plumiExponentials and logarithms: WJEC A‑Level Maths questions
Every WJEC A-Level Maths exam question on P.6 Exponentials and logarithms, 2018–2025, with its mark scheme and examiner’s report.
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![Summer 2025 AS Unit 1, question 15: 15. (a) Showing all your working, solve the following equation. log336 – 2log318 + log3180 + log3x = 2 [5] (b) Showing all your working, solve the following equ](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun25-15-qp.webp)
![Summer 2024 AS Unit 1, question 11: 3x y 11. (a) Sketch the graph of . Clearly label the coordinates of the point where the graph crosses the y-axis. [2] 3 x ( 1) y (b) On the same set of ax](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun24-11-qp.webp)
![Summer 2023 Unit 3, question 12: 2 The rate of change of a variable y with respect to x is directly proportional to y. a) Write down a differential equation satisfied by y. [1] When x = 1 and y](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun23-12-qp.webp)
![Summer 2023 AS Unit 1, question 10: Solve the following equations for values of x. 1 0 ( ) = 3 a) ln 2x + 5 [2] b) 2 5 x 1 14 [3] ( ) + log7 x = log3 81 ( ) − log7 8x2 c) 3log7 2x [6]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun23-10-qp.webp)
![Summer 2022 AS Unit 1, question 10: Showing all your working, solve the equation 2x = 53 . Give your answer correct to two 1 0 decimal places. [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun22-10-qp.webp)
![Summer 2022 AS Unit 1, question 15: 5 Solve the simultaneous equations ⎛ ⎞ ( ) − loga x2y2 ( ) + loga 9 3loga x2y ⎠⎟= loga 36 , ⎝⎜ x2y2 ( ) = 0 . loga y − loga x + 3 [8]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun22-15-qp.webp)
![Summer 2019 AS Unit 1, question 10: 0 a) Solve the following simultaneous equations. 33x × 9 y = 27 2−3x × 8−y = 1 [6] 64 b) Find the value of x satisfying the equation loga3 + 2logax – loga(x – 1](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun19-10-qp.webp)
![Summer 2018 Unit 3, question 12: Given that f is a function, 1 2 a) state the condition for f –1 to exist, i) find ff –1(x). ii) [2] The functions g and h, are given by b) g(x) = x2 – 1, h(x) =](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun18-12-qp.webp)
![Summer 2018 AS Unit 1, question 17: 7 a) Solve 2log10x = 1 + log105 – log102. [4] Solve 3 = 2e0·5x. b) [2] Express 4x – 10 × 2x in terms of y, where y = 2x. c) Hence solve the equation 4x – 10 × 2](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun18-17-qp.webp)
All 18 questions on Exponentials and logarithms, as a list
- Summer 2025, Unit 3, Q6 (8 marks): ex y 6. The diagram below shows a sketch of the curve with equation and the straight line with y 3 x equation . y x O The straight line intersects the curve
- Summer 2025, AS Unit 1, Q15 (11 marks): 15. (a) Showing all your working, solve the following equation. log336 – 2log318 + log3180 + log3x = 2 [5] (b) Showing all your working, solve the following equ
- Summer 2024, Unit 3, Q15 (5 marks): 15. Robert wants to deposit £P into a savings account. He has a choice of two accounts. • Account A offers an annual compound interest rate of 1%. • Account B o
- Summer 2024, AS Unit 1, Q11 (4 marks): 3x y 11. (a) Sketch the graph of . Clearly label the coordinates of the point where the graph crosses the y-axis. [2] 3 x ( 1) y (b) On the same set of ax
- Summer 2024, AS Unit 1, Q17 (7 marks): f x ( ) log (2 x ) 17. A function f is defined by . Another function g is defined by 10 y f x ( ) g x ( ) log (5 x ) . The diagram below shows a sketc
- Summer 2023, Unit 3, Q12 (7 marks): 2 The rate of change of a variable y with respect to x is directly proportional to y. a) Write down a differential equation satisfied by y. [1] When x = 1 and y
- Summer 2023, AS Unit 1, Q10 (11 marks): Solve the following equations for values of x. 1 0 ( ) = 3 a) ln 2x + 5 [2] b) 2 5 x 1 14 [3] ( ) + log7 x = log3 81 ( ) − log7 8x2 c) 3log7 2x [6]
- Summer 2023, AS Unit 1, Q14 (6 marks): 4 a) Two variables, x and y, are such that the rate of change of y with respect to x is proportional to y. State a model which may be appropriate for y in terms
- Summer 2022, Unit 4, Q9 (8 marks): 9 Megan wants to make some ice cubes. She fills a plastic ice cube tray with water of temperature 10°C and places it directly into the freezer. The temperature
- Summer 2022, AS Unit 1, Q1 (3 marks): 1 Write down the inverse function of y = ex. On the same set of axes, sketch the graphs of y = ex and its inverse function, clearly labelling the coordinates of
- Summer 2022, AS Unit 1, Q10 (3 marks): Showing all your working, solve the equation 2x = 53 . Give your answer correct to two 1 0 decimal places. [3]
- Summer 2022, AS Unit 1, Q15 (8 marks): 5 Solve the simultaneous equations ⎛ ⎞ ( ) − loga x2y2 ( ) + loga 9 3loga x2y ⎠⎟= loga 36 , ⎝⎜ x2y2 ( ) = 0 . loga y − loga x + 3 [8]
- Summer 2019, Unit 3, Q13 (8 marks): Wildflowers grow on the grass verge by the side of a motorway. The area populated by 1 3 wildflowers at time t years is A m2. The rate of increase of A is direc
- Summer 2019, AS Unit 1, Q10 (13 marks): 0 a) Solve the following simultaneous equations. 33x × 9 y = 27 2−3x × 8−y = 1 [6] 64 b) Find the value of x satisfying the equation loga3 + 2logax – loga(x – 1
- Summer 2019, AS Unit 1, Q11 (4 marks): Two quantities are related by the equation Q = 1.25P3. Explain why the graph of 1 1 log10Q against log10P is a straight line. State the gradient of the straight
- Summer 2018, Unit 3, Q12 (10 marks): Given that f is a function, 1 2 a) state the condition for f –1 to exist, i) find ff –1(x). ii) [2] The functions g and h, are given by b) g(x) = x2 – 1, h(x) =
- Summer 2018, AS Unit 1, Q15 (6 marks): 5 The value of a car, £V, may be modelled as a continuous variable. At time t years, the value of the car is given by V = Aekt, where A and k are constants. Whe
- Summer 2018, AS Unit 1, Q17 (11 marks): 7 a) Solve 2log10x = 1 + log105 – log102. [4] Solve 3 = 2e0·5x. b) [2] Express 4x – 10 × 2x in terms of y, where y = 2x. c) Hence solve the equation 4x – 10 × 2
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