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Straight-line graphs: OCR GCSE Maths questions

Every OCR GCSE Maths exam question on A9 Straight-line graphs, 2017–2025, with its mark scheme and examiner’s report.

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921 questions

  1. Q5

    June 2025 · Paper 4

    4 marksA9 Straight-line graphsA3 Expressions, equations, formulae and identities
    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 - -

  2. Q7

    June 2025 · Paper 5

    6 marksA19 Simultaneous equationsA9 Straight-line graphs
    The whole paper ↗
    June 2025 Paper 5, question 7: The graph of the line x y 3 is shown on this grid. + = y 5 4 3 2 1 x 0 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 (a) By drawing a suitable line on the grid, solve

  3. Q10

    November 2024 · Paper 5

    3 marksA10 Gradients and interceptsA9 Straight-line graphs
    The whole paper ↗
    November 2024 Paper 5, question 10: A straight line has equation y 4 x 9 . = + (a) Write down the gradient of the line. (a) (b) Casey says the graph of y 4 x 9 passes through the point (3, 23). =

  4. Q16

    November 2024 · Paper 5

    7 marksA22 InequalitiesA9 Straight-line graphs
    The whole paper ↗
    November 2024 Paper 5, question 16: In the diagram below, the shaded region is a parallelogram. The parallelogram can be identified by four inequalities. Two of the inequalities are y 6 and y x .

  5. Q20

    November 2023 · Paper 4

    6 marksA16 Equation of a circle and tangentsA9 Straight-line graphs
    The whole paper ↗
    November 2023 Paper 4, question 20: The diagram shows a circle, centre the origin, with the tangent to the circle at the point (4, 2). y 20 (4, 2) x O - 20 20 - 20 (a) Write down the equation of t

  6. Q12

    November 2023 · Paper 5

    2 marksA9 Straight-line graphs
    The whole paper ↗
    November 2023 Paper 5, question 12: Write down an equation for the line that is parallel to y 3 x 5 and passes through the point = - (0, 1).

  7. Q17

    June 2023 · Paper 5

    4 marksA9 Straight-line graphs
    The whole paper ↗
    June 2023 Paper 5, question 17: A rhombus is drawn on a coordinate grid. 1 One diagonal of the rhombus has equation y x 3 . = + 2 The other diagonal passes through the point (1, 7). Find the e

  8. Q17

    November 2022 · Paper 4

    3 marksA9 Straight-line graphs
    The whole paper ↗
    November 2022 Paper 4, question 17: Find the equation of the line through (4, 5) that is perpendicular to y 2 3 . x = -

  9. Q15

    November 2022 · Paper 6

    8 marksA22 InequalitiesA9 Straight-line graphs
    The whole paper ↗
    November 2022 Paper 6, question 15: The region R is shown on this grid. A is the point (0, 3) and B is the point (3, 4.5). y 6 B 4 A R 2 x 0 2 4 6 (a) Show that an equation of the straight line th

  10. Q19

    June 2022 · Paper 5

    7 marksA16 Equation of a circle and tangentsA9 Straight-line graphs
    The whole paper ↗
    June 2022 Paper 5, question 19: The graph below shows a circle with centre (0, 0) and equation x2 + y2 = 169. y 13 x -13 O 13 -13 (a) Show that the point (-12, 5) lies on the circumference of

  11. Q13

    November 2021 · Paper 6

    4 marksA9 Straight-line graphs
    The whole paper ↗
    November 2021 Paper 6, question 13: A straight line passes through the point (8, 1) and is perpendicular to the line y 4 x 2 . = - Find the equation of the line, giving your answer in the form y m

  12. Q7

    November 2020 · Paper 4

    3 marksA9 Straight-line graphsA10 Gradients and intercepts
    The whole paper ↗
    November 2020 Paper 4, question 7: This graph shows part of a straight line. y 10 8 6 4 2 x 0 -4 -3 -2 -1 1 2 3 4 -2 -4 -6 -8 -10 -12 (a) Show that the gradient of the line is 2.5. (b) Write down

  13. Q14

    November 2019 · Paper 4

    5 marksA16 Equation of a circle and tangentsA9 Straight-line graphs
    The whole paper ↗
    November 2019 Paper 4, question 14: The diagram shows a circle with centre (0, 0) and a tangent at the point (–12, 16). y Not to scale (–12, 16) x O The tangent crosses the y-axis at the point (0,

  14. Q18

    November 2019 · Paper 5

    6 marksA22 InequalitiesA9 Straight-line graphs
    The whole paper ↗
    November 2019 Paper 5, question 18: The graph of y 3 6 13 is drawn on the grid. x + = y 5 4 3 2 1 x -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 The region R satisfies these inequalities. 3 6 13 2 3 y x y x x

  15. Q8

    June 2019 · Paper 6

    4 marksA9 Straight-line graphs
    The whole paper ↗
    June 2019 Paper 6, question 8: The graph shows two parallel lines, Line A and Line B. y Line A Line B Not to scale x 0 Line A has equation y 6 x 7 . = + Line B passes through the point (4, 26

  16. Q18

    November 2018 · Paper 4

    5 marksA9 Straight-line graphs
    The whole paper ↗
    November 2018 Paper 4, question 18: P is the point (0, -1) and Q is the point (5, 9). Find the equation of the line through P that is perpendicular to the line PQ.

