plumiSketching and interpreting graphs: AQA Level 2 Further Maths questions
Every AQA Level 2 Further Maths exam question on 2.13 Sketching and interpreting graphs, 2021–2025, with its mark scheme and examiner’s report.
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All 14 questions on Sketching and interpreting graphs, as a list
- June 2025, Paper 1, Q5 (3 marks): Here is a sketch of y = x2 + bx + c The graph passes through (–1, 0) and (5, 0) Work out the values of b and c. b = c =
- June 2025, Paper 1, Q13 (1 mark): Here are four sketch graphs. Circle the letter of the sketch graph that represents y = 5x
- June 2025, Paper 2, Q9 (2 marks): f(x) = x2 + px x ⩽ 1 = 2p – 2 1 x x > 1 A sketch of y = f(x) is shown. Work out the value of p. p =
- June 2024, Paper 1, Q10 (5 marks): A function f is given by f(x) = – 1 2 x + 21 0 ⩽ x ⩽ 2 = ax2 + bx 2 < x ⩽ 6 A sketch of y = f(x) is shown. Work out the values of a and b. a = b =
- June 2024, Paper 2, Q7 (2 marks): The equation of a curve is y = 4 – (x – 3)2 7 (a) Circle the coordinates of the point where the curve crosses the y-axis. (–5, 0) (0, –5) (–13, 0) (0, –13) 7 (b
- June 2023, Paper 2, Q7 (3 marks): Here is a sketch of the curve y = ax2 + bx + c where a, b and c are constants. The curve intersects the x-axis at (–4, 0) and (p, 0) The turning point has x-coo
- June 2023, Paper 2, Q15 (4 marks): The function g is given by g(x) = a × bx where a and b are constants. The domain of the function is –1 ⩽ x ⩽ 2 P 1 0, 2 and Q 3 1, 2 are
- June 2022, Paper 1, Q3 (6 marks): (a) f(x) = 4 – x 0 ⩽ x < 1 = 4x – x 2 1 ⩽ x < 4 = 2x – 8 4 ⩽ x ⩽ 6 On the grid, draw the graph of y = f(x) 3 (b) g(x) = 6 – 3x Work out g–1(x). Answer
- June 2022, Paper 2, Q10 (1 mark): Here are four sketch graphs. Circle the letter of the sketch graph that represents y = 3 × 2 x
- November 2021, Paper 1, Q13 (3 marks): Here is a sketch of y = kx where k > 0 A 2, 1 316 is a point on the curve. 13 (a) Work out the value of k. Answer 13 (b) B is a point on the curve with
- November 2021, Paper 1, Q17 (3 marks): Here is the graph of y = x2 − 6x + 5 for values of x between 0 and 6 By drawing a suitable linear graph on the grid, work out approximate solutions to x2 − 7x +
- November 2021, Paper 2, Q8 (4 marks): A function f is given by f(x) = 4x x < 0 = x2 – 8x 0 ⩽ x ⩽ 8 = 16 – 2x x > 8 A sketch of y = f(x) is shown. Work out all the values of x for which f(x) = –12 An
- Specimen, Paper 2, Q5 (2 marks): Here is a sketch of y = f(x) where f(x) is a quadratic function. The graph intersects the x-axis at A (–1, 0) and B has a maximum point at (0.5, 6) y x B O A No
- Specimen, Paper 2, Q15 (4 marks): Here is a sketch of the curve x y ab− = where a and b are positive constants. (0, 3) and (2, 0.48) lie on the curve. x (2, 0.48) y O (0, 3) Not drawn accurately
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