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Recognising and sketching graphs: OCR GCSE Maths questions

Every OCR GCSE Maths exam question on A12 Recognising and sketching graphs, 2017–2025, with its mark scheme and examiner’s report.

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921 questions

  1. Q16

    June 2025 · Paper 6

    3 marksA12 Recognising and sketching graphs
    The whole paper ↗
    June 2025 Paper 6, question 16: (a) On the axes below, sketch the graph y = x . y x O (b) Write down a possible equation for the graph sketched below. y O x 180° 360° (b) y =

  2. Q22

    November 2024 · Paper 6

    4 marksA12 Recognising and sketching graphsA13 Graph transformations
    The whole paper ↗
    November 2024 Paper 6, question 22: (a) For each graph below, select its possible equation from this list. 4 x 4 y x 4 y 4 y x y = - = = = x 1 x = d n 2 2 2 - y y 4 x y 4 cos x y 4 x = = = - 4 (i)

  3. Q22

    June 2024 · Paper 5

    4 marksA12 Recognising and sketching graphs
    The whole paper ↗
    June 2024 Paper 5, question 22: (a) Sketch the graph of y 8 . = Indicate any values where the graph crosses the axes. y x O (b) Sketch the graph of cos for ° 0 360 ° . y x x = G G Indicate any

  4. Q1

    June 2024 · Paper 6

    3 marksA12 Recognising and sketching graphsR10 Direct and inverse proportion
    The whole paper ↗
    June 2024 Paper 6, question 1: Below are six graphs, numbered 1 to 6, that show different relationships between x and y. Graph 1 Graph 2 Graph 3 y y y O x O x O x Graph 4 Graph 5 Graph 6 y y

  5. Q8

    June 2024 · Paper 6

    6 marksA12 Recognising and sketching graphsA18 Quadratic equations
    The whole paper ↗
    June 2024 Paper 6, question 8: (a) Complete this table for y x 3 x . = - x 0 1 2 3 4 2 1 - - 0 16 y 20 2 4 - - - 3 2 (b) Draw the graph of y x 3 x for values of x from 2 - to 4. = - y 20 15 1

  6. Q8

    November 2023 · Paper 4

    2 marksR14 Gradient as a rate of changeA12 Recognising and sketching graphs
    The whole paper ↗
    November 2023 Paper 4, question 8: Here are sketches of six graphs, labelled A to F. A B C y y y x x x O O O E F D y y y x x x O O O Write the letter of the graph that represents the following re

  7. Q13

    November 2023 · Paper 5

    5 marksA12 Recognising and sketching graphsA14 Graphs in real contexts
    The whole paper ↗
    November 2023 Paper 5, question 13: (a) Complete the table for y x 4 x . = + -5 -4.5 -4 -3 -2 -1 x 0 1 -25 -10.1 y 0 9 8 0 5 3 2 for - (b) Draw the graph of y x 4 x 5 x G . 1 = + G y 10 5 x -5 -4

  8. Q13

    November 2023 · Paper 6

    5 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2023 Paper 6, question 13: (a) The graph of y 3 is sketched below. = y x y = 3 x O x On the same axes, sketch the graph of y 2 . = (b) Charlie sketches this graph. y x O Charlie says The

  9. Q7

    June 2023 · Paper 4

    4 marksA12 Recognising and sketching graphsA14 Graphs in real contexts
    The whole paper ↗
    June 2023 Paper 4, question 7: Here is a table of values for y 2 x . = - x -4 -3 -2 -1 x 1 2 3 4 -4 -1 -4 -6.5 6.5 4 1 4 y 6 for - (a) Draw the graph of y 2 x 4 x 4 , x 0 . = - ! G G x y 7 6

  10. Q19

    November 2022 · Paper 5

    4 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2022 Paper 5, question 19: (a) Sketch the graph of y 5 indicating any values where the graph crosses the axes. = y x O (b) Sketch the graph of y tan x for ° 0 x 360 ° indicating any value

