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OCR GCSE Maths questions by topic

Every question from every OCR GCSE Mathematics (J560), Higher tier paper, 2017–2025, question by question. Filter by topic, paper or year, open the mark scheme under any question, and download a set as a PDF.

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921 questions

  1. Q1

    June 2025 · Paper 4

    2 marks
    The whole paper ↗
    June 2025 Paper 4, question 1: Calculate. 3 4 5 . 3 6 . + 2 1 8 . 2 4 . Give your answer correct to 3 significant figures.

  2. Q2

    June 2025 · Paper 4

    2 marks
    The whole paper ↗
    June 2025 Paper 4, question 2: The ratio 40 grams to 1 kilogram can be written in the form 1 : n. Find the value of n. n =

  3. Q3

    June 2025 · Paper 4

    4 marks
    The whole paper ↗
    June 2025 Paper 4, question 3: The diagram shows a shape formed from a rectangle measuring 8 cm by 17 cm with a semicircle removed from one side. 4 cm 3 cm Not to scale 8 cm 17 cm Calculate t

  4. Q4

    June 2025 · Paper 4

    4 marks
    The whole paper ↗
    June 2025 Paper 4, question 4: (a) Describe the correlation shown in each of these scatter diagrams. (b) A theatre records the number of seats sold and the profit made for 10 performances. Th

  5. Q5

    June 2025 · Paper 4

    4 marks
    The whole paper ↗
    June 2025 Paper 4, question 5: (a) For each of the algebraic statements below decide whether it is an equation or an identity. ( x 1 )( x 2 ) 12 is an - - = 2 ( x 1 )( x 2 ) x 3 x 2 is an - -

  6. Q6

    June 2025 · Paper 4

    5 marks
    The whole paper ↗
    June 2025 Paper 4, question 6: The distance of a car race is 420 km. A car completes the first 210 km at an average speed of 150 km/h. The same car completes the final 210 km at an average sp

  7. Q7

    June 2025 · Paper 4

    6 marks
    The whole paper ↗
    June 2025 Paper 4, question 7: T he diagram shows a regular pentagon and part of another regular polygon meeting at point P. One of the angles at point P is 92°. Not to scale P 92° (a) Show t

  8. Q8

    June 2025 · Paper 4

    3 marks
    The whole paper ↗
    June 2025 Paper 4, question 8: A town council are going to do a survey on how people travel to work or school and for how long they travel. One day their interviewer stands outside the town r

  9. Q9

    June 2025 · Paper 4

    5 marks
    The whole paper ↗
    June 2025 Paper 4, question 9: (a) Write 0.0037 in standard form. (a) (b) A country consists of a south island and a north island. The table below shows the population and area of each island

  10. Q10

    June 2025 · Paper 4

    3 marks
    The whole paper ↗
    June 2025 Paper 4, question 10: Find the value of k. 3 k 25 ( 5 ) # 19 5 = 4 5 k =

  11. Q11

    June 2025 · Paper 4

    5 marks
    The whole paper ↗
    June 2025 Paper 4, question 11: Function A and function B are shown below. Function A: Input - 5 # a Output Function B: Input + b # 3 Output When the input for both machines is 11, the output

  12. Q12

    June 2025 · Paper 4

    5 marks
    The whole paper ↗
    June 2025 Paper 4, question 12: The diagram shows a trapezium. 17.2 cm Not to scale 7 cm 7 cm 25.6 cm Calculate the area of the trapezium. You must show your working. 2 cm

  13. Q13

    June 2025 · Paper 4

    3 marks
    The whole paper ↗
    June 2025 Paper 4, question 13: A, B, and C are points on a circle, centre O. B Not to scale A 110° x° C O (a) Explain why OABC is not a cyclic quadrilateral. (b) Work out the value of x. x =

  14. Q14

    June 2025 · Paper 4

    5 marks
    The whole paper ↗
    June 2025 Paper 4, question 14: The cumulative frequency graph shows the distribution of the examination scores for 120 students. 120 100 80 Cumulative frequency 60 40 20 0 0 10 20 30 40 50 60

  15. Q15

    June 2025 · Paper 4

    3 marks
    The whole paper ↗
    June 2025 Paper 4, question 15: y is inversely proportional to the square of x. y 5 when x 6 . = = Find a formula linking x and y.

  16. Q16

    June 2025 · Paper 4

    6 marks
    The whole paper ↗
    June 2025 Paper 4, question 16: The population of fish, P, in a pond is predicted by the formula n P 640 1 025 . = # where n is the number of years after 1st January 2020. (a) Write down the p

  17. Q17

    June 2025 · Paper 4

    5 marks
    The whole paper ↗
    June 2025 Paper 4, question 17: The diagram shows a circle, centre (0, 0). y 4 x -4 4 O -4 (a) Write down the equation of the circle. (a) (b) Point A has coordinates (2.3, 3.3). Show that poin

  18. Q18

    June 2025 · Paper 4

    6 marks
    The whole paper ↗
    June 2025 Paper 4, question 18: (a) A sequence is defined by u ku 2 , u 7 and u 29 5 . . 1 = - 2 = 3 = n n + Find the value of k. (a) k = (b) Another sequence is defined by u 6 u 7 . 1 = - n n

  19. Q19

    June 2025 · Paper 4

    3 marks
    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.

  20. Q20

    June 2025 · Paper 4

    3 marks
    The whole paper ↗
    June 2025 Paper 4, question 20: The diagram shows triangle ABC. A Not to scale 40° 12 cm C 58° B AC 12 cm , angle CAB = 40 ° and angle ABC = 58 ° . = Calculate length BC. cm

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