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Ratio notation: AQA GCSE Maths questions

Every AQA GCSE Maths exam question on R4 Ratio notation, 2017–2025, with its mark scheme and examiner’s report.

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1,304 questions

  1. Q7

    June 2025 · Paper 1H

    4 marksP1 Frequency trees and probability experimentsR4 Ratio notation
    The whole paper ↗
    June 2025 Paper 1H, question 7: 330 students from Year 10 and Year 11 take part in a competition. • number of students in Year 10 : number of students in Year 11 = 1 : 2 • 125 students win a m

  2. Q7

    June 2025 · Paper 3H

    4 marksR3 One quantity as a fraction of anotherR4 Ratio notation
    The whole paper ↗
    June 2025 Paper 3H, question 7: (a) Write 2 weeks as a fraction of 8 days. Give your answer in its simplest form. Answer 7 (b) Write 56 centimetres : 2.73 metres as a ratio in the form 1 : n A

  3. Q23

    November 2024 · Paper 2H

    6 marksG10 Circle theoremsR4 Ratio notation
    The whole paper ↗
    November 2024 Paper 2H, question 23: (a) Not drawn accurately Line DAE is a tangent at A to the circle with centre O. Work out the size of angle x. x = ° 23 (b) Here is a cyclic quadrilateral. f :

  4. Q7

    November 2024 · Paper 3H

    4 marksR4 Ratio notationR5 Sharing in a ratio
    The whole paper ↗
    November 2024 Paper 3H, question 7: (a) At a school there are 912 students the ratio of students to teachers is 15.2 : 1 The number of students stays the same. The number of teachers increases by

  5. Q25

    June 2024 · Paper 2H

    5 marksG16 Area of 2D shapes and volume of prismsR4 Ratio notation
    The whole paper ↗
    June 2024 Paper 2H, question 25: Here is a right-angled triangular prism. The ratio of the edges is a : b : c : d = 3 : 4 : 5 : 12 The volume of the prism is 1125 cm3 Work out the total length

  6. Q14

    June 2024 · Paper 3H

    3 marksG3 Angles and polygonsR4 Ratio notation
    The whole paper ↗
    June 2024 Paper 3H, question 14: Not drawn accurately b = 45° and a : b = 7 : 3 and x : y = 4 : 1 Show that a : y = 5 : 2

  7. Q8

    November 2023 · Paper 1H

    3 marksG16 Area of 2D shapes and volume of prismsR4 Ratio notation
    The whole paper ↗
    November 2023 Paper 1H, question 8: In the diagrams, all lengths are in centimetres. The two shapes have equal areas. Work out k : m Not drawn accurately Answer :

  8. Q22

    November 2023 · Paper 1H

    3 marksG10 Circle theoremsR4 Ratio notation
    The whole paper ↗
    November 2023 Paper 1H, question 22: Here is a cyclic quadrilateral. a : b : c = 9 : 5 : 3 Work out the size of angle d. Not drawn accurately d = °

  9. Q25

    November 2023 · Paper 3H

    3 marksR4 Ratio notationR7 Proportion as equal ratios
    The whole paper ↗
    November 2023 Paper 3H, question 25: a is three quarters of c 6b = 5c Work out the ratio a : b : c Give your answer in its simplest form, where a, b and c are integers. Answer : :

  10. Q17

    June 2023 · Paper 1H

    3 marksG17 Circles, surface area and volumeR4 Ratio notation
    The whole paper ↗
    June 2023 Paper 1H, question 17: A solid hemisphere has radius x. A solid cylinder has radius 3x and height x. Work out the ratio total surface area of the hemisphere : total surface area of th

  11. Q1

    June 2023 · Paper 2H

    1 markR4 Ratio notation
    The whole paper ↗
    June 2023 Paper 2H, question 1: Write 30 : 12 in the form n : 1 Answer : 1

  12. Q5

    June 2023 · Paper 2H

    4 marksR4 Ratio notation
    The whole paper ↗
    June 2023 Paper 2H, question 5: Jess saves 2p, 5p and 10p coins. She has • 45 10p coins • 8 times as many 2p coins as 10p coins • £17.70 in total. Work out total value of 2p coins : total valu

  13. Q18

    November 2022 · Paper 1H

    3 marksR4 Ratio notation
    The whole paper ↗
    November 2022 Paper 1H, question 18: A road has three sections, D, E and F. The lengths of D, E and F are in the ratios D : E = 3 : 5 E : F = 7 : 4 What fraction of the length of the road is sectio

