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Exact calculation and surds: OCR GCSE Maths questions

Every OCR GCSE Maths exam question on N8 Exact calculation and surds, 2017–2025, with its mark scheme and examiner’s report.

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921 questions

  1. Q19

    June 2025 · Paper 4

    3 marksN8 Exact calculation and surds
    The whole paper ↗
    June 2025 Paper 4, question 19: Multiply out and simplify. _ _i i 5 1 15 3 + - Give your answer in the form a b, where a and b are integers. You must show each step in your working.

  2. Q20

    November 2024 · Paper 5

    2 marksN8 Exact calculation and surds
    The whole paper ↗
    November 2024 Paper 5, question 20: Simplify. 160 2 '

  3. Q16

    November 2024 · Paper 6

    4 marksG22 Sine and cosine rulesN8 Exact calculation and surds
    The whole paper ↗
    November 2024 Paper 6, question 16: Work out the exact value of x in this triangle. Not to scale 7 cm x cm 30° 6 3 cm x =

  4. Q19

    June 2024 · Paper 4

    5 marksN8 Exact calculation and surds
    The whole paper ↗
    June 2024 Paper 4, question 19: Show that . 6 48 6 - You must show each step in your working.

  5. Q22

    November 2023 · Paper 4

    6 marksN8 Exact calculation and surds
    The whole paper ↗
    November 2023 Paper 4, question 22: You are given this identity. 2 3 18 - a 2 b = + 18 4 + Find the value of a and the value of b. You must show each step in your working. a = b =

  6. Q13

    June 2023 · Paper 5

    6 marksG20 Pythagoras and trigonometryN8 Exact calculation and surds
    The whole paper ↗
    June 2023 Paper 5, question 13: The diagram shows a triangle, ABC, with perpendicular height BD. Not to scale B 12 cm 45° 30° A C D BC = 12 cm, angle BCD = 30° and angle BAD = 45°. (a) Work ou

  7. Q19

    June 2023 · Paper 6

    5 marksN8 Exact calculation and surds
    The whole paper ↗
    June 2023 Paper 6, question 19: (a) Show that 11 22 11 2 . = # 11 can be written in the form a 11 11 2 - (b) Show that where a and b are integers. b 13 22 +

  8. Q15

    November 2022 · Paper 5

    7 marksN8 Exact calculation and surds
    The whole paper ↗
    November 2022 Paper 5, question 15: (a) Simplify. 3 15 # (a) (b) Rationalise the denominator and simplify. 40 15 (b) (c) Work out. 4 273 (c)

  9. Q17

    November 2022 · Paper 5

    3 marksG23 Area of a triangle (½ab sin C)N8 Exact calculation and surds
    The whole paper ↗
    November 2022 Paper 5, question 17: The diagram shows triangle ABC. C 7 m Not to scale 45° B A 8 m Find the area of the triangle. Give your answer in the form a b where a and b are integers. 2 m

  10. Q15

    November 2021 · Paper 5

    3 marksN8 Exact calculation and surds
    The whole paper ↗
    November 2021 Paper 5, question 15: Write 20 45 in the form k 5. +

  11. Q11

    November 2020 · Paper 5

    4 marksN7 Laws of indicesN8 Exact calculation and surds
    The whole paper ↗
    November 2020 Paper 5, question 11: (a) Work out. 1 - 16 2 (a) (b) Simplify. 6 3 # (b)

  12. Q13

    November 2019 · Paper 5

    5 marksN10 Fractions, decimals and recurring decimalsN8 Exact calculation and surds
    The whole paper ↗
    November 2019 Paper 5, question 13: (a) (i) Write 3 (a)(i) 1 as a recurring decimal. (ii) Write 30 (ii) (b) Simplify fully by rationalising the denominator. 20 5 (b)

  13. Q21

    November 2019 · Paper 5

    6 marksA16 Equation of a circle and tangentsN8 Exact calculation and surds
    The whole paper ↗
    November 2019 Paper 5, question 21: In this question all units are in cm. 2 2 A circle has equation x y 36 . + = (a) Write down the radius and centre of the circle. (a) radius: cm centre: ( , ) (b

  14. Q11

    June 2019 · Paper 5

    3 marksN8 Exact calculation and surdsN7 Laws of indices
    The whole paper ↗
    June 2019 Paper 5, question 11: (a) Simplify fully. 200 (a) (b) Evaluate. 1 83 (b)

  15. Q13

    November 2018 · Paper 5

    8 marksG20 Pythagoras and trigonometryN8 Exact calculation and surds
    The whole paper ↗
    November 2018 Paper 5, question 13: In the diagram, ABC is a right-angled triangle. P is a point on AB. BC = 40 m, AP = 20 m and angle ABC = 30 °. C 40 m Not to scale 30° A B P 20 m (a) Show that

