plumiGraphs of functions and curve sketching: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on B.7 Graphs of functions and curve sketching, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 6 questions on Graphs of functions and curve sketching, as a list
- June 2025, Paper 3, Q9 (5 marks): (a) Describe a sequence of two transformations which maps the graph with equation y = 1 x onto the graph with equation y = 3 x – 4 [2 marks] 9 (b) State the equ
- June 2024, Paper 1, Q11 (5 marks): It is given that f (x) = x(x – a)(x – 6) where 0 < a < 6 11 (a) Sketch the graph of y = f (x) on the axes below. [3 marks] y x O 11 (b) Sketch the graph of y =
- June 2023, Paper 3, Q6 (9 marks): (a) Sketch the curve with equation y = x2(2x + a) where a > 0 [3 marks] O y x 6 (b) The polynomial p(x) is given by p(x) = x2(2x + a) + 36 6 (b) (i) It is given
- June 2022, Paper 1, Q11 (10 marks): The polynomial p(x) is given by p(x) = x3 + (b + 2)x2 + 2(b + 2)x + 8 where b is a constant. 11 (a) Use the factor theorem to prove that (x + 2) is a factor of
- June 2022, Paper 2, Q8 (5 marks): (a) Sketch the graph of y = 1 x2 [2 marks] x y 8 (b) The graph of y = 1 x2 can be transformed onto the graph of y = 9 x2 using a stretch in one direction. Beth
- June 2019, Paper 2, Q7 (10 marks): (a) Sketch the graph of any cubic function that has both three distinct real roots and a positive coefficient of x3 [2 marks] x y 7 (b) The function f (x) is de
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