  11. Q14

    June 2022 · Paper 6

    3 marksA12 Recognising and sketching graphs
    The whole paper ↗
    June 2022 Paper 6, question 14: Sketch the graph of cos - for 1 0 ° 720 ° . y x x = G G y 3 2 1 x 0 90° 180° 270° 360° 450° 540° 630° 720° -1 -2 -3

  12. Q16

    June 2022 · Paper 6

    5 marksA11 Quadratic graphs and turning pointsA12 Recognising and sketching graphs
    The whole paper ↗
    June 2022 Paper 6, question 16: Frankie sketches this quadratic graph. y Not to scale x O -3 5 Frankie says The y-intercept is 15. (a) Show that what Frankie says could be correct. (b) Explain

  13. Q18

    November 2021 · Paper 4

    6 marksA12 Recognising and sketching graphsA13 Graph transformations
    The whole paper ↗
    November 2021 Paper 4, question 18: (a) For each graph below, select its possible equation from this list. 1 2 y x y x y = = = x sin cos tan y x y x y x = = = 1 x = d n x y 3 y = 3 (i) y x O (a)(i

  14. Q8

    November 2021 · Paper 5

    4 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2021 Paper 5, question 8: (a) Complete the table for y . = x -6 -3 -2 -1 x 1 2 3 6 -1 -2 -6 6 3 2 1 y 6 for - (b) Draw the graph of y 6 6 , x 0 . x ! = G G x y 7 6 5 4 3 2 1 x 0 -7 -6 -5

  15. Q13

    November 2020 · Paper 5

    4 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2020 Paper 5, question 13: (a) Sketch the graph of for ° 0 360 ° . y x x = G G y 2 1 0 x 90° 180° 270° 360° -1 -2 (b) The graph of y cos ( x 30 ) for ° 0 x 360 ° crosses the x-axis in two

  16. Q17

    November 2019 · Paper 4

    2 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2019 Paper 4, question 17: Sketch the graph of y 3 . = Give the value of the y-intercept. y x O

  17. Q20

    November 2019 · Paper 5

    6 marksA11 Quadratic graphs and turning pointsA12 Recognising and sketching graphs
    The whole paper ↗
    November 2019 Paper 5, question 20: (a) Write x 6 11 in the form . x x a b + - + (a) 2 (b) Sketch the graph of 6 11 . y x x = - + Show clearly the coordinates of any turning points. y x O for Ques

  18. Q7

    November 2019 · Paper 6

    10 marksA12 Recognising and sketching graphsA18 Quadratic equations
    The whole paper ↗
    November 2019 Paper 6, question 7: (a) Complete the table for y 4 + . 1 x x = - -1 x 0 1 2 3 4 5 -2 y 1 6 2 + for -1 (b) Draw the graph of y x 4 x 1 x 5 . = - G G y 8 6 4 2 x 0 -1 1 2 3 4 5 -2 -4

  19. Q13

    June 2019 · Paper 5

    2 marksA12 Recognising and sketching graphs
    The whole paper ↗
    June 2019 Paper 5, question 13: Shirley is asked to sketch a graph of y 5 for x 0 . = H She produces the following. y x O The graph has two errors. How should they be corrected? 1 2

