plumiTrigonometry: CAIE IGCSE Additional Maths questions
Every CAIE IGCSE Additional Maths exam question on 10 Trigonometry, June 2024 and the specimen papers, with its mark scheme and examiner’s report.
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![June 2024 Paper 1, question 5: (a) The diagram shows the graph of y a cos bx c , for 360 ° x 360 ° , where a, b and c are = + - G G constants. Find the values of a, b and c. [3] y 2 1 0 x – 3](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060611-jun24-05-qp.webp)
![June 2024 Paper 1, question 7: Given that 2 cot 3 x and sin y , find y in terms of x. [3] + i = i =](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060611-jun24-07-qp.webp)
![June 2024 Paper 1, question 8: b l r . 8 Solve the equation 4 sin 2 2 r 1 for r Give your answers in terms of r. [5] a - = - G a G 3 2 2](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060611-jun24-08-qp.webp)
![June 2024 Paper 2, question 10: sin x + 10 (a) Show that ( tan x sec x 2 ) can be written as . [4] + 1 sin x - (b) Hence solve the equation ( tan 3 sec 3 ) 2 6 for ° 0 180 ° . [4] i + i = G i](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060621-jun24-10-qp.webp)
![Specimen Paper 1, question 3: In this question, all angles are in radians. (a) Write down the amplitude of cos x − . [1] 2 1 3 (b) Write down the period of cos x − . [1] 2 1 3 − for –π ⩽ x ⩽](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060601-spec-03-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)
![Specimen Paper 2, question 8: x cos 2 2 8 (a) (i) Show that = 1 – sin 2x . [2] x 1 + sin 2 = 1 for 0° ⩽ x ⩽ 90° . 2 x 3 cos 2 (ii) Hence solve the equation for [4] x 1 + sin 2 , where y is i](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060602-spec-08-qp.webp)
All 9 questions on Trigonometry, as a list
- June 2024, Paper 1, Q5 (5 marks): (a) The diagram shows the graph of y a cos bx c , for 360 ° x 360 ° , where a, b and c are = + - G G constants. Find the values of a, b and c. [3] y 2 1 0 x – 3
- June 2024, Paper 1, Q7 (3 marks): Given that 2 cot 3 x and sin y , find y in terms of x. [3] + i = i =
- June 2024, Paper 1, Q8 (5 marks): b l r . 8 Solve the equation 4 sin 2 2 r 1 for r Give your answers in terms of r. [5] a - = - G a G 3 2 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 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, Q10 (8 marks): sin x + 10 (a) Show that ( tan x sec x 2 ) can be written as . [4] + 1 sin x - (b) Hence solve the equation ( tan 3 sec 3 ) 2 6 for ° 0 180 ° . [4] i + i = G i
- Specimen, Paper 1, Q3 (5 marks): In this question, all angles are in radians. (a) Write down the amplitude of cos x − . [1] 2 1 3 (b) Write down the period of cos x − . [1] 2 1 3 − for –π ⩽ x ⩽
- 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, Q8 (9 marks): x cos 2 2 8 (a) (i) Show that = 1 – sin 2x . [2] x 1 + sin 2 = 1 for 0° ⩽ x ⩽ 90° . 2 x 3 cos 2 (ii) Hence solve the equation for [4] x 1 + sin 2 , where y is i
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