plumiIntegration by substitution: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 8.6 Integration by substitution, 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 9 questions on Integration by substitution, as a list
- June 2025, Pure 1, Q13 (5 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Show that x x x ( ) 2 1 2 25 3 0 2 d (
- June 2025, Pure 1, Q16 (7 marks): O 1 C R x y 3 Figure 5 Figure 5 shows a sketch of the curve C with equation y = 1 4 2 2 x x − 0 < x < 2 The region R, shown shaded in Figure 5, is bounded by C,
- June 2025, Pure 2, Q15 (13 marks): R y x P Q O –1 1 Figure 5 In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Figure 5 sho
- June 2024, Pure 1, Q13 (8 marks): (a) Given that a is a positive constant, use the substitution x = a sin 2 θ to show that 1 2 2 2 2 0 0 1 d sin 2 d 2 π a x a x x a θ θ (4) (b) Hence use algebra
- June 2023, Pure 2, Q13 (13 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Find the first three term
- November 2021, Pure 2, Q12 (7 marks): (a) Use the substitution u = 1 + x to show that x x 1 0 16 + ∫ dx = 2 1 3 ( ) u u p q − ∫ du where p and q are constants to be found. (3) (b) Hence show that x
- November 2020, Pure 1, Q10 (10 marks): (a) Use the substitution x = u2 + 1 to show that 3 1 3 2 1 6 3 2 5 10 d d x x x u u u p q − ( ) + − ( ) = + ( ) ∫ ∫ where p and q are positive constants to be f
- June 2019, Pure 2, Q14 (15 marks): (a) Use the substitution u í h to show that dh h 4 − íOQ|í h |í h + k where k is a constant (6) A team of scientists is studying a species of
- June 2018, Pure 1, Q13 (7 marks): Show that 2 2 32 15 2 2 0 2 x x x + = + ( ) ∫ d (7)
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