

3⁴ × 10³

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$Question 1, shown as an image$

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(c)

5.6 − 3.82

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(d)

$Question 1, shown as an image$

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(e)

0.2 × 0.3

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Unit 1: Non-calculator November 2017 Intermediate tier, Question 13, also on the Higher paper 4 marks

(a)

Express 0·000 42 in standard form.

[1]

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$Question 13, shown as an image$

Give your answer in standard form.

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$Question 13, shown as an image$

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Unit 2: Calculator-allowed November 2017 Intermediate tier, Question 10, also on the Higher paper 3 marks

Simplify each of the following and circle the correct answer in each case.

(a)

6p⁶ × 3p³

$Question 10, shown as an image$

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(b)

3·4g⁸ ÷ 13·6g²

$Question 10, shown as an image$

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$Question 10, shown as an image$

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Unit 1: Non-calculator November 2017 Higher tier, Question 5, also on the Intermediate paper 4 marks

(a)

Express 0·000 42 in standard form.

[1]

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$Question 5, shown as an image$

Give your answer in standard form.

[1]

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$Question 5, shown as an image$

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Unit 1: Non-calculator November 2017 Higher tier, Question 15 4 marks

(a)

[2]

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Unit 2: Calculator-allowed November 2017 Higher tier, Question 1, also on the Intermediate paper 3 marks

Simplify each of the following and circle the correct answer in each case.

(a)

6p⁶ × 3p³

$Question 1, shown as an image$

[1]

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(b)

3·4g⁸ ÷ 13·6g²

$Question 1, shown as an image$

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$Question 1, shown as an image$

$Question 1, shown as an image$

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Unit 1: Non-calculator June 2017 Intermediate tier, Question 12, also on the Higher paper 4 marks

(a)

Express 700 as a product of its prime factors in index form.

[3]

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(b)

$Question 12, shown as an image$

(b)

Explain how this tells you that 33 554 432 is not a square number.

[1]

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Unit 1: Non-calculator June 2017 Higher tier, Question 3, also on the Intermediate paper 4 marks

(a)

Express 700 as a product of its prime factors in index form.

[3]

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(b)

$Question 3, shown as an image$

(b)

Explain how this tells you that 33 554 432 is not a square number.

[1]

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Unit 1: Non-calculator June 2017 Higher tier, Question 11 6 marks

(a)

$Question 11, shown as an image$

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(b)

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Unit 2: Calculator-allowed June 2017 Higher tier, Question 17 1 mark

Figure for question 17

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