plumiRecognising and sketching graphs: AQA GCSE Maths questions
Every AQA GCSE Maths exam question on A12 Recognising and sketching graphs, 2017–2025, with its mark scheme and examiner’s report.
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All 35 questions on Recognising and sketching graphs, as a list
- June 2025, Paper 1H, Q9 (1 mark): y = x 1 Which of these values of x gives the greatest value of y ? Circle your answer. 9 20 2 5 – 80 95
- June 2025, Paper 1H, Q14 (4 marks): (a) Complete the table of values for y = 2x x –1 0 1 2 3 y 1 4 14 (b) Draw the graph of y = 2x for values of x from –1 to 3
- November 2024, Paper 1H, Q21 (3 marks): Here is a sketch of the graph of y = tan x where 0° ⩽ x ⩽ 360° You are given that tan 78.69° = 5 21 (a) Work out the other value of x where tan x = 5 and 0° ⩽ x
- November 2024, Paper 3H, Q10 (3 marks): A car will travel 60 miles. Draw a graph to show the average speed of the car for times taken between 1 hour and 6 hours. You may use the table to help you. Tim
- November 2024, Paper 3H, Q23 (3 marks): The distance of a particle from a point is d metres after t seconds. d = a × bt where a and b are constants Work out the values of a and b. a = b =
- June 2024, Paper 2H, Q14 (4 marks): A graph passes through the points (3, 15) and (7, w) 14 (a) Assume that the equation of the graph has the form y = x2 + c Work out the value of w that this woul
- November 2023, Paper 1H, Q29 (2 marks): Here are the equations of three graphs. y = sin x y = cos x y = tan x 29 (a) Which statement is true? Tick one box. y = sin x passes through (180°, –1) y = cos
- November 2023, Paper 2H, Q27 (4 marks): g(x) = a × bx where a and b are constants. g = 8 and g = 343 Work out the value of g Answer
- November 2023, Paper 3H, Q4 (1 mark): At what point does the graph y = x3 – 1 cross the y axis? Answer ( , )
- June 2023, Paper 1H, Q9 (2 marks): Erika tries to sketch the graph y = x 1 with x ≠ 0 Make two different criticisms of her sketch. Criticism 1 Criticism 2
- June 2023, Paper 3H, Q7 (4 marks): (a) Complete the table of values for y = x2 + 2x x –3 –2 –1 0 1 y 3 –1 0 7 (b) Draw the graph of y = x2 + 2x for values of x from –3 to 1
- November 2022, Paper 2H, Q16 (1 mark): Here is a sketch of a graph. Circle the possible equation of the graph. y = x2 + 1 y = x 1 + 1 y = x3 + 1 y = 1 – x2
- November 2022, Paper 3H, Q26 (2 marks): Here is a sketch of the graph of y = 5x In parts (a) and (b) the sketch of y = 5x is shown as a dashed line. 26 (a) On the axes below, sketch the graph of y = –
- June 2022, Paper 1H, Q16 (1 mark): Circle the letter of the possible sketch graph of y = x3 – 4
- June 2022, Paper 3H, Q24 (4 marks): Here is a sketch of the graphs of y = k x and y = x2 + c k and c are positive constants. Work out the value of r. r =
- November 2021, Paper 1H, Q4 (1 mark): Here is a sketch of a graph. Circle the equation of the graph. k is a constant. y = kx y = k + x y = k – x y = x k
- November 2020, Paper 1H, Q24 (1 mark): y is an obtuse angle. Which statement is true? Tick one box. sin y > 0 and cos y > 0 sin y > 0 and cos y < 0 sin y < 0 and cos y > 0 sin y < 0 and cos y < 0
- November 2020, Paper 2H, Q21 (2 marks): (a) Circle the point that is on the graph of y = 1 x (–1, 1) (0.3, 3) (0.8, 0.2) (2.5, 0.4) 21 (b) Leo wants to draw the graph of y = 2x for values of x from 0
- November 2020, Paper 2H, Q22 (1 mark): One of these is the graph of y = 1 + sin x for 0° ⩽ x ⩽ 360° Circle the letter above the correct graph.
- November 2019, Paper 2H, Q4 (1 mark): Here is the sketch of a graph. Circle the equation of the graph. y = x y = –x2 y = –x3 y = x 1
- November 2019, Paper 2H, Q19 (1 mark): Circle the word that describes the graph y = sin x periodic exponential cubic quadratic
- November 2019, Paper 3H, Q14 (3 marks): A graph has equation y = x3 + a where a is an integer. The graph passes through the point (3, 29) Draw the graph for values of x from –3 to 3
- June 2019, Paper 1H, Q24 (1 mark): f(x) = sin(x – 90°) Circle the value of f(0°) 1 0 1 2 − –1
- June 2019, Paper 2H, Q8 (2 marks): On the axes, sketch the curve y = x3 – 2 You must show the coordinates of the y-intercept.
- June 2019, Paper 3H, Q23 (2 marks): Here is a sketch of the curve y = 2x On the axes above, sketch the curve y = 3x
- November 2018, Paper 1H, Q27 (2 marks): Here is a sketch of y = cos x for values of x from 0° to 360° α° is an acute angle. cos α° = k Not drawn accurately 27 (a) Circle the value of cos (180° – α°) 1
- November 2018, Paper 3H, Q12 (1 mark): Lewis wants to draw the graph y = x3 for values of x from –2 to 2 Here is his graph. Make one criticism of his graph.
- June 2018, Paper 1H, Q25 (2 marks): Here is a sketch of the graph of y = cos x for values of x from 0° to 360° 25 (a) cos x = cos 60° Work out the value of x when 90° ⩽ x ⩽ 360° Answer degrees 25
- June 2018, Paper 3H, Q14 (3 marks): Draw the graph of y = 0.8x for values of x from 0 to 6 x 0 1 2 3 4 5 6 y
- November 2017, Paper 1H, Q29 (2 marks): Here is a sketch of y = sin x° for –360 ⩽ x ⩽ 360 29 (a) Write down the coordinates of P. Answer ( , ) 29 (b) Write down the coordinates of Q. Answer ( , )
- November 2017, Paper 2H, Q3 (1 mark): Circle the point that does not lie on the curve y = x3 − − 8 1 , 2 1 (5, 125) 9 1 , 3 1 (–1, –1)
- November 2017, Paper 2H, Q21 (4 marks): (a) Meera is using a graphical method to solve 2x2 – 3x = 0 She draws the graph of y = 2x2 and a straight line graph on the same grid. Here is the graph of y =
- November 2017, Paper 3H, Q28 (5 marks): y = p × q x – 1 where p and q are numbers. y = 10 when x = 1 y = 0.3125 when x = 6 Work out the value of y when x = 3 Answer
- June 2017, Paper 3H, Q18 (1 mark): Nick sketches the graph of y = 0.5x for x ⩾ 0 Make one criticism of his sketch.
- Specimen, Paper 1H, Q4 (1 mark): One of these graphs is a sketch of y = 1 2x Which one? Circle the correct letter. A B O y x y x O 1 1 –2 y x y x O O C D –2
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