  16. Q20

    June 2018 · Paper 5

    9 marksN7 Laws of indicesN8 Exact calculation and surds
    The whole paper ↗
    June 2018 Paper 5, question 20: In the following equation, n is an integer greater than 1. _ i n = 2 k 2 (a) (i) Find k when n = 7. (a)(i) k = (ii) Find n when k = 64. (ii) n = 14 (b) Show tha

  17. Q15

    November 2017 · Paper 4

    4 marksN8 Exact calculation and surds
    The whole paper ↗
    November 2017 Paper 4, question 15: Show that . 2 5 1 -

  18. Q16

    November 2017 · Paper 5

    6 marksN8 Exact calculation and surdsN7 Laws of indices
    The whole paper ↗
    November 2017 Paper 5, question 16: (a) Write 12 75 in the form k 3. + (a) (b) Work out. 3 - 16 4 (b)

  19. Q15

    June 2017 · Paper 5

    7 marksN8 Exact calculation and surdsN7 Laws of indices
    The whole paper ↗
    June 2017 Paper 5, question 15: (a) Simplify fully. (i) 50 2 + (a)(i) 10 (ii) 6 (ii) - 2 (b) There are two errors in Sam’s method for finding the value of 64 3 shown below. Find the cube root

  20. Q17

    June 2017 · Paper 6

    3 marksN8 Exact calculation and surds
    The whole paper ↗
    June 2017 Paper 6, question 17: Show that can be written as 33 3
All 20 questions on Exact calculation and surds, as a list
  1. June 2025, Paper 4, Q19 (3 marks): Multiply out and simplify. _ _i i 5 1 15 3 + - Give your answer in the form a b, where a and b are integers. You must show each step in your working.
  2. November 2024, Paper 5, Q20 (2 marks): Simplify. 160 2 '
  3. November 2024, Paper 6, Q16 (4 marks): Work out the exact value of x in this triangle. Not to scale 7 cm x cm 30° 6 3 cm x =
  4. June 2024, Paper 4, Q19 (5 marks): Show that . 6 48 6 - You must show each step in your working.
  5. November 2023, Paper 4, Q22 (6 marks): You are given this identity. 2 3 18 - a 2 b = + 18 4 + Find the value of a and the value of b. You must show each step in your working. a = b =
  6. June 2023, Paper 5, Q13 (6 marks): The diagram shows a triangle, ABC, with perpendicular height BD. Not to scale B 12 cm 45° 30° A C D BC = 12 cm, angle BCD = 30° and angle BAD = 45°. (a) Work ou
  7. June 2023, Paper 6, Q19 (5 marks): (a) Show that 11 22 11 2 . = # 11 can be written in the form a 11 11 2 - (b) Show that where a and b are integers. b 13 22 +
  8. November 2022, Paper 5, Q15 (7 marks): (a) Simplify. 3 15 # (a) (b) Rationalise the denominator and simplify. 40 15 (b) (c) Work out. 4 273 (c)
  9. November 2022, Paper 5, Q17 (3 marks): The diagram shows triangle ABC. C 7 m Not to scale 45° B A 8 m Find the area of the triangle. Give your answer in the form a b where a and b are integers. 2 m
  10. November 2021, Paper 5, Q15 (3 marks): Write 20 45 in the form k 5. +
  11. November 2020, Paper 5, Q11 (4 marks): (a) Work out. 1 - 16 2 (a) (b) Simplify. 6 3 # (b)
  12. November 2019, Paper 5, Q13 (5 marks): (a) (i) Write 3 (a)(i) 1 as a recurring decimal. (ii) Write 30 (ii) (b) Simplify fully by rationalising the denominator. 20 5 (b)
  13. November 2019, Paper 5, Q21 (6 marks): In this question all units are in cm. 2 2 A circle has equation x y 36 . + = (a) Write down the radius and centre of the circle. (a) radius: cm centre: ( , ) (b
  14. June 2019, Paper 5, Q11 (3 marks): (a) Simplify fully. 200 (a) (b) Evaluate. 1 83 (b)
  15. November 2018, Paper 5, Q13 (8 marks): In the diagram, ABC is a right-angled triangle. P is a point on AB. BC = 40 m, AP = 20 m and angle ABC = 30 °. C 40 m Not to scale 30° A B P 20 m (a) Show that
  16. June 2018, Paper 5, Q20 (9 marks): In the following equation, n is an integer greater than 1. _ i n = 2 k 2 (a) (i) Find k when n = 7. (a)(i) k = (ii) Find n when k = 64. (ii) n = 14 (b) Show tha
  17. November 2017, Paper 4, Q15 (4 marks): Show that . 2 5 1 -
  18. November 2017, Paper 5, Q16 (6 marks): (a) Write 12 75 in the form k 3. + (a) (b) Work out. 3 - 16 4 (b)
  19. June 2017, Paper 5, Q15 (7 marks): (a) Simplify fully. (i) 50 2 + (a)(i) 10 (ii) 6 (ii) - 2 (b) There are two errors in Sam’s method for finding the value of 64 3 shown below. Find the cube root
  20. June 2017, Paper 6, Q17 (3 marks): Show that can be written as 33 3

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