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Quadratic graphs and turning points: OCR GCSE Maths questions

Every OCR GCSE Maths exam question on A11 Quadratic graphs and turning points, 2017–2025, with its mark scheme and examiner’s report.

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921 questions

  1. Q23

    June 2025 · Paper 4

    7 marksA4 Simplifying, expanding and factorisingA11 Quadratic graphs and turning points
    The whole paper ↗
    June 2025 Paper 4, question 23: (a) Write this expression in its simplest factorised form. 2 2 ( x 4 )( x 4 ) x ( x 5 ) + - - - You must show your working. (a) (b) Use your answer to part (a)

  2. Q15

    June 2025 · Paper 5

    5 marksA11 Quadratic graphs and turning points
    The whole paper ↗
    June 2025 Paper 5, question 15: (a) Write x 6 x 5 in the form ( x a ) b . + - - (a) 2 (b) Write down the coordinates of the turning point of y x 6 x 5 . = - + (b) ( , )

  3. Q10

    November 2024 · Paper 4

    6 marksA11 Quadratic graphs and turning points
    The whole paper ↗
    November 2024 Paper 4, question 10: Here is a table of values for y x x 8 . = - - -4 -3 -2 -1 0 1 2 3 4 x -2 -6 -8 -8 -6 -2 y 12 4 4 2 for -4 (a) Draw the graph of y x x 8 x 4 . = - - G G y 12 10

  4. Q15

    June 2024 · Paper 4

    10 marksA18 Quadratic equationsA11 Quadratic graphs and turning points
    The whole paper ↗
    June 2024 Paper 4, question 15: (a) Solve by factorisation. 2 + 3 x 10 x 8 0 - = (a) x = or x = 2 + 2 (b) Write x 8 x 11 in the form ( x a ) b . + + - (b) 2 (c) (i) Write down the coordinates

  5. Q7

    June 2023 · Paper 6

    4 marksA18 Quadratic equationsA11 Quadratic graphs and turning points
    The whole paper ↗
    June 2023 Paper 6, question 7: The diagram shows the graph of y 2 , where k is an integer. kx x = - + y 4 3 2 1 x 0 -1 1 2 3 4 -1 -2 -3 (a) Show that k 3 . = 2 (b) Use the graph to solve x 3

  6. Q20

    June 2023 · Paper 6

    7 marksA11 Quadratic graphs and turning pointsA4 Simplifying, expanding and factorising
    The whole paper ↗
    June 2023 Paper 6, question 20: (a) Write ( 2 5 )( 4 ) in the form ( 2 ) . x x x a b - + + - You must show your working. (a) (b) Charlie, Dev and Eve all attempt to sketch the graph of y ( 2 x

  7. Q18

    November 2022 · Paper 5

    8 marksA18 Quadratic equationsA11 Quadratic graphs and turning points
    The whole paper ↗
    November 2022 Paper 5, question 18: (a) By factorising, find the roots of y 18 77 . x x = + + (a) x = and x = 2 2 (b) (i) Write y 18 77 in the form ( ) . x x y x a b = + + = + - (b)(i) y = 2 (ii)

  8. Q8

    June 2022 · Paper 4

    6 marksA11 Quadratic graphs and turning points
    The whole paper ↗
    June 2022 Paper 4, question 8: Here is a table of values for y 2 2 . x x = + - -4 -3 -2 -1 x 0 1 2 -2 -3 -2 y 6 1 1 6 2 for -4 G x G 2. (a) Draw the graph of y x 2 x 2 = + - y 7 6 5 4 3 2 1 -

  9. 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

  10. Q19

    June 2022 · Paper 6

    5 marksA18 Quadratic equationsA11 Quadratic graphs and turning points
    The whole paper ↗
    June 2022 Paper 6, question 19: (a) Write x 8 9 in the form x . x a b + - - (a) (b) Use your answer from part (a) to solve. 2 - 8 9 0 x x + = Give your answers in exact form. You must show you

