plumiDifferentiation from first principles: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on G.1 Differentiation from first principles, 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 7 questions on Differentiation from first principles, as a list
- June 2024, Paper 3, Q10 (5 marks): It is given that f (x) = 5x3 + x Use differentiation from first principles to prove that f ' (x) = 15x2 + 1 [5 marks]
- June 2022, Paper 1, Q4 (1 mark): The graph of y = f (x) where f (x) = ax2 + bx + c is shown in Figure 1. Figure 1 x y Which of the following shows the graph of y = f 0(x) ? Tick (3) one box. [1
- June 2022, Paper 2, Q2 (1 mark): State the value of lim h ! 0 sin (p + h) − sinp h Circle your answer. [1 mark] cos h −1 0 1
- November 2021, Paper 3, Q3 (1 mark): f (x) = 3x2 Obtain lim h ! 0 f (x + h) − f (x) h Circle your answer. [1 mark] 3h2 h x3 3(x + h)2 − 3x2 h 6x for the next question
- November 2020, Paper 3, Q6 (7 marks): The graph of y = f (x) is shown below. (2, 6) (0, 2) O (–2, –2) (–1, 0) x y 6 (a) Sketch the graph of y = f (−x) [2 marks] x O y 6 (b) Sketch the graph of y = 2
- June 2019, Paper 1, Q11 (4 marks): Jodie is attempting to use differentiation from first principles to prove that the gradient of y = sinx is zero when x = p 2 Jodie’s teacher tells her that she
- June 2018, Paper 1, Q15 (6 marks): A curve has equation y = x3 − 48x The point A on the curve has x coordinate −4 The point B on the curve has x coordinate −4 + h 15 (a) Show that the gradient of
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