plumiCAIE A‑Level Maths questions by topic
Every question from the CAIE AS & A Level Mathematics (9709) papers Cambridge International publishes, June 2024 and the specimen papers, question by question. Cambridge keeps its other papers on its School Support Hub, for schools. Filter by topic or paper, open the mark scheme under any question, and download a set as a PDF.
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![June 2024 Paper 3, question 1: Expand ( 3 x )( 1 2 x ) 1 in ascending powers of x, up to and including the term in x2, simplifying the + - 2 coefficients. [4]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970931-jun24-01-qp.webp)
![June 2024 Paper 3, question 2: Solve the equation ln ( x 5 ) 7 ln x . Give your answer correct to 2 decimal places. [4] - = -](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970931-jun24-02-qp.webp)
![June 2024 Paper 3, question 5: esinx 5 The equation of a curve is y for 0 x 2 r. = G G cos 2 x d and hence find the x-coordinates of the stationary points of the curve. y Find x [7] d](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970931-jun24-05-qp.webp)
![June 2024 Paper 3, question 6: (a) By sketching a suitable pair of graphs, show that the equation cosec x 1 ex - has exactly one 3 = 2 root, denoted by a, in the interval 0 1 x 1 . [2] r (b)](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970931-jun24-06-qp.webp)
![June 2024 Paper 3, question 7: (a) On a single Argand diagram sketch the loci given by the equations z 3 2i = 2 and - + w 3 2 i w 3 4 i where z and w are complex numbers. [4] - + = + - (b) He](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970931-jun24-07-qp.webp)
![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)
![June 2024 Paper 1, question 1: (a) Express y 3 2 - 12 y 15 in the form ( 3 y a ) 2 + , where a and b are constants. b [2] - + (b) Hence find the exact solutions of the equation x 3 4 12 x 2 1](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/970911-jun24-01-qp.webp)
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