  11. Q14

    November 2021 · Paper 4

    4 marksA11 Quadratic graphs and turning points
    The whole paper ↗
    November 2021 Paper 4, question 14: Find the coordinates of the turning point of the graph of y 6 17 . x x = + + ( , )

  12. Q19

    November 2020 · Paper 5

    7 marksA11 Quadratic graphs and turning pointsA18 Quadratic equations
    The whole paper ↗
    November 2020 Paper 5, question 19: (a) Write x 10 22 in the form ( ) . x x a b + - - (a) 2 (b) Sketch the graph of y 10 22 . x x = - + Show clearly the coordinates of any turning points and the v

  13. Q19

    November 2020 · Paper 6

    7 marksA18 Quadratic equationsA11 Quadratic graphs and turning points
    The whole paper ↗
    November 2020 Paper 6, question 19: The graph of y 2 3 9 is drawn below. x x = + - y 11 10 9 8 7 6 5 4 3 2 1 x 0 -3 -2 -1 1 2 3 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 2 + (a) Use the graph to solve x 2 3

  14. 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

  15. 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

  16. Q10

    November 2018 · Paper 4

    2 marksA18 Quadratic equationsA11 Quadratic graphs and turning points
    The whole paper ↗
    November 2018 Paper 4, question 10: Here is the graph of y 6 . x x = + - y 6 5 4 3 2 1 x –4 –3 –2 –1 0 1 2 3 –1 –2 –3 –4 –5 –6 –7 2 + Use the graph to solve the equation x 6 0 . x - = x = or x =

  17. Q18

    November 2018 · Paper 5

    10 marksA18 Quadratic equationsA11 Quadratic graphs and turning points
    The whole paper ↗
    November 2018 Paper 5, question 18: (a) (i) Write x 4 16 in the form ( ) . x x a b - + - (a)(i) 2 + (ii) Solve the equation x 4 16 0 . x - = Give your answers in surd form as simply as possible. (

  18. Q15

    June 2018 · Paper 4

    7 marksA11 Quadratic graphs and turning pointsA13 Graph transformations
    The whole paper ↗
    June 2018 Paper 4, question 15: (a) Write x2 – 8x + 25 in the form (x – a)2 + b. (a) (b) Write down the coordinates of the turning point of the graph of y = x2 – 8x + 25. (b) ( , ) (c) Hence d

  19. Q16

    November 2017 · Paper 4

    5 marksA11 Quadratic graphs and turning points
    The whole paper ↗
    November 2017 Paper 4, question 16: (a) Write x 6 20 in the form ( ) . x x a b + - + (a) 2 (b) Write down the turning point of the graph of y 6 20 . x x = - + (b) ( , )

