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Recognising and sketching graphs: Edexcel GCSE Maths questions

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

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  1. Q17

    June 2025 · Paper 2H

    2 marksA12 Recognising and sketching graphsR10 Direct and inverse proportion
    The whole paper ↗
    June 2025 Paper 2H, question 17: Here is a sketch of part of the graph of y = k x where k is a positive constant. y (–1, 1.5) x O The graph passes through the point with coordinates (–1, 1.5) F

  2. Q13

    June 2025 · Paper 3H

    3 marksA12 Recognising and sketching graphs
    The whole paper ↗
    June 2025 Paper 3H, question 13: Here are some graphs. A B C y y y O O x x O x D E F y y y O O O x x x G H y y O x O x Each equation in the table is the equation of one of the graphs. Complete

  3. Q21

    November 2024 · Paper 3H

    4 marksA13 Graph transformationsA12 Recognising and sketching graphs
    The whole paper ↗
    November 2024 Paper 3H, question 21: Here is the graph of y = f (x) y y = f (x) O x (a) On the grid, draw the graph of y = −f (x) Here is a sketch of the graph of y = sin x° y O x P The point marke

  4. Q23

    November 2024 · Paper 3H

    5 marksA11 Quadratic graphs and turning pointsA12 Recognising and sketching graphs
    The whole paper ↗
    November 2024 Paper 3H, question 23: Sketch the graph of 2 – 6px – 7 where p > 0 y = x showing the coordinates of the turning point, in terms of p, and the coordinates of the intercept with the y-a

  5. Q12

    June 2024 · Paper 1H

    3 marksA12 Recognising and sketching graphs
    The whole paper ↗
    June 2024 Paper 1H, question 12: Here are some graphs. y y y A B C x x x O O O y y y D E F x x x O O O y y y G H J x x x O O O Write down the letter of the graph that could have the equation (i

  6. Q22

    June 2024 · Paper 1H

    4 marksA12 Recognising and sketching graphs
    The whole paper ↗
    June 2024 Paper 1H, question 22: (a) Sketch the graph of y = sin x° for 0  x  360 y O x 90 180 270 360 (b) Solve the equation 2 sin x° = –1 for 0  x  360

  7. Q19

    November 2023 · Paper 1H

    3 marksA12 Recognising and sketching graphsA13 Graph transformations
    The whole paper ↗
    November 2023 Paper 1H, question 19: Here is the graph of y = sin x° for –180  x  180 y 1 O x –180 –90 90 180 –1 (a) Use the graph to find estimates for the solutions of sin x° = 0.3 for –180  x

  8. Q19

    June 2023 · Paper 3H

    1 markA12 Recognising and sketching graphs
    The whole paper ↗
    June 2023 Paper 3H, question 19: Sana needs to draw the graph of y = 3 x for 0  x  4 She draws the graph shown on the grid. y 90 80 70 60 50 40 30 20 10 x O 1 2 3 4 5 Write down one thing San

  9. Q9

    November 2022 · Paper 1H

    4 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2022 Paper 1H, question 9: (a) Complete the table of values for y = 6x − x3 −3 −2 −1 0 1 2 3 x 9 4 −9 y (b) On the grid, draw the graph of y = 6x − x3 for values of x from −3 to 3 y 10 8

  10. Q21

    November 2022 · Paper 1H

    2 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2022 Paper 1H, question 21: y O x P The diagram shows a sketch of part of the curve with equation y = cos x° P is a minimum point on the curve. Write down the coordinates of P. ( , )

  11. Q18

    November 2021 · Paper 2H

    4 marksA12 Recognising and sketching graphsA13 Graph transformations
    The whole paper ↗
    November 2021 Paper 2H, question 18: Here is a graph of y = sin x° for 0  x  360 y 1 O 90 180 270 x 360 –1 (a) Using this graph, find estimates of all four solutions of sin x° = 0.6 for 0  x  7

  12. Q8

    November 2021 · Paper 3H

    2 marksR14 Gradient as a rate of changeA12 Recognising and sketching graphs
    The whole paper ↗
    November 2021 Paper 3H, question 8: (a) Using the axes below, sketch a graph to represent the statement y is directly proportional to x y O x (b) Using the axes below, sketch a graph to represent

  13. Q3

    November 2020 · Paper 1H

    2 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2020 Paper 1H, question 3: The diagram shows four graphs. y y O O x x Graph A Graph B y y O O x x Graph C Graph D Each of the equations in the table is the equation of one of the graphs.

