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.
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AS content is usually taught in Year 12. The full A Level adds the Year 13 content. Sitting AS exams or mocks? See the AS Level Maths checklist.
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 | Papers 1, 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, one with its full mark scheme open. 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 7-day free trial.
Given that $y = \ln(4x^3)$, express $y$ in the form $A\ln x + B$, where $A$ and $B$ are constants to be found.
Every question here has a full worked solution. See them all →
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 7-day 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.
Revision notes: Exponentials and logarithms
The table shows the number of bacteria (in thousands) after x hours. Change a and b so that y = a·bˣ fits the data (the check wants R² of at least 0.99). What do a and b mean in this context?
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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 2025, June 2024, June 2023 Paper 2: June 2025, June 2024, June 2023 |
| AQA 7357 | Paper 1: June 2025, June 2024, June 2023 Paper 2: June 2025, June 2024, June 2023 Paper 3: June 2025, June 2024, June 2023 |
| OCR H240 | Paper 1: June 2025, June 2024, June 2023 Paper 2: June 2025, June 2024, June 2023 Paper 3: June 2025, June 2024, June 2023 |
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 Papers 1, 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.
Stretch yourself: original algebra problems at Senior level (ages 16 to 18), with hints and full solutions: Problem S90 · Problem S25 · Problem S89 · Problem S24. All 22 →
Formulas in this topic: Laws of logarithms. All formulas A–Z
Applying for maths, computer science or economics? TMUA practice on this topic: Exponential graphs and laws of logarithms · Exponential equations. TMUA preparation: notes, questions and mock papers →
Thinking about an EPQ? Maths EPQ ideas that use this topic: What makes e the natural base? · Modelling the UK population · How fast does a cup of tea cool? · all 93 ideas
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