How much of Edexcel A-Level Mathematics is Pure mathematics?

Pure mathematics is about two thirds of the qualification and fills Paper 1 and Paper 2, while Statistics and Mechanics share Paper 3. Every applied topic relies on pure skills such as algebra, calculus and trigonometry, so mastering pure content lifts your marks everywhere. Expect the largest share of questions, including the longest multi-step problems, to come from this content.

Which pure topics carry the most marks in Edexcel Maths?

Calculus (differentiation and integration) and algebra and functions are the heaviest, because they appear in almost every paper and underpin coordinate geometry, trigonometry and the applied modules. Trigonometry, exponentials and logarithms, and proof also recur reliably. Build fluency in algebra first, then calculus, because weak algebra costs marks throughout.

What techniques recur across the Edexcel Pure mathematics content?

Manipulating algebraic expressions and surds, completing the square, the binomial expansion, partial fractions, differentiating with the chain, product and quotient rules, integrating by substitution and by parts, solving trigonometric equations using identities, and working with logarithms. The proof topic threads through everything, since clear logical reasoning is rewarded across the paper.

What is the single most common mistake in Pure mathematics?

Sign and algebra slips in the middle of long questions, especially forgetting the constant of integration, dropping the inner derivative in the chain rule, or losing solutions when solving trigonometric equations. Edexcel rewards correct method, so show every step and check answers against the original equation.

How should I revise the Edexcel Pure mathematics content?

Work topic by topic against the specification, drilling each technique until it is automatic, then practise mixed problems under timed conditions. Always show working and state final answers clearly. Keep a list of standard results, such as derivatives and integrals of common functions and the trigonometric identities, and rehearse them until recall is instant.

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Edexcel A-Level Mathematics Pure mathematics: a complete overview of proof, algebra, calculus, trigonometry and vectors

A deep-dive Edexcel A-Level Mathematics guide to the Pure mathematics content. Covers proof, algebra and functions, coordinate geometry, sequences and series, trigonometry, exponentials and logarithms, differentiation, integration, numerical methods and vectors, with the techniques and exam patterns Edexcel repeats across Papers 1 and 2.

Generated by Claude Opus 4.822 min read9MA0Updated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

What the Pure mathematics content demands
Proof and algebra
Coordinate geometry and sequences
Trigonometry, exponentials and logarithms
Calculus
Numerical methods and vectors
How the Pure content is examined
Check your knowledge

What the Pure mathematics content demands

Pure mathematics is the backbone of Edexcel A-Level Mathematics (9MA0). It develops the algebra, calculus, trigonometry and reasoning that every other part of the course depends on. Papers 1 and 2 are both Pure mathematics papers, so this content is examined twice. The examiners test two linked skills: fluent technique with standard methods, and the judgement to choose and combine those methods in unfamiliar multi-step problems.

This guide walks through all ten pure topics in specification order, then sets out the exam patterns Edexcel repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together.

Proof and algebra

The content opens with proof: deduction, exhaustion, disproof by counter-example and contradiction, including the classic results that $\sqrt{2}$ is irrational and that there are infinitely many primes. Clear logical layout earns marks across the whole paper.

Algebra and functions is the most reused topic. You manipulate surds and indices, solve quadratics by factorising, the formula and completing the square, work with the discriminant, handle simultaneous equations and inequalities, divide polynomials and use the factor theorem, split expressions into partial fractions, sketch curves, transform graphs, and use composite and inverse functions. Weak algebra leaks marks everywhere, so it is the first thing to master.

Coordinate geometry and sequences

Coordinate geometry covers straight lines, gradients, the equation of a circle, the relationship between tangents, chords and radii, and parametric curves. Sequences and series introduces arithmetic and geometric sequences, sigma notation, the sum formulae, recurrence relations, the condition for a convergent geometric series, and the binomial expansion for any rational power.

Trigonometry, exponentials and logarithms

Trigonometry works in radians, with the arc length and sector area formulae, exact values, the Pythagorean and addition identities, the double angle formulae, the reciprocal and inverse functions, the $R$ form, and solving equations over a given interval. Exponentials and logarithms introduces the number $e$ , the natural logarithm, the laws of logarithms, solving exponential equations, and using logarithms to linearise data and model growth and decay.