  14. Q4

    November 2020 · Paper 2H

    4 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2020 Paper 2H, question 4: (a) Complete the table of values for y = 5 – x3 x –2 –1 0 1 2 y 6 (b) On the grid below, draw the graph of y = 5 – x3 for values of x from –2 to 2 y 14 12 10 8

  15. Q21

    November 2019 · Paper 1H

    5 marksA11 Quadratic graphs and turning pointsA12 Recognising and sketching graphs
    The whole paper ↗
    November 2019 Paper 1H, question 21: Sketch the graph of y = 2x2 – 8x – 5 showing the coordinates of the turning point and the exact coordinates of any intercepts with the coordinate axes.

  16. Q5

    November 2019 · Paper 2H

    2 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2019 Paper 2H, question 5: Here are six graphs. A B C y y y O O O x x x D E F y y y O O O x x x Write down the letter of the graph that could have the equation (a) y = x3 (b) y = 1 x

  17. Q17

    November 2019 · Paper 3H

    4 marksA18 Quadratic equationsA12 Recognising and sketching graphs
    The whole paper ↗
    November 2019 Paper 3H, question 17: Here is the graph of y = x2 – 3 y 10 8 6 4 2 O x –4 –3 –2 –1 1 2 3 4 –2 –4 Use the graph to find estimates for the solutions to the equation x2 – 2x – 2 = 0 You

  18. Q17

    June 2019 · Paper 3H

    2 marksA12 Recognising and sketching graphs
    The whole paper ↗
    June 2019 Paper 3H, question 17: Here are four graphs. Graph A Graph B f(x) f(x) O O x x Graph C Graph D f(x) f(x) O O x x The graphs represent four different types of function f. Match each de

  19. Q14

    November 2018 · Paper 2H

    2 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2018 Paper 2H, question 14: On the grid, sketch the curve with equation y = 2x Give the coordinates of any points of intersection with the axes. y O x

