plumiIntegration with partial fractions: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.08.8 Integration with partial fractions, 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 4 questions on Integration with partial fractions, as a list
- June 2025, Paper 1, Q12 (11 marks): 4 x + 12 (a) Express ( in partial fractions. [4] x 1 x )( 1 x ) + - d = y 2 4 x + The gradient of a curve is given by and the curve passes through the d x x ( 1
- June 2023, Paper 1, Q12 (10 marks): x 12 (a) Use the substitution u e - to show that 2 = c c x 7 e 8 7 u 6 - + dd d x dd d u . = x 2 2 ( e 2 ) u ( u 2 ) - + [3] e e (b) Hence show that c ln 6 x 7
- November 2020, Paper 1, Q12 (9 marks): Find the general solution of the differential equation d y 3 2 ( 2 x 3 x 11 x 6 ) y ( 20 x 35 ) . - - + = - d x Give your answer in the form y = f(x). [9]
- June 2019, Paper 3, Q6 (10 marks): y x O 2 x 1 - The diagram shows part of the curve y . = 2 x x ( 2 3 )( 1 ) + + Find the exact area of the shaded region, giving your answer in the form p q ln r
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