  14. Q12

    November 2022 · Paper 2H

    4 marksA21 Forming and solving equationsR4 Ratio notation
    The whole paper ↗
    November 2022 Paper 2H, question 12: The length of this rectangle is 6 times the width. Two of these rectangles are joined, with no overlap, to make this L-shape. The perimeter of the L-shape is 98

  15. Q26

    November 2021 · Paper 1H

    3 marksR4 Ratio notationA5 Formulae and changing the subject
    The whole paper ↗
    November 2021 Paper 1H, question 26: d = 2f – – e f d e = 1 4 Work out the ratio e : f Answer :

  16. Q2

    November 2021 · Paper 2H

    1 markR4 Ratio notation
    The whole paper ↗
    November 2021 Paper 2H, question 2: A is half of B. Work out the ratio A : B Circle your answer. 1 : 2 2 : 1 1 : 3 3 : 1

  17. Q12

    November 2020 · Paper 1H

    5 marksR4 Ratio notationG18 Arcs and sectors
    The whole paper ↗
    November 2020 Paper 1H, question 12: Two wire shapes make an earring. The shapes are a circle with radius 21 mm and a quarter circle. Not drawn accurately radius of circle : radius of quarter circl

  18. Q15

    November 2020 · Paper 1H

    1 markR4 Ratio notation
    The whole paper ↗
    November 2020 Paper 1H, question 15: 3x = 2 1 y Circle the ratio x : y 6 : 1 1 : 6 3 : 2 2 : 3

  19. Q16

    November 2019 · Paper 1H

    4 marksR9 PercentagesR4 Ratio notation
    The whole paper ↗
    November 2019 Paper 1H, question 16: In a box there are some buttons. 45 are large and the rest are small. Some are yellow and the rest are green. The number of small is 3 5 of the number of large.

