plumiIntegration: CAIE A‑Level Maths questions
Every CAIE A-Level Maths exam question on 3.5 Integration, June 2024 and the specimen papers, with its mark scheme and examiner’s report.
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![June 2024 Paper 3, question 10: , show that y d 2 10 (a) Given that 2 = x tan y . [3] = d x 1 4 x 2 + 3 y (b) Hence find the exact value of 2 x tan - 1 ( 2 x ) d x . [7] 1 2](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970931-jun24-10-qp.webp)
![Specimen Paper 3, question 5: d x 2 5 (a) Show that dx x ( − tan − 1 x ) = . [2] 1 + x 2 3 (b) Show that y x tan − 1 x x d = 2 − 1 3 . [5] r 3 2 0](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970903-spec-05-qp.webp)
![Specimen Paper 3, question 9: y M x O 1 2π The diagram shows the curve y = sin2 2x cos x for 0 ⩽ x ⩽ 2 1 π, and its maximum point M. (a) Find the x-coordinate of M. [6] 17 (b) Using the subs](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970903-spec-09-qp.webp)
All 6 questions on Integration, as a list
- June 2024, Paper 3, Q8 (7 marks): Use the substitution u 1 sin x to find the exact value of = - y 3 r sin 2 x 2 d x . 1 sin x - r Give your answer in the form a b 2 where a and b are rational nu
- June 2024, Paper 3, Q10 (10 marks): , show that y d 2 10 (a) Given that 2 = x tan y . [3] = d x 1 4 x 2 + 3 y (b) Hence find the exact value of 2 x tan - 1 ( 2 x ) d x . [7] 1 2
- June 2024, Paper 3, Q11 (11 marks): In a field there are 300 plants of a certain species, all of which can be infected by a particular disease. At time t after the first plant is infected there ar
- Specimen, Paper 3, Q5 (7 marks): d x 2 5 (a) Show that dx x ( − tan − 1 x ) = . [2] 1 + x 2 3 (b) Show that y x tan − 1 x x d = 2 − 1 3 . [5] r 3 2 0
- Specimen, Paper 3, Q9 (10 marks): y M x O 1 2π The diagram shows the curve y = sin2 2x cos x for 0 ⩽ x ⩽ 2 1 π, and its maximum point M. (a) Find the x-coordinate of M. [6] 17 (b) Using the subs
- Specimen, Paper 3, Q10 (11 marks): In a chemical reaction, a compound X is formed from two compounds Y and Z. The masses in grams of X, Y and Z present at time t seconds after the start of the re
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