plumiDifferentiation from first principles: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.07.1 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 2025, Paper 3, Q6 (12 marks): The compound angle formulae for sin A ( B ) and sin A ( B ) are + - sin ( A B ) sin A cos B cos A sin B and + = + sin ( A B ) sin A cos B cos A sin B . - = - (a
- June 2023, Paper 1, Q3 (7 marks): 3 (a) Given that ( ) f x x 2 x , use differentiation from first principles to show that f ( )x 2 x 2 . l = + = + [4] d = y (b) The gradient of a curve is given
- June 2023, AS Paper 1, Q3 (4 marks): The diagram shows the graph of y f( ) x , where f( )x is a quadratic function of x. = A copy of the diagram is given in the Printed Answer Booklet. y x (a) On t
- June 2022, AS Paper 2, Q8 (11 marks): + 8 (a) The quadratic polynomial ax bx , where a and b are constants, is denoted by ( ) f x . Use differentiation from first principles to determine, in terms o
- November 2021, Paper 2, Q7 (4 marks): Differentiate cos x with respect to x, from first principles. [4]
- November 2021, AS Paper 2, Q4 (5 marks): - is denoted by f (x). 4 The quadratic polynomial x 2 3 Use differentiation from first principles to determine the value of f ′(2). [5]
- June 2019, Paper 1, Q6 (6 marks): 2 6 Let ( )x f 2 x 3 x . Use differentiation from first principles to show that f ( )x 6 x 3 . [6] = + l = +
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