plumiOCR A‑Level Further Maths questions by topic
Every question from every OCR A-Level Further Maths paper, 2018–2025, question by question. Filter by topic, paper or year, open the mark scheme under any question, and download a set as a PDF.
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![June 2025 Pure Core 1, question 1: J N 5 0 KK OO. 1 (a) A matrix M is given by M = 0 5 L P Describe the transformation represented by M. [2] (b) Write down the 2 # matrix that represents a rotati](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y54001-jun25-01-qp.webp?v=3)
![June 2025 Pure Core 1, question 2: - b y d in terms of x. l, find x 1 1 2 (a) Given that y cosh x [1] = d 3 - b l at the point where x 1 1 (b) Determine an equation of the normal to the curve y c](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y54001-jun25-02-qp.webp?v=3)
![June 2025 Pure Core 1, question 4: 2 4 The equation x 5 4 x 10 0 has roots a, b and c. - + = (a) Write down the values of a + , ab and abc. [2] + + + b c bc ca )2 2 2 2 2 2 2 (b) By expanding ( ,](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y54001-jun25-04-qp.webp?v=3)
![June 2025 Pure Core 1, question 10: In this question you must show detailed reasoning. (a) Use de Moivre’s Theorem to show that, if cos5 0 , i ! 5 3 tan 10 tan 5 tan - + i i i tan 5 . [4] i / 4 2](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y54001-jun25-10-qp.webp?v=3)
![June 2025 Pure Core 2, question 3: J N J N 1 3 3 3 - = - - KKK OOO and B KKK OOO. 3 Matrices A and B are given by A = 4 8 1 2 L P L P (a) Find the matrix AB. [1] (b) Verify that det ( AB ) det (](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y54101-jun25-03-qp.webp?v=3)
![June 2025 Pure Core 2, question 4: In this question you must show detailed reasoning. Determine the sum of all cube numbers from 216 to 512 000 inclusive. [4]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y54101-jun25-04-qp.webp?v=3)
![June 2025 Pure Core 2, question 7: In this question you must show detailed reasoning. 2 4 x 5 x 17 - + - (a) Express x in partial fractions. [6] 3 2 x 3 x 3 - + - y 3 2 4 x 5 x 17 - + - (b) Hence](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y54101-jun25-07-qp.webp?v=3)
![June 2025 Pure Core 2, question 10: u 10 (a) Find e - as a percentage of sinh u for the following values of u. 2 • u = 2 • u = 5 [1] (b) Find, as a percentage of sinh u, the difference between sin](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y54101-jun25-10-qp.webp?v=3)
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