  20. Q11

    November 2018 · Paper 3H

    2 marksA12 Recognising and sketching graphs
    The whole paper ↗
    November 2018 Paper 3H, question 11: Sketch the graph of y = tan x° for 0 - x - 360 y 0 x 90 180 270 360
All 24 questions on Recognising and sketching graphs, as a list
  1. June 2025, Paper 2H, Q17 (2 marks): Here is a sketch of part of the graph of y = k x where k is a positive constant. y (–1, 1.5) x O The graph passes through the point with coordinates (–1, 1.5) F
  2. June 2025, Paper 3H, Q13 (3 marks): Here are some graphs. A B C y y y O O x x O x D E F y y y O O O x x x G H y y O x O x Each equation in the table is the equation of one of the graphs. Complete
  3. November 2024, Paper 3H, Q21 (4 marks): Here is the graph of y = f (x) y y = f (x) O x (a) On the grid, draw the graph of y = −f (x) Here is a sketch of the graph of y = sin x° y O x P The point marke
  4. November 2024, Paper 3H, Q23 (5 marks): Sketch the graph of 2 – 6px – 7 where p > 0 y = x showing the coordinates of the turning point, in terms of p, and the coordinates of the intercept with the y-a
  5. June 2024, Paper 1H, Q12 (3 marks): Here are some graphs. y y y A B C x x x O O O y y y D E F x x x O O O y y y G H J x x x O O O Write down the letter of the graph that could have the equation (i
  6. June 2024, Paper 1H, Q22 (4 marks): (a) Sketch the graph of y = sin x° for 0  x  360 y O x 90 180 270 360 (b) Solve the equation 2 sin x° = –1 for 0  x  360
  7. November 2023, Paper 1H, Q19 (3 marks): Here is the graph of y = sin x° for –180  x  180 y 1 O x –180 –90 90 180 –1 (a) Use the graph to find estimates for the solutions of sin x° = 0.3 for –180  x
  8. June 2023, Paper 3H, Q19 (1 mark): Sana needs to draw the graph of y = 3 x for 0  x  4 She draws the graph shown on the grid. y 90 80 70 60 50 40 30 20 10 x O 1 2 3 4 5 Write down one thing San
  9. November 2022, Paper 1H, Q9 (4 marks): (a) Complete the table of values for y = 6x − x3 −3 −2 −1 0 1 2 3 x 9 4 −9 y (b) On the grid, draw the graph of y = 6x − x3 for values of x from −3 to 3 y 10 8
  10. November 2022, Paper 1H, Q21 (2 marks): y O x P The diagram shows a sketch of part of the curve with equation y = cos x° P is a minimum point on the curve. Write down the coordinates of P. ( , )
  11. November 2021, Paper 2H, Q18 (4 marks): Here is a graph of y = sin x° for 0  x  360 y 1 O 90 180 270 x 360 –1 (a) Using this graph, find estimates of all four solutions of sin x° = 0.6 for 0  x  7
  12. November 2021, Paper 3H, Q8 (2 marks): (a) Using the axes below, sketch a graph to represent the statement y is directly proportional to x y O x (b) Using the axes below, sketch a graph to represent
  13. November 2020, Paper 1H, Q3 (2 marks): The diagram shows four graphs. y y O O x x Graph A Graph B y y O O x x Graph C Graph D Each of the equations in the table is the equation of one of the graphs.
  14. November 2020, Paper 2H, Q4 (4 marks): (a) Complete the table of values for y = 5 – x3 x –2 –1 0 1 2 y 6 (b) On the grid below, draw the graph of y = 5 – x3 for values of x from –2 to 2 y 14 12 10 8
  15. November 2019, Paper 1H, Q21 (5 marks): Sketch the graph of y = 2x2 – 8x – 5 showing the coordinates of the turning point and the exact coordinates of any intercepts with the coordinate axes.
  16. November 2019, Paper 2H, Q5 (2 marks): Here are six graphs. A B C y y y O O O x x x D E F y y y O O O x x x Write down the letter of the graph that could have the equation (a) y = x3 (b) y = 1 x
  17. November 2019, Paper 3H, Q17 (4 marks): Here is the graph of y = x2 – 3 y 10 8 6 4 2 O x –4 –3 –2 –1 1 2 3 4 –2 –4 Use the graph to find estimates for the solutions to the equation x2 – 2x – 2 = 0 You
  18. June 2019, Paper 3H, Q17 (2 marks): Here are four graphs. Graph A Graph B f(x) f(x) O O x x Graph C Graph D f(x) f(x) O O x x The graphs represent four different types of function f. Match each de
  19. November 2018, Paper 2H, Q14 (2 marks): On the grid, sketch the curve with equation y = 2x Give the coordinates of any points of intersection with the axes. y O x
  20. November 2018, Paper 3H, Q11 (2 marks): Sketch the graph of y = tan x° for 0 - x - 360 y 0 x 90 180 270 360
  21. June 2018, Paper 1H, Q18 (2 marks): Here is the graph of y = sin xƒIRUí- x - 180 y 4 2 –180 –90 O x 90 180 –2 –4 On the grid, sketch the graph of y = sin xƒ±IRUí- x - 180
  22. November 2017, Paper 1H, Q7 (1 mark): Brogan needs to draw the graph of y = x2 + 1 Here is her graph. y y = x2 + 1 10 9 8 7 6 5 4 3 2 1 –5 –4 –3 –2 –1 O 1 2 3 4 5 x Write down one thing that is wron
  23. June 2017, Paper 2H, Q14 (3 marks): Here are some graphs. A B C y y y O O x O x x D E F y y y O x O x O x G H I y y y O O x x O x In the table below, match each equation with the letter of its gra
  24. June 2017, Paper 3H, Q20 (4 marks): The equation of a curve is y = ax A is the point where the curve intersects the y-axis. (a) State the coordinates of A. ( , ) The equation of circle C is x2 + y

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