plumiLogarithms and the laws of logs: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.06.2 Logarithms and the laws of logs, 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 7 questions on Logarithms and the laws of logs, as a list
- June 2025, AS Paper 1, Q6 (7 marks): In this question you must show detailed reasoning. Solve the following equations. (a) log ( x 32 ) log ( 2 x ) log 2 2 [4] + - + = 3 3 3 c m 1 3 (b) log – [3] =
- June 2024, AS Paper 1, Q1 (3 marks): In this question you must show detailed reasoning. ` j ` j 3 2 Solve the equation ln x x , where x 2 . [3] ln 5 ln 2 0 - =
- June 2022, Paper 1, Q5 (8 marks): 2x 2x 4 5 (a) The graph of y can be transformed to the graph of y + either by a translation or = = by a stretch. (i) Give full details of the translation. [2] (
- June 2022, AS Paper 2, Q6 (12 marks): y C x O A B The shape ABC shown in the diagram is a student’s design for the sail of a small boat. a k 3 The curve AC has equation y 2 log x and the curve BC ha
- November 2020, AS Paper 2, Q2 (5 marks): k 2 Two curves have equations y ln x and y , where k is a positive constant. = = x (a) Sketch the curves on a single diagram. [3] (b) Explain how your diagram s
- November 2020, AS Paper 2, Q4 (9 marks): In this question you must show detailed reasoning. 3 2 The cubic polynomial x 6 kx 57 x 20 is denoted by f (x). It is given that ( 2 x 1 ) is a factor of + + -
- June 2018, Paper 2, Q6 (13 marks): In this question you must show detailed reasoning. ln x y A curve has equation . = x (i) Find the x-coordinate of the point where the curve crosses the x axis.
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