A-Level Maths · Pure · Exponentials and logarithms · last updated 21 October 2026

Exponentials and logarithms practice questions (A-Level Maths)

This pure topic covers exponential functions and their graphs, the function e to the x and natural logarithms, the laws of logarithms, solving exponential equations, exponential models, and reducing relationships to linear form. There are no free sample questions on it yet, so this page gives 6 key terms with the formulas typeset, and a door to make an A-Level Maths-style paper on this topic from your own notes. The free exams are typeset PDFs with an answer key; the exam downloads without a signup.

Make a practice exam from your notes →Upload your notesA-Level Maths style preselected; tick "Pure · Exponentials and logarithms" on the next screen. Free to try, no card.

Sample questions

No free sample questions on exponentials and logarithms yet. The key terms below cover what A-Level Maths expects you to know for this topic; to practise it, make a paper from your notes or from the A-Level outline with the unit ticked.

Make a practice exam from your notes →Upload your notes

Key terms

The definitions and formulas A-Level Maths expects for exponentials and logarithms, typeset as they appear on the paper.

Exponential function and its graph: $y = a^x$ for $a > 0$ passes through $(0, 1)$ and has the $x$ -axis as an asymptote; it increases for $a > 1$ and decreases for $0 < a < 1$ . $y = e^x$ is the one whose gradient equals its value.
$\frac{d}{dx} e^{kx} = k e^{kx}$
Natural logarithm: The inverse of $e^x$ : $\ln x$ is the power to which $e$ must be raised to give $x$ . Its graph is the reflection of $y = e^x$ in $y = x$ , with the $y$ -axis as asymptote.
$y = \ln x \iff x = e^y, \qquad \frac{d}{dx}\ln x = \frac{1}{x}$
Laws of logarithms: The three rules for combining logs of the same base, plus the facts $\log_a a = 1$ and $\log_a 1 = 0$ . Check solutions: a log of a negative number or zero is undefined.
$\log_a xy = \log_a x + \log_a y, \quad \log_a \frac{x}{y} = \log_a x - \log_a y, \quad \log_a x^k = k\log_a x$
Solving exponential equations: Take logs of both sides and bring the power down. Equations with $a^{2x}$ and $a^x$ are quadratics in $a^x$ .
$a^x = b \;\Rightarrow\; x = \frac{\ln b}{\ln a}$
Exponential models: Growth and decay with a constant proportional rate: populations, temperature, radioactive decay. Interpret $A$ as the initial value and $k$ as the rate; comment on long-term behaviour and the model's limitations.
$N = A e^{kt}$
Reducing to linear form: Taking logs turns a power law or an exponential relationship into a straight line, so the constants can be found from the gradient and intercept of a plotted line.
$y = ax^n \Rightarrow \log y = \log a + n\log x, \qquad y = kb^x \Rightarrow \log y = \log k + x\log b$

Frequently asked questions

Are there free exponentials and logarithms practice questions for A-Level Maths?

Not as a ready-made sample yet. The key terms on this page cover what A-Level Maths expects for exponentials and logarithms. To practise it, open the generator with the A-Level Maths style, tick "Pure · Exponentials and logarithms" and the questions are written from the A-Level outline for that topic; or upload your own notes on it.

How do I make an A-Level Maths practice paper on exponentials and logarithms from my notes?

Open the create page with the A-Level Maths style preselected, tick "Pure · Exponentials and logarithms" under the units to cover (or upload your notes and slides on it), choose the question mix and time limit, and generate. You get a typeset PDF in the A-Level format with a separate answer key, in about a minute. It is free to try, no card needed.

What does A-Level Maths expect you to know about exponentials and logarithms?

This pure topic covers exponential functions and their graphs, the function e to the x and natural logarithms, the laws of logarithms, solving exponential equations, exponential models, and reducing relationships to linear form. The terms to have cold: Exponential function and its graph, Natural logarithm, Laws of logarithms, Solving exponential equations, Exponential models. Each is defined below with its formula typeset where one applies.

What is the A-Level Maths exam format?

The A-Level Maths guide explains the papers, their timing and mark allocation, with a sample question and mark scheme and the common mistakes, and links to the generator with the A-Level Maths style preselected.

Make an A-Level Maths paper on exponentials and logarithms from your notes

Open "Pick your exam" with the A-Level Maths style preselected and tick "Pure · Exponentials and logarithms", or upload your notes on it. You get a typeset paper in the A-Level format with a separate answer key.