  17. Q18

    June 2018 · Paper 5

    9 marksA9 Straight-line graphsA19 Simultaneous equations
    The whole paper ↗
    June 2018 Paper 5, question 18: (a) A straight line passes through the point (0, 6) and is perpendicular to y 4 x 5 . = - Find the equation of this line, giving your answer in the form y mx c

  18. Q5

    June 2018 · Paper 6

    10 marksA9 Straight-line graphsG11 Geometry on coordinate axes
    The whole paper ↗
    June 2018 Paper 6, question 5: The diagram shows a straight line that passes through points A and B, and a curve that passes through points P and Q. y Not to scale P (-4, 12) Q B (4, 5) A (0,

  19. Q17

    November 2017 · Paper 6

    8 marksA16 Equation of a circle and tangentsA9 Straight-line graphs
    The whole paper ↗
    November 2017 Paper 6, question 17: The diagram shows a circle, centre the origin. y 10 5 x 0 –10 –5 5 10 –5 –10 (a) Write down the equation of the circle. (a) (b) Point P has coordinates (8, –6).

  20. Q5

    June 2017 · Paper 6

    6 marksA9 Straight-line graphs
    The whole paper ↗
    June 2017 Paper 6, question 5: y Not to scale A (-4, 6) B (8, 3) x O (a) (i) Find the gradient of line AB. (a)(i) (ii) Find the equation of line AB. (ii) (b) Point P has coordinates (0, -2).
All 20 questions on Straight-line graphs, as a list
  1. June 2025, Paper 4, Q5 (4 marks): (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 - -
  2. June 2025, Paper 5, Q7 (6 marks): The graph of the line x y 3 is shown on this grid. + = y 5 4 3 2 1 x 0 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 (a) By drawing a suitable line on the grid, solve
  3. November 2024, Paper 5, Q10 (3 marks): A straight line has equation y 4 x 9 . = + (a) Write down the gradient of the line. (a) (b) Casey says the graph of y 4 x 9 passes through the point (3, 23). =
  4. November 2024, Paper 5, Q16 (7 marks): In the diagram below, the shaded region is a parallelogram. The parallelogram can be identified by four inequalities. Two of the inequalities are y 6 and y x .
  5. November 2023, Paper 4, Q20 (6 marks): The diagram shows a circle, centre the origin, with the tangent to the circle at the point (4, 2). y 20 (4, 2) x O - 20 20 - 20 (a) Write down the equation of t
  6. November 2023, Paper 5, Q12 (2 marks): Write down an equation for the line that is parallel to y 3 x 5 and passes through the point = - (0, 1).
  7. June 2023, Paper 5, Q17 (4 marks): A rhombus is drawn on a coordinate grid. 1 One diagonal of the rhombus has equation y x 3 . = + 2 The other diagonal passes through the point (1, 7). Find the e
  8. November 2022, Paper 4, Q17 (3 marks): Find the equation of the line through (4, 5) that is perpendicular to y 2 3 . x = -
  9. November 2022, Paper 6, Q15 (8 marks): The region R is shown on this grid. A is the point (0, 3) and B is the point (3, 4.5). y 6 B 4 A R 2 x 0 2 4 6 (a) Show that an equation of the straight line th
  10. June 2022, Paper 5, Q19 (7 marks): The graph below shows a circle with centre (0, 0) and equation x2 + y2 = 169. y 13 x -13 O 13 -13 (a) Show that the point (-12, 5) lies on the circumference of
  11. November 2021, Paper 6, Q13 (4 marks): A straight line passes through the point (8, 1) and is perpendicular to the line y 4 x 2 . = - Find the equation of the line, giving your answer in the form y m
  12. November 2020, Paper 4, Q7 (3 marks): This graph shows part of a straight line. y 10 8 6 4 2 x 0 -4 -3 -2 -1 1 2 3 4 -2 -4 -6 -8 -10 -12 (a) Show that the gradient of the line is 2.5. (b) Write down
  13. November 2019, Paper 4, Q14 (5 marks): The diagram shows a circle with centre (0, 0) and a tangent at the point (–12, 16). y Not to scale (–12, 16) x O The tangent crosses the y-axis at the point (0,
  14. November 2019, Paper 5, Q18 (6 marks): The graph of y 3 6 13 is drawn on the grid. x + = y 5 4 3 2 1 x -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 The region R satisfies these inequalities. 3 6 13 2 3 y x y x x
  15. June 2019, Paper 6, Q8 (4 marks): The graph shows two parallel lines, Line A and Line B. y Line A Line B Not to scale x 0 Line A has equation y 6 x 7 . = + Line B passes through the point (4, 26
  16. November 2018, Paper 4, Q18 (5 marks): P is the point (0, -1) and Q is the point (5, 9). Find the equation of the line through P that is perpendicular to the line PQ.
  17. June 2018, Paper 5, Q18 (9 marks): (a) A straight line passes through the point (0, 6) and is perpendicular to y 4 x 5 . = - Find the equation of this line, giving your answer in the form y mx c
  18. June 2018, Paper 6, Q5 (10 marks): The diagram shows a straight line that passes through points A and B, and a curve that passes through points P and Q. y Not to scale P (-4, 12) Q B (4, 5) A (0,
  19. November 2017, Paper 6, Q17 (8 marks): The diagram shows a circle, centre the origin. y 10 5 x 0 –10 –5 5 10 –5 –10 (a) Write down the equation of the circle. (a) (b) Point P has coordinates (8, –6).
  20. June 2017, Paper 6, Q5 (6 marks): y Not to scale A (-4, 6) B (8, 3) x O (a) (i) Find the gradient of line AB. (a)(i) (ii) Find the equation of line AB. (ii) (b) Point P has coordinates (0, -2).

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