  20. Q17

    June 2019 · Paper 5

    7 marksA11 Quadratic graphs and turning pointsA12 Recognising and sketching graphs
    The whole paper ↗
    June 2019 Paper 5, question 17: (a) Write x 8 3 in the form x . x a b + + - (a) 2 (b) Sketch the graph of y 8 3 . x x = + + Show clearly the coordinates of any turning points and the y-interce
All 31 questions on Recognising and sketching graphs, as a list
  1. June 2025, Paper 6, Q16 (3 marks): (a) On the axes below, sketch the graph y = x . y x O (b) Write down a possible equation for the graph sketched below. y O x 180° 360° (b) y =
  2. November 2024, Paper 6, Q22 (4 marks): (a) For each graph below, select its possible equation from this list. 4 x 4 y x 4 y 4 y x y = - = = = x 1 x = d n 2 2 2 - y y 4 x y 4 cos x y 4 x = = = - 4 (i)
  3. June 2024, Paper 5, Q22 (4 marks): (a) Sketch the graph of y 8 . = Indicate any values where the graph crosses the axes. y x O (b) Sketch the graph of cos for ° 0 360 ° . y x x = G G Indicate any
  4. June 2024, Paper 6, Q1 (3 marks): Below are six graphs, numbered 1 to 6, that show different relationships between x and y. Graph 1 Graph 2 Graph 3 y y y O x O x O x Graph 4 Graph 5 Graph 6 y y
  5. June 2024, Paper 6, Q8 (6 marks): (a) Complete this table for y x 3 x . = - x 0 1 2 3 4 2 1 - - 0 16 y 20 2 4 - - - 3 2 (b) Draw the graph of y x 3 x for values of x from 2 - to 4. = - y 20 15 1
  6. November 2023, Paper 4, Q8 (2 marks): Here are sketches of six graphs, labelled A to F. A B C y y y x x x O O O E F D y y y x x x O O O Write the letter of the graph that represents the following re
  7. November 2023, Paper 5, Q13 (5 marks): (a) Complete the table for y x 4 x . = + -5 -4.5 -4 -3 -2 -1 x 0 1 -25 -10.1 y 0 9 8 0 5 3 2 for - (b) Draw the graph of y x 4 x 5 x G . 1 = + G y 10 5 x -5 -4
  8. November 2023, Paper 6, Q13 (5 marks): (a) The graph of y 3 is sketched below. = y x y = 3 x O x On the same axes, sketch the graph of y 2 . = (b) Charlie sketches this graph. y x O Charlie says The
  9. June 2023, Paper 4, Q7 (4 marks): Here is a table of values for y 2 x . = - x -4 -3 -2 -1 x 1 2 3 4 -4 -1 -4 -6.5 6.5 4 1 4 y 6 for - (a) Draw the graph of y 2 x 4 x 4 , x 0 . = - ! G G x y 7 6
  10. November 2022, Paper 5, Q19 (4 marks): (a) Sketch the graph of y 5 indicating any values where the graph crosses the axes. = y x O (b) Sketch the graph of y tan x for ° 0 x 360 ° indicating any value
  11. June 2022, Paper 6, Q14 (3 marks): Sketch the graph of cos - for 1 0 ° 720 ° . y x x = G G y 3 2 1 x 0 90° 180° 270° 360° 450° 540° 630° 720° -1 -2 -3
  12. June 2022, Paper 6, Q16 (5 marks): Frankie sketches this quadratic graph. y Not to scale x O -3 5 Frankie says The y-intercept is 15. (a) Show that what Frankie says could be correct. (b) Explain
  13. November 2021, Paper 4, Q18 (6 marks): (a) For each graph below, select its possible equation from this list. 1 2 y x y x y = = = x sin cos tan y x y x y x = = = 1 x = d n x y 3 y = 3 (i) y x O (a)(i
  14. November 2021, Paper 5, Q8 (4 marks): (a) Complete the table for y . = x -6 -3 -2 -1 x 1 2 3 6 -1 -2 -6 6 3 2 1 y 6 for - (b) Draw the graph of y 6 6 , x 0 . x ! = G G x y 7 6 5 4 3 2 1 x 0 -7 -6 -5
