A Level Maths · Pure · Year 12 and 13
Exponentials and logarithms are almost entirely Year 12 content but reappear in Year 13 calculus. The topic mixes pure technique (laws of logs, solving equations) with modelling growth and decay.
AS content is usually taught in Year 12. The full A Level adds the Year 13 content.
A curve has the equation $y = ab^x$, where $a$ and $b$ are constants and $b > 0$. The curve passes through the points $(1, 10)$ and $(3, 40)$. Find the values of $a$ and $b$.
Then practise: skills to practise · open exponentials and logarithms practice questions.
Every board examines the same A Level Maths content, set by the Department for Education. Only the paper it appears on and the section numbering differ.
| Board | Specification reference | Examined in |
|---|---|---|
| AQA 7357 | AQA section F | Paper 1, and Section A of Papers 2 and 3 |
| Edexcel 9MA0 | Edexcel topic Pure 6 | Paper 1 and Paper 2 |
| OCR A H240 | OCR reference 1.06 | Paper 1, and the pure sections of Papers 2 and 3 |
Three examples from the question bank. Every question comes with a step-by-step mark scheme (M, A and B marks) once you start practising.
State the coordinates of the point where the graph of $y = 5^{x-2} + 1$ crosses the y-axis.
Mark scheme: in the 48-hour free trial.
Sketch the graph of $y = e^{-x} + 2$. State the equation of the horizontal asymptote and the coordinates of the y-intercept.
Mark scheme: in the 48-hour free trial.
Given that $\log_2 x = p$ and $\log_2 y = q$, express $\log_2(8x^2 y^3)$ in terms of $p$ and $q$.
Mark scheme: in the 48-hour free trial.
Questions are original and written in the style of Edexcel 9MA0, and cover content that AQA and OCR examine too. They are not past-paper questions.
These skills sit in the Pure II unit of the UK A Level practice engine. Pick any mix of them, set the difficulty, and check each answer against its mark scheme.
Exponentials and logarithms can come up on these papers (from each board's paper structure). We haven't mapped individual questions yet, so open a recent paper and look for it.
| Board | Recent papers that can test it |
|---|---|
| Edexcel 9MA0 | Paper 1: June 2024, June 2023, June 2022 Paper 2: June 2024, June 2023, June 2022 |
| AQA 7357 | Paper 1: June 2023, June 2022, November 2021 Paper 2: June 2023, June 2022, November 2021 Paper 3: June 2023, June 2022, November 2021 |
| OCR H240 | Paper 1: June 2024, June 2023, June 2022 Paper 2: June 2024, June 2023, June 2022 Paper 3: June 2024, June 2023, June 2022 |
Papers are © the exam boards; each page links to the official question paper and mark scheme. All A Level Maths past papers →
Yes. Exponentials and Logarithms is part of the A Level Maths content that every board examines: AQA section F, Edexcel Pure 6, OCR 1.06. It is assessed in AQA Paper 1, and Section A of Papers 2 and 3; Edexcel Paper 1 and Paper 2; OCR A Paper 1, and the pure sections of Papers 2 and 3.
Both. The AS content, usually taught in Year 12, is: Exponential functions y = aˣ and y = eˣ, and their graphs; Logarithms, the laws of logarithms and ln x as the inverse of eˣ; Solving equations of the form aˣ = b; Exponential growth and decay models and their limitations; Using logarithmic graphs to estimate parameters in y = axⁿ and y = kbˣ. The full A Level adds: Differentiating and integrating eˣ and ln x (see the calculus pages).
Take logarithms of both sides: log y = log k + x log b. Plotting log y against x gives a straight line with gradient log b and intercept log k.
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