  20. Q11

    November 2019 · Paper 3H

    3 marksN6 Powers and rootsR4 Ratio notation
    The whole paper ↗
    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 :
All 36 questions on Ratio notation, as a list
  1. June 2025, Paper 1H, Q7 (4 marks): 330 students from Year 10 and Year 11 take part in a competition. • number of students in Year 10 : number of students in Year 11 = 1 : 2 • 125 students win a m
  2. June 2025, Paper 3H, Q7 (4 marks): (a) Write 2 weeks as a fraction of 8 days. Give your answer in its simplest form. Answer 7 (b) Write 56 centimetres : 2.73 metres as a ratio in the form 1 : n A
  3. November 2024, Paper 2H, Q23 (6 marks): (a) Not drawn accurately Line DAE is a tangent at A to the circle with centre O. Work out the size of angle x. x = ° 23 (b) Here is a cyclic quadrilateral. f :
  4. November 2024, Paper 3H, Q7 (4 marks): (a) At a school there are 912 students the ratio of students to teachers is 15.2 : 1 The number of students stays the same. The number of teachers increases by
  5. June 2024, Paper 2H, Q25 (5 marks): Here is a right-angled triangular prism. The ratio of the edges is a : b : c : d = 3 : 4 : 5 : 12 The volume of the prism is 1125 cm3 Work out the total length
  6. June 2024, Paper 3H, Q14 (3 marks): Not drawn accurately b = 45° and a : b = 7 : 3 and x : y = 4 : 1 Show that a : y = 5 : 2
  7. November 2023, Paper 1H, Q8 (3 marks): In the diagrams, all lengths are in centimetres. The two shapes have equal areas. Work out k : m Not drawn accurately Answer :
  8. November 2023, Paper 1H, Q22 (3 marks): Here is a cyclic quadrilateral. a : b : c = 9 : 5 : 3 Work out the size of angle d. Not drawn accurately d = °
  9. November 2023, Paper 3H, Q25 (3 marks): a is three quarters of c 6b = 5c Work out the ratio a : b : c Give your answer in its simplest form, where a, b and c are integers. Answer : :
  10. June 2023, Paper 1H, Q17 (3 marks): A solid hemisphere has radius x. A solid cylinder has radius 3x and height x. Work out the ratio total surface area of the hemisphere : total surface area of th
  11. June 2023, Paper 2H, Q1 (1 mark): Write 30 : 12 in the form n : 1 Answer : 1
  12. June 2023, Paper 2H, Q5 (4 marks): Jess saves 2p, 5p and 10p coins. She has • 45 10p coins • 8 times as many 2p coins as 10p coins • £17.70 in total. Work out total value of 2p coins : total valu
  13. November 2022, Paper 1H, Q18 (3 marks): A road has three sections, D, E and F. The lengths of D, E and F are in the ratios D : E = 3 : 5 E : F = 7 : 4 What fraction of the length of the road is sectio
  14. November 2022, Paper 2H, Q12 (4 marks): The length of this rectangle is 6 times the width. Two of these rectangles are joined, with no overlap, to make this L-shape. The perimeter of the L-shape is 98
  15. November 2021, Paper 1H, Q26 (3 marks): d = 2f – – e f d e = 1 4 Work out the ratio e : f Answer :
  16. November 2021, Paper 2H, Q2 (1 mark): A is half of B. Work out the ratio A : B Circle your answer. 1 : 2 2 : 1 1 : 3 3 : 1
  17. November 2020, Paper 1H, Q12 (5 marks): Two wire shapes make an earring. The shapes are a circle with radius 21 mm and a quarter circle. Not drawn accurately radius of circle : radius of quarter circl
  18. November 2020, Paper 1H, Q15 (1 mark): 3x = 2 1 y Circle the ratio x : y 6 : 1 1 : 6 3 : 2 2 : 3
  19. November 2019, Paper 1H, Q16 (4 marks): In a box there are some buttons. 45 are large and the rest are small. Some are yellow and the rest are green. The number of small is 3 5 of the number of large.
  20. 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 :
  21. November 2019, Paper 3H, Q23 (1 mark): x : y = 4 1 : 3 2 What is x as a fraction of y? Circle your answer. 3 8 1 6 7 3 8 3
  22. June 2019, Paper 1H, Q14 (3 marks): Here is a quadrilateral. a = 90° and a : b = 5 : 3 x : y = 1 : 3 Show that b = x Not drawn accurately
  23. June 2019, Paper 2H, Q3 (1 mark): 2a is five times bigger than b. Circle the ratio a : b 10 : 1 1 : 10 5 : 2 2 : 5
  24. June 2019, Paper 2H, Q11 (2 marks): Joe and Kyle share an amount of money in the ratio 7 : n Joe gets 35% of the money. Work out the value of n. Answer
  25. June 2019, Paper 2H, Q18 (3 marks): In a bag there are blue discs, green discs and white discs. There are four times as many blue discs as green discs. number of blue discs : number of white discs
  26. June 2019, Paper 3H, Q14 (1 mark): For Class X, number of boys : number of girls = 7 : 8 For Class Y, number of boys : number of girls = 3 : 4 Which statement must be true? Tick one box. Class X
  27. November 2018, Paper 1H, Q13 (3 marks): e : f = 2 : 3 and f : g = 5 : 4 Work out e : g Give your answer in its simplest form. Answer :
  28. November 2018, Paper 3H, Q24 (4 marks): A sphere has radius 2x cm A cone has radius 3x cm perpendicular height h cm The sphere and the cone have the same volume. Work out radius of cone : perpendicula
  29. June 2018, Paper 1H, Q14 (5 marks): Patterns are made using straight lines and arcs. 14 (a) More rows are added to Pattern B so that number of straight lines : number of arcs = 10 : 9 How many row
  30. June 2018, Paper 1H, Q16 (1 mark): The value of y is 20% more than the value of x. Circle the ratio x : y 5 : 6 6 : 5 4 : 5 5 : 4
  31. June 2018, Paper 1H, Q26 (3 marks): b is two thirds of c. 5a = 4c Work out the ratio a : b : c Give your answer in its simplest form where a, b and c are integers. Answer : :
  32. June 2018, Paper 2H, Q3 (1 mark): y is 1 2 1 times x. Circle the ratio that is equivalent to y : x 2 : 5 5 : 2 3 : 2 2 : 3
  33. June 2018, Paper 2H, Q8 (3 marks): Theo starts with savings of £18 James starts with no savings. Each week from now, Theo will save £4.50 and James will save £4 In how many weeks will Theo and Ja
  34. November 2017, Paper 1H, Q13 (3 marks): x : y = 7 : 4 x + y = 88 Work out the value of x – y Answer
  35. November 2017, Paper 3H, Q2 (1 mark): y is 100% more than x. Circle the ratio x : y 1 : 100 100 : 1 1 : 2 2 : 1
  36. November 2017, Paper 3H, Q24 (3 marks): a : b = 9 : 4 and 10b = 7c Work out a : c in its simplest form. Answer :

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