  15. November 2020, Paper 5, Q13 (4 marks): (a) Sketch the graph of for ° 0 360 ° . y x x = G G y 2 1 0 x 90° 180° 270° 360° -1 -2 (b) The graph of y cos ( x 30 ) for ° 0 x 360 ° crosses the x-axis in two
  16. November 2019, Paper 4, Q17 (2 marks): Sketch the graph of y 3 . = Give the value of the y-intercept. y x O
  17. November 2019, Paper 5, Q20 (6 marks): (a) Write x 6 11 in the form . x x a b + - + (a) 2 (b) Sketch the graph of 6 11 . y x x = - + Show clearly the coordinates of any turning points. y x O for Ques
  18. November 2019, Paper 6, Q7 (10 marks): (a) Complete the table for y 4 + . 1 x x = - -1 x 0 1 2 3 4 5 -2 y 1 6 2 + for -1 (b) Draw the graph of y x 4 x 1 x 5 . = - G G y 8 6 4 2 x 0 -1 1 2 3 4 5 -2 -4
  19. June 2019, Paper 5, Q13 (2 marks): Shirley is asked to sketch a graph of y 5 for x 0 . = H She produces the following. y x O The graph has two errors. How should they be corrected? 1 2
  20. June 2019, Paper 5, Q17 (7 marks): (a) Write x 8 3 in the form x . x a b + + - (a) 2 (b) Sketch the graph of y 8 3 . x x = + + Show clearly the coordinates of any turning points and the y-interce
  21. June 2019, Paper 5, Q19 (6 marks): The graph of y 2 is drawn on the grid. x x = - - y 8 7 6 5 4 3 2 1 x 0 -1 -0.5 0.5 1 1.5 2 2.5 -1 -2 -3 -4 -5 3 2 (a) Use the graph to solve x x 2 0 . - - = Giv
  22. June 2019, Paper 6, Q16 (3 marks): Sketch the graph of for 0 ° 360 ° . y x x =- G G y 2 1 x 0 90° 180° 270° 360° -1 -2
  23. November 2018, Paper 4, Q21 (6 marks): The number of gannets on an island is assumed to follow this exponential growth model. x N 0 45 . 1 07 . = # N is the number of gannets, in thousands. x is the
  24. November 2018, Paper 6, Q18 (4 marks): (a) Sketch the graph of y cos x + for ° 1 0 x 720 ° . = G G y 3 2 1 0 x 90° 180° 270° 360° 450° 540° 630° 720° –1 –2 –3 (b) Explain why the equation cosx 1 2 7
  25. June 2018, Paper 4, Q17 (3 marks): For each graph below, select its possible equation from this list. = a k x 1 1 y y = x2 y = 2x y y = cos x = 2 x 1 y = y = 2-x y = x3 y = sin x y = tan x 2 x (a
  26. June 2018, Paper 5, Q9 (5 marks): (a) Complete the table for y 3 . x x = - -3 -2 -1 x 0 1 2 3 -18 -2 -2 y 0 2 18 3 for -3 G x G 3. (b) Draw the graph of y x 3 x = - y 20 15 10 5 3 x 0 –3 –2 –1 1
  27. June 2018, Paper 6, Q9 (6 marks): The root of the equation x3 - 7x - 12 = 0 is p. y x p O (a) Calculate y when x = 3. (a) y = (b) Show that 3 1 p 1 4. (c) Find a smaller interval that contains t
  28. November 2017, Paper 4, Q5 (12 marks): (a) Complete this table for y x x 4 . = + - -4 -3 -2 -1 0 1 2 3 x -4 -4 y 2 2 2 for -4 (b) Draw the graph of y 4 3 . x x x = + - G G y 10 9 8 7 6 5 4 3 2 1 -4 -
  29. June 2017, Paper 5, Q4 (3 marks): Rashid invests money into an account which pays a fixed rate of compound interest each year. The value, £V, of his investment after t years is given by the form
  30. June 2017, Paper 5, Q19 (8 marks): (a) Sketch the graph of y x 2 3 . = - - Show the coordinates of any turning points. y x O 2 (b) The sketch shows part of a graph which has equation y . ax bx c
  31. June 2017, Paper 6, Q15 (6 marks): (a) Sketch the graph of y = sin x for 0° G x G 360°. y 2 1 x 0 90° 180° 270° 360° -1 -2 (b) Solve the equation 5 sin x = -3. Give all of the solutions in the ra

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