plumiOCR MEI A‑Level Maths questions by topic
Every question from every OCR MEI A-Level 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 Paper 1, question 1: (a) Sketch the function y 2 x 3 . [2] = - (b) In this question you must show detailed reasoning. Solve the equation x 2 3 4 - . x [3] - =](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64001-jun25-01-qp.webp?v=3)
![June 2025 Paper 1, question 2: x 25 - 2 Express ( in partial fractions. [4] 2 x x 1 )( 4 ) - -](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64001-jun25-02-qp.webp?v=3)
![June 2025 Paper 1, question 3: (a) Evaluate 4 =/ 1 r r 1 giving your answer as a fraction in its lowest terms. [1] (b) Write the sum 1 + + + + in a similar way to the series in part (a). 3 5](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64001-jun25-03-qp.webp?v=3)
![June 2025 Paper 1, question 4: The diagram shows part of a circle with centre O and radius 5 cm. The circle passes through the points A and B. The length AB is 5 cm. O A B 5cm [4] Calculate t](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64001-jun25-04-qp.webp?v=3)
![June 2025 Paper 1, question 7: In this question you must show detailed reasoning. 2 Show that the area of the finite region enclosed by the curves y x x 7 + 2 = - 125 . 2 and y x x [7] 14 9 i](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64001-jun25-07-qp.webp?v=3)
![June 2025 Paper 1, question 8: (a) Determine the two values of k for which the line y x 3 + is a tangent to the curve 5 = x2 y k kx [4] . = - - x2 (b) These values of k are used to define two](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64001-jun25-08-qp.webp?v=3)
![June 2025 Paper 1, question 10: x2 e 10 The diagram shows part of the graph of the function y + which is defined for x 2- . 1 = x 1 y 4 3 2 1 0 x –1 1 d . y (a) Find an expression for x [3] d](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64001-jun25-10-qp.webp?v=3)
![June 2025 Paper 1, question 11: The curve in the graph below is defined implicitly by ( 2 x y )( y 1 ) 6 . + - = y x d = y 2 1 ( y ) - (a) Show that . [4] d x 2 y 2 x 1 + - (b) Find the equati](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64001-jun25-11-qp.webp?v=3)
![June 2025 Paper 2, question 1: 2 1 The equation of a circle is ( x 4 ) ( y 5 ) 64 0 . - + + - = (a) State the coordinates of the centre of the circle. [1] (b) State the radius of the circle.](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64002-jun25-01-qp.webp?v=3)
![June 2025 Paper 2, question 2: Determine the coefficient of x3 in the expansion of ( 12 2 1 2 )x . [2] +](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64002-jun25-02-qp.webp?v=3)
![June 2025 Paper 2, question 4: 2 4 (a) Use the factor theorem to show that ( x 3 ) is a factor of x 4 8 x 11 x - . 3 [1] - - - 3 2 2 (b) Hence show that 4 x 8 x 11 x 3 ( x 3 )( ax b ) , where](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64002-jun25-04-qp.webp?v=3)
![June 2025 Paper 2, question 5: Prove that the sum of the first n positive odd numbers is a square number. [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64002-jun25-05-qp.webp?v=3)
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