plumiDifferentiation from first principles: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 7.1 Differentiation from first principles, 2010–2025, 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 Differentiation from first principles, as a list
- June 2025, AS Pure, Q12 (5 marks): y x O C Figure 5 Figure 5 shows a sketch of the curve C. The curve has a minimum turning point on the y-axis and a maximum turning point in quadrant 2. (a) On D
- June 2024, Pure 1, Q4 (3 marks): Given that y = x 2, use differentiation from first principles to show that d d y x = 2x (3)
- June 2023, Pure 1, Q12 (5 marks): y = sin x where x is measured in radians. Use differentiation from first principles to show that d d y x = cos x You may • use without proof the formula for sin
- June 2022, Pure 2, Q4 (3 marks): Given that y = 2x 2 use differentiation from first principles to show that d d y x = 4x (3)
- November 2021, AS Pure, Q5 (6 marks): O Q P(2, 10) y x Figure 1 Figure 1 shows part of the curve with equation y = 3x 2 – 2 The point P(2, 10) lies on the curve. (a) Find the gradient of the tangent
- June 2018, Pure 2, Q9 (5 marks): Given that θ is measured in radians, prove, from first principles, that ( ) d cos sin d θ θ θ = − You may assume the formula for cos (A ± B) and that as h → 0,
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