Exponentials and logarithms is Pure Topic 6, and it counts as AS/Year 1 content — examinable from your first assessments, not just in Year 13. Across a typical series it's worth roughly 16 of the 300 raw marks over Papers 1–3, though that figure shifts a little year to year and ignores the log and exponential steps buried inside other topics' questions.
The topic runs in sequence: exponential functions and their graphs, logarithms as the inverse of aˣ (with e and ln as the key case), the log laws, then solving aˣ = b. Most marks sit in the last two applications — reducing a curved relationship to a straight line, and modelling growth or decay — and the linearising method reappears almost unchanged in Statistics when fitting a model to data.
Because it's AS foundation material, questions rarely test logs or exponentials alone — they usually sit inside a longer modelling or data question, so an early slip can cost marks somewhere that looks unrelated.
The specification statements this topic covers. AS = Year-1 content, also assessed in the standalone AS course (8MA0); A2 = full A level only. Typical share of a 300-mark series: ≈16 marks — our estimate from the 2018–2025 papers, not an official weighting.
| Ref | Spec statement | Level |
|---|---|---|
| 6.1 | aˣ and eˣ | AS |
| 6.2 | Gradient of e^kx | AS |
| 6.3 | Logarithms as inverses | AS |
| 6.4 | Laws of logarithms | AS |
| 6.5 | Solving aˣ = b | AS |
| 6.6 | Reduction to linear form | AS |
| 6.7 | Exponential growth and decay | AS |
In linearising and growth/decay questions, examiners repeatedly note candidates finding the gradient, intercept or growth constant and stopping there. The mark is for substituting those values back into the full model, such as y = kbˣ or P = ae^(−kt), not for the bare numbers.
When a question asks for an exact solution to aˣ = b, a rounded decimal loses the mark even if it's correct to several figures. Leave the answer in log form, e.g. x = ln 7 / ln 3, unless you're told to round.
Discarding a root that makes a log's argument zero or negative needs a precise reason, not 'a log can't be negative'. State which expression is undefined and substitute the root back in to show it.
A generic 'it's just a model' earns nothing in growth/decay questions. Name the specific breakdown — a population that can't grow forever, or a concentration that can't turn negative.
log(a + b) isn't log a + log b, and log a ÷ log b isn't log(a/b). The laws only convert products, quotients and powers inside one log — never sums, and never two separate logs combined by division.
A log equation often produces two algebraic roots, but only one survives once you check the original arguments are positive — substitute each candidate back in before giving a final answer.
After taking logs of y = kbˣ or y = axⁿ, the measured gradient and intercept aren't k, b, a or n directly — write Y = mX + c first and identify what m and c stand for before touching the numbers.
In growth/decay modelling, 'initial' means t = 0, not the first data point given — substitute t = 0 directly into the model rather than reading it off a table row.
Solving aˣ = b under 'exact' instructions and rounding early throws away the accuracy mark, even when the method used to get there is otherwise correct.
We haven’t published checked questions for this topic yet — a worked sample appears here only once a question has passed every check. In the meantime you can practise in the app.
The log laws — product, quotient, power, and the special cases for negative and half-integer powers — need to be memorised outright, along with x = aⁿ ⇔ n = log_a x. Change of base and e^(x ln a) = aˣ are given in the formulae booklet, so it's knowing when to reach for them, rather than the formula itself, that's worth practising.
Calculator discipline matters: it will solve aˣ = b numerically, but 'exact' or 'using algebra' instructions mean a decimal-only answer won't score. Write down the equation before reaching for the calculator, and give a log-form answer unless told to round.
When practising linearising and growth/decay questions, finish each one properly — write the full final equation and a context-specific limitations comment rather than stopping at the constants, since that's where marks are usually lost. It's also worth revisiting this topic once you reach fitting models to data in Statistics, since the method there is the same.
All 19 topics: Edexcel A level Maths topic guides. Reference: formula booklet vs memorise and grade boundaries.
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Original questions written for the Pearson Edexcel A Level Mathematics (9MA0) specification. Not affiliated with or endorsed by Pearson.