  20. Q16

    June 2017 · Paper 4

    3 marksA11 Quadratic graphs and turning pointsA4 Simplifying, expanding and factorising
    The whole paper ↗
    June 2017 Paper 4, question 16: Write x 10 x 16 in the form x a b . + + +
All 22 questions on Quadratic graphs and turning points, as a list
  1. June 2025, Paper 4, Q23 (7 marks): (a) Write this expression in its simplest factorised form. 2 2 ( x 4 )( x 4 ) x ( x 5 ) + - - - You must show your working. (a) (b) Use your answer to part (a)
  2. June 2025, Paper 5, Q15 (5 marks): (a) Write x 6 x 5 in the form ( x a ) b . + - - (a) 2 (b) Write down the coordinates of the turning point of y x 6 x 5 . = - + (b) ( , )
  3. November 2024, Paper 4, Q10 (6 marks): Here is a table of values for y x x 8 . = - - -4 -3 -2 -1 0 1 2 3 4 x -2 -6 -8 -8 -6 -2 y 12 4 4 2 for -4 (a) Draw the graph of y x x 8 x 4 . = - - G G y 12 10
  4. June 2024, Paper 4, Q15 (10 marks): (a) Solve by factorisation. 2 + 3 x 10 x 8 0 - = (a) x = or x = 2 + 2 (b) Write x 8 x 11 in the form ( x a ) b . + + - (b) 2 (c) (i) Write down the coordinates
  5. June 2023, Paper 6, Q7 (4 marks): The diagram shows the graph of y 2 , where k is an integer. kx x = - + y 4 3 2 1 x 0 -1 1 2 3 4 -1 -2 -3 (a) Show that k 3 . = 2 (b) Use the graph to solve x 3
  6. June 2023, Paper 6, Q20 (7 marks): (a) Write ( 2 5 )( 4 ) in the form ( 2 ) . x x x a b - + + - You must show your working. (a) (b) Charlie, Dev and Eve all attempt to sketch the graph of y ( 2 x
  7. November 2022, Paper 5, Q18 (8 marks): (a) By factorising, find the roots of y 18 77 . x x = + + (a) x = and x = 2 2 (b) (i) Write y 18 77 in the form ( ) . x x y x a b = + + = + - (b)(i) y = 2 (ii)
  8. June 2022, Paper 4, Q8 (6 marks): Here is a table of values for y 2 2 . x x = + - -4 -3 -2 -1 x 0 1 2 -2 -3 -2 y 6 1 1 6 2 for -4 G x G 2. (a) Draw the graph of y x 2 x 2 = + - y 7 6 5 4 3 2 1 -
  9. 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
  10. June 2022, Paper 6, Q19 (5 marks): (a) Write x 8 9 in the form x . x a b + - - (a) (b) Use your answer from part (a) to solve. 2 - 8 9 0 x x + = Give your answers in exact form. You must show you
  11. November 2021, Paper 4, Q14 (4 marks): Find the coordinates of the turning point of the graph of y 6 17 . x x = + + ( , )
  12. November 2020, Paper 5, Q19 (7 marks): (a) Write x 10 22 in the form ( ) . x x a b + - - (a) 2 (b) Sketch the graph of y 10 22 . x x = - + Show clearly the coordinates of any turning points and the v
  13. November 2020, Paper 6, Q19 (7 marks): The graph of y 2 3 9 is drawn below. x x = + - y 11 10 9 8 7 6 5 4 3 2 1 x 0 -3 -2 -1 1 2 3 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 2 + (a) Use the graph to solve x 2 3
  14. 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
  15. 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
  16. November 2018, Paper 4, Q10 (2 marks): Here is the graph of y 6 . x x = + - y 6 5 4 3 2 1 x –4 –3 –2 –1 0 1 2 3 –1 –2 –3 –4 –5 –6 –7 2 + Use the graph to solve the equation x 6 0 . x - = x = or x =
  17. November 2018, Paper 5, Q18 (10 marks): (a) (i) Write x 4 16 in the form ( ) . x x a b - + - (a)(i) 2 + (ii) Solve the equation x 4 16 0 . x - = Give your answers in surd form as simply as possible. (
  18. June 2018, Paper 4, Q15 (7 marks): (a) Write x2 – 8x + 25 in the form (x – a)2 + b. (a) (b) Write down the coordinates of the turning point of the graph of y = x2 – 8x + 25. (b) ( , ) (c) Hence d
  19. November 2017, Paper 4, Q16 (5 marks): (a) Write x 6 20 in the form ( ) . x x a b + - + (a) 2 (b) Write down the turning point of the graph of y 6 20 . x x = - + (b) ( , )
  20. June 2017, Paper 4, Q16 (3 marks): Write x 10 x 16 in the form x a b . + + +
  21. 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
  22. June 2017, Paper 6, Q7 (5 marks): (a) Complete the table for y x 2 x . = - -1 0 1 2 3 4 x -1 3 0 0 3 y for -1 2 (b) Draw the graph of y 2 4 . x x x = - G G y 10 9 8 7 6 5 4 3 2 1 x 0 -1 1 2 3 4

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