plumiCalculus: CAIE IGCSE Additional Maths questions
Every CAIE IGCSE Additional Maths exam question on 14 Calculus, June 2024 and the specimen papers, with its mark scheme and examiner’s report.
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![June 2024 Paper 1, question 6: c 4 dd e 2 3 o 6 Find d x , giving your answer in exact form. [4] - 2 x - 3 ( 3 x 5 ) 2 e 2 -](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060611-jun24-06-qp.webp)
![June 2024 Paper 1, question 12: ln 3 x 12 (a) It is given that y for x 2 0 . = x 2 d y A B ln 3 x + Find . Give your answer in the form , where A and B are integers. [4] d x x 3 < ln 3 d x x (](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060611-jun24-12-qp.webp)
![Specimen Paper 1, question 6: (a) f(x) = 3e2x + 1 for x∈ℝ 6 g(x) = x + 1 for x∈ℝ (i) Write down the range of f and the range of g. [2] (ii) Find g2(0) . [1] (iii) Hence find fg2(0) . [2] 9 (](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060601-spec-06-qp.webp)
![Specimen Paper 1, question 8: J N a 8 (a) Given that y KK 2 3 − 1 OO x , where a > 1 , find the value of a. [7] 2 x + 3 + 3 x - 1 x d = ln 2 4 . 1 L P 13 d (b) (i) Find d x (6 sin3kx) , wher](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060601-spec-08-qp.webp)
![Specimen Paper 2, question 5: − r , −r to h 5 Given that y = tan x , use calculus to find the approximate change in y as x increases from 4 4 where h is small. [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060602-spec-05-qp.webp)
All 14 questions on Calculus, as a list
- June 2024, Paper 1, Q6 (4 marks): c 4 dd e 2 3 o 6 Find d x , giving your answer in exact form. [4] - 2 x - 3 ( 3 x 5 ) 2 e 2 -
- June 2024, Paper 1, Q10 (9 marks): In this question, all distances are in metres and time, t, is in seconds. A particle P is at a fixed point O at time t 0 . = The velocity, v, of P is given by v
- June 2024, Paper 1, Q11 (10 marks): The tangent to the curve y ( 3 x 1 ) 1 at the point where x = meets the coordinate axes at the 3 = - 3 points A and B. The point with coordinates ( , ) a a lies
- June 2024, Paper 1, Q12 (8 marks): ln 3 x 12 (a) It is given that y for x 2 0 . = x 2 d y A B ln 3 x + Find . Give your answer in the form , where A and B are integers. [4] d x x 3 < ln 3 d x x (
- June 2024, Paper 2, Q6 (5 marks): Variables x and y are such that y cos sin x 2 x . Use differentiation to find the approximate change in = y as x increases from 3 to 3 + , where h is small. h [
- June 2024, Paper 2, Q7 (4 marks): x 7 It is given that y mx 2 + , where m and n are non-zero constants. It is also given that n = + 2 3 d f 2 y p e d y o 2 y for all values of x. Find the values
- June 2024, Paper 2, Q11 (7 marks): In this question all lengths are in centimetres. A B x D C The diagram shows a rectangle ABCD with BC x . = The area of the rectangle is 400 cm2. Two identical
- Specimen, Paper 1, Q6 (12 marks): (a) f(x) = 3e2x + 1 for x∈ℝ 6 g(x) = x + 1 for x∈ℝ (i) Write down the range of f and the range of g. [2] (ii) Find g2(0) . [1] (iii) Hence find fg2(0) . [2] 9 (
- Specimen, Paper 1, Q8 (11 marks): J N a 8 (a) Given that y KK 2 3 − 1 OO x , where a > 1 , find the value of a. [7] 2 x + 3 + 3 x - 1 x d = ln 2 4 . 1 L P 13 d (b) (i) Find d x (6 sin3kx) , wher
- Specimen, Paper 1, Q9 (8 marks): In this question, the units are metres and seconds. − , where t ⩾ 0 . A particle P is travelling in a straight line. Its acceleration, a, away from a fixed poin
- Specimen, Paper 2, Q5 (3 marks): − r , −r to h 5 Given that y = tan x , use calculus to find the approximate change in y as x increases from 4 4 where h is small. [3]
- Specimen, Paper 2, Q6 (7 marks): . The normal to the curve at the point where 6 A curve has equation y = ln(5 – 3x) where x < 3 x = –5 , cuts the x-axis, at the point P. Find the equation of th
- Specimen, Paper 2, Q11 (8 marks): In this question, all lengths are in centimetres. y x 2 + y 2 NOT TO SCALE x The diagram shows a cone of base radius x, height y and sloping edge x 2 y 2 . The
- Specimen, Paper 2, Q12 (9 marks): y y = (9 – x)(x – 3) C(k, k – 3) y = k – 3 O A B x The diagram shows part of the curve y = (9 – x)(x – 3) and the line y = k – 3 , where k > 3 . The line throug
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