plumiIntegration: CAIE A‑Level Further Maths questions
Every CAIE A-Level Further Maths exam question on 2.4 Integration, June 2024 and the specimen papers, with its mark scheme and examiner’s report.
Find questions56
![June 2024 Paper 2, question 4: = y ln 3 4 It is given that, for n H 0 , I sec h n x d x . n 0 (a) Show that, for n 2 , H ` j b 3 l n - 2 b 4 l ` j n 1 I n 2 I . [5] - = + - n 5 5 n - 2 d ` j](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/923121-jun24-04-qp.webp)
![June 2024 Paper 2, question 7: (a) Use the substitution u 1 x 2 to find = + y x d x . [2] 1 x 2 + (b) Find the solution of the differential equation d y x x y x 2 sinh - 1 x , - = d = ` j. gi](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/923121-jun24-07-qp.webp)
![Specimen Paper 2, question 2: > 1 2 Find the exact value of d x . [6] 3 4 x − 4 x 2 + 0](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/923102-spec-02-qp.webp)
![Specimen Paper 2, question 5: , for 0 ⩽ t ⩽ 2. 5 The curve C has parametric equations x = et – 4t + 3, y = 8e t 2 (a) Find, in terms of e, the length of C. [5] 9 (b) Find, in terms of π and](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/923102-spec-05-qp.webp)
All 6 questions on Integration, as a list
- June 2024, Paper 2, Q4 (8 marks): = y ln 3 4 It is given that, for n H 0 , I sec h n x d x . n 0 (a) Show that, for n 2 , H ` j b 3 l n - 2 b 4 l ` j n 1 I n 2 I . [5] - = + - n 5 5 n - 2 d ` j
- June 2024, Paper 2, Q5 (11 marks): y x 0 1 2 n 1 1 - n n n The diagram shows the curve with equation y 2 x x 2 for 0 x G , together with a set of n 1 = - G 1 . rectangles of width n y 1 ` j (a) B
- June 2024, Paper 2, Q7 (12 marks): (a) Use the substitution u 1 x 2 to find = + y x d x . [2] 1 x 2 + (b) Find the solution of the differential equation d y x x y x 2 sinh - 1 x , - = d = ` j. gi
- Specimen, Paper 2, Q2 (6 marks): > 1 2 Find the exact value of d x . [6] 3 4 x − 4 x 2 + 0
- Specimen, Paper 2, Q4 (8 marks): y x 0 1 2 3 n − 1 n 1 The diagram shows the curve with equation y = x 2 for x > 0, together with a set of (n – 1) rectangles of unit width. (a) By considering t
- Specimen, Paper 2, Q5 (10 marks): , for 0 ⩽ t ⩽ 2. 5 The curve C has parametric equations x = et – 4t + 3, y = 8e t 2 (a) Find, in terms of e, the length of C. [5] 9 (b) Find, in terms of π and
Questions, mark schemes and examiner’s reports are © Cambridge University Press & Assessment, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every CAIE A-Level Further Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.