plumiDifferentiation from first principles: OCR MEI A‑Level Maths questions
OCR MEI A-Level Maths past-paper questions on 7.1 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 10 questions on Differentiation from first principles, as a list
- June 2025, Paper 3, Q8 (3 marks): The diagram below shows the graph of y as a function of x. Point D is the fixed point on the graph where x 10 . = Point E is the point on the graph where x 10 +
- June 2025, AS Paper 2, Q12 (4 marks): 12 The equation of a curve is ( ) f x 3 x 2 x . = + (a) Determine an expression for the gradient of the chord joining the points ^ h and ^ h. Express your answe
- June 2024, Paper 1, Q6 (4 marks): 6 Given that ( )x f 2 x + , show from first principles that 3 f ( )x 4 x . [4] l = =
- June 2024, Paper 3, Q10 (3 marks): The diagram below shows the curve y f ( ) x . = y x 0 –4 –3 –2 –1 1 2 3 4 Sketch the graph of the gradient function, y f ( ) x , on the copy of the diagram in t
- June 2022, AS Paper 1, Q12 (6 marks): x2 12 Below is a faulty argument that appears to show that the gradient of the curve y at the point = (3, 9) is 1. Consider the chord joining (3, 9) to the poin
- November 2021, Paper 3, Q4 (3 marks): x c m - x 4 The diagram shows points A and B on the curve y . = 4 The x-coordinate of A is 1 and the x-coordinate of B is 1.1. y B A x O (a) Find the gradient o
- November 2020, Paper 1, Q12 (9 marks): 12 A function is defined by ( )x f x - . x = x h x (a) By considering ( f ) f ( ) + - 2 , show from first principles that f ( )x 3 x 1 . [4] l = - h (b) Sketch
- November 2020, AS Paper 1, Q5 (4 marks): 5 Fig. 5.1 shows part of the curve y x2 . P is the point (1, 1) and Q is the point on the curve with = x-coordinate 1 +h. y Q P x O Fig. 5.1 Table 5.2 shows, fo
- November 2020, AS Paper 1, Q7 (6 marks): In this question you must show detailed reasoning. 3 2 A curve has equation y 4 x 6 x 9 x + . 4 = - - (a) Sketch the gradient function for this curve, clearly i
- June 2019, AS Paper 1, Q10 (7 marks): In this question you must show detailed reasoning. 3 2 3 (a) Sketch the gradient function for the curve y 24 x x x . [5] = - - 3 2 3 (b) Determine the set of va
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