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Powers and roots: AQA GCSE Maths questions

Every AQA GCSE Maths exam question on N6 Powers and roots, 2017–2025, with its mark scheme and examiner’s report.

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1,304 questions

  1. Q13

    June 2025 · Paper 1H

    The whole paper ↗
    June 2025 Paper 1H, question 13: c and d are consecutive cube numbers, where c < 4.53 < d Work out the value of d – c Answer
  2. Q1

    November 2024 · Paper 1H

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    November 2024 Paper 1H, question 1: Work out the value of 1.52 Answer
  3. Q3

    June 2023 · Paper 1H

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    June 2023 Paper 1H, question 3: Work out the value of       2 3 2 Give your answer as a mixed number. Answer
  4. Q7

    November 2022 · Paper 2H

    The whole paper ↗
    November 2022 Paper 2H, question 7: (a) k is a whole number between 40 and 50 The cube root of k is 3, to the nearest whole number. Work out the largest possible value of k. Answer 7 (b) Fay tries
  5. Q1

    November 2022 · Paper 3H

    The whole paper ↗
    November 2022 Paper 3H, question 1: 2x = 32 Circle the value of x. 4 5 6 7
  6. Q3

    November 2020 · Paper 1H

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    November 2020 Paper 1H, question 3: Which one of these is a square number and a cube number? Circle your answer. 100 1000 10 000 1 000 000
  7. Q21

    November 2020 · Paper 1H

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    November 2020 Paper 1H, question 21: Write these numbers in order of size. 15.6 3 23 2.14 3 47 Start with the smallest. Smallest Largest
  8. Q4

    November 2020 · Paper 2H

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    November 2020 Paper 2H, question 4: Circle the expression that has the largest value when a < –1 2 1 a a a 2 a 3
  9. Q11

    November 2019 · Paper 3H

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    November 2019 Paper 3H, question 11: Work out cube root of 512 : reciprocal of 0.4 Give your answer in the form n : 1 Answer :
  10. Q1

    June 2018 · Paper 1H

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    June 2018 Paper 1H, question 1: Work out 3 1000 64 × Circle your answer. 40 80 400 4000  
  11. Q18

    June 2018 · Paper 2H

    The whole paper ↗
    June 2018 Paper 2H, question 18: The solution of 3x = 300 lies between two consecutive integers. Work out the two integers. Answer and
  12. Q6

    November 2017 · Paper 3H

    The whole paper ↗
    November 2017 Paper 3H, question 6: Show that 268 can be written as the sum of a power of 3 and a square number. Answer
  13. Q2

    June 2017 · Paper 3H

    The whole paper ↗
    June 2017 Paper 3H, question 2: Which of these values of n makes 2.7 × 10n a cube number? Circle your answer. 0 1 2 3
  14. Q1

    Specimen · Paper 3H

    The whole paper ↗
    Specimen Paper 3H, question 1: Work out the square root of 100 million. Circle your answer. 1000 10 000 100 000 1 000 000   5   2
  15. Q12

    Specimen · Paper 3H

    The whole paper ↗
    Specimen Paper 3H, question 12: Tick whether each statement is true or false. Give a reason for your answer. 12 (a) When x2 = 16 the only value that x can be is 4 True False Reason 12 (b) When
All 15 questions on Powers and roots, as a list
  1. June 2025, Paper 1H, Q13 (2 marks): c and d are consecutive cube numbers, where c < 4.53 < d Work out the value of d – c Answer
  2. November 2024, Paper 1H, Q1 (2 marks): Work out the value of 1.52 Answer
  3. June 2023, Paper 1H, Q3 (1 mark): Work out the value of       2 3 2 Give your answer as a mixed number. Answer
  4. November 2022, Paper 2H, Q7 (3 marks): (a) k is a whole number between 40 and 50 The cube root of k is 3, to the nearest whole number. Work out the largest possible value of k. Answer 7 (b) Fay tries
  5. November 2022, Paper 3H, Q1 (1 mark): 2x = 32 Circle the value of x. 4 5 6 7
  6. November 2020, Paper 1H, Q3 (1 mark): Which one of these is a square number and a cube number? Circle your answer. 100 1000 10 000 1 000 000
  7. November 2020, Paper 1H, Q21 (2 marks): Write these numbers in order of size. 15.6 3 23 2.14 3 47 Start with the smallest. Smallest Largest
  8. November 2020, Paper 2H, Q4 (1 mark): Circle the expression that has the largest value when a < –1 2 1 a a a 2 a 3
  9. November 2019, Paper 3H, Q11 (3 marks): Work out cube root of 512 : reciprocal of 0.4 Give your answer in the form n : 1 Answer :
  10. June 2018, Paper 1H, Q1 (1 mark): Work out 3 1000 64 × Circle your answer. 40 80 400 4000  
  11. June 2018, Paper 2H, Q18 (1 mark): The solution of 3x = 300 lies between two consecutive integers. Work out the two integers. Answer and
  12. November 2017, Paper 3H, Q6 (2 marks): Show that 268 can be written as the sum of a power of 3 and a square number. Answer
  13. June 2017, Paper 3H, Q2 (1 mark): Which of these values of n makes 2.7 × 10n a cube number? Circle your answer. 0 1 2 3
  14. Specimen, Paper 3H, Q1 (1 mark): Work out the square root of 100 million. Circle your answer. 1000 10 000 100 000 1 000 000   5   2
  15. Specimen, Paper 3H, Q12 (3 marks): Tick whether each statement is true or false. Give a reason for your answer. 12 (a) When x2 = 16 the only value that x can be is 4 True False Reason 12 (b) When

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