plumiIndices: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.02.1 Indices, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 10 questions on Indices, as a list
- June 2025, Paper 1, Q1 (8 marks): Express each of the following in the form pxq, where p and q are constants. 1 2 (a) [1] 4 x ^ h 3 (b) x x [2] 5 3 5 (c) x x [2] 2 8 # ^ h 1 5 6 3 (d) x x [3] 27
- June 2025, Paper 2, Q2 (9 marks): In this question you must show detailed reasoning. Solve the following equations. 2 3 (a) ( x 5 ) 8 [3] - = 2 3 = y (b) e 2 [2] 4 2 (c) x 3 x 4 0 [4] - - =
- June 2025, AS Paper 1, Q1 (8 marks): In this question you must show detailed reasoning. Solve the following equations. 2 - (a) x 11 = 5 [2] 6 3 (b) y 7 y 8 0 [4] + - = 10 = 3 z (c) 2 - 16 [2]
- June 2024, Paper 1, Q2 (6 marks): You are given that y is inversely proportional to x6 and z is directly proportional to the cube root 2 of y. (a) (i) Find an equation for z in terms of x and k,
- June 2024, Paper 3, Q1 (4 marks): Simplify each of the following. ^ h 3 2 3 1 (a) 2 a a - [2] # 4 2 4 x 9 - (b) ^ h [2] 2 2 x 5 x 12 2 ( x 3 ) + - +
- June 2024, AS Paper 1, Q9 (5 marks): a 7 a 5 - m n 9 Express 2 2 in the form a a , where m and n are integers and a 0 or 1 . [5] + ! a 3 a - 2
- June 2022, Paper 2, Q1 (8 marks): In this question you must show detailed reasoning. Solve the following equations. x x 1 - (a) x 0 [3] - = x 1 2 + + 8 7 (b) 1 0 [3] 6 - - = 3 x x 1 x 7 (c) 3 2
- November 2020, Paper 1, Q2 (8 marks): Simplify fully. 5 (a) 12 a 3 a [2] # 1 1 3 4 (b) ( 64 b ) ( 4 b ) - [2] # 3 2 3 c 2 c (c) 7 9 4 27 [4] - # #
- November 2020, AS Paper 1, Q6 (13 marks): In this question you must show detailed reasoning. 2 (a) Solve the inequality x x 6 0 , giving your answer in set notation. [4] 2 + - 3 3 (b) Solve the equation
- June 2018, AS Paper 1, Q1 (5 marks): In this question you must show detailed reasoning. 7 in the form a b, where a is an integer and b is a prime number. (i) Express 32 [2] 2 (ii) Express 1 in the
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