Calculus

Differentiation runs from first principles to the chain, product and quotient rules, derivatives of standard functions, implicit and parametric differentiation, stationary points and their nature, and optimisation. Integration reverses this with indefinite and definite integrals, areas, standard integrals, substitution, integration by parts, partial fractions and differential equations. Calculus carries the most marks in the pure content.

Numerical methods and vectors

Numerical methods locate roots by sign change, use iteration and the Newton-Raphson method, and apply the trapezium rule, with attention to when methods fail. Vectors cover two and three dimensions, magnitude and direction, components, position vectors and geometric applications.

How the Pure content is examined

A typical Edexcel profile for Pure mathematics:

Short technique questions. Differentiating and integrating standard functions, solving quadratics and trigonometric equations, and manipulating logarithms.
Multi-step problems. Combining calculus with coordinate geometry to find tangents and areas, or trigonometry with algebra to solve equations.
Proof and reasoning. Constructing deductive and contradiction proofs and disproving statements by counter-example.
Applied calculus. Optimisation, connected rates of change, and using numerical methods when exact answers are not available.

Check your knowledge

A mix of recall and technique questions covering the Pure content. Attempt them under timed conditions, then check against the solutions.

Differentiate $y = 3x^4 - 2x$ . (2 marks)
Find $\int (6x^2 + 4)\,dx$ . (2 marks)
Solve $\sin x = \frac{1}{2}$ for $0 \le x \le 2\pi$ . (3 marks)
Solve $5^x = 30$ , giving your answer to three significant figures. (2 marks)
Find the magnitude of the vector $3\mathbf{i} - 4\mathbf{j}$ . (2 marks)
Use the trapezium rule with two strips to estimate $\int_0^2 x^2\,dx$ . (3 marks)

Solutions

Six short questions covering the Pure mathematics content.

Step 1: Q1 - Differentiating a polynomial

Differentiate each term by multiplying by the power and reducing the power by one. The constant term $0$ vanishes and the linear term $-2x$ differentiates to $-2$ .

\frac{dy}{dx} = 12x^3 - 2

Final answer: $\dfrac{dy}{dx} = 12x^3 - 2$ .

Step 2: Q2 - Integrating a polynomial

Integrate each term by increasing the power by one and dividing by the new power. A constant of integration $c$ must always be included for an indefinite integral.

\int (6x^2 + 4)\,dx = 2x^3 + 4x + c

Final answer: $2x^3 + 4x + c$ .

Step 3: Q3 - Solving a trigonometric equation in a given interval

The principal value of $\arcsin\frac{1}{2}$ is $\frac{\pi}{6}$ . The sine function is also positive in the second quadrant, so the second solution within $[0, 2\pi]$ is $\pi - \frac{\pi}{6} = \frac{5\pi}{6}$ .

x = \frac{\pi}{6} \quad \text{or} \quad x = \frac{5\pi}{6}

Final answer: $x = \dfrac{\pi}{6}$ or $x = \dfrac{5\pi}{6}$ .

Step 4: Q4 - Solving an exponential equation with logarithms

Taking logarithms of both sides converts the exponential equation to a linear one. Applying the change-of-base rule or dividing $\ln$ values gives the exact form, which is then evaluated to three significant figures.

x = \dfrac{\ln 30}{\ln 5} \approx 2.11

Final answer: $x \approx 2.11$ (to 3 significant figures).

Step 5: Q5 - Magnitude of a two-dimensional vector

The magnitude of a vector is found using Pythagoras's theorem applied to its components. Here the components are $3$ and $-4$ , and the negative sign disappears when squaring.

\left|3\mathbf{i} - 4\mathbf{j}\right| = \sqrt{3^2 + (-4)^2} = \sqrt{25} = 5

Final answer: $5$ .

Step 6: Q6 - Trapezium rule with two strips

Two strips of equal width $h = 1$ span the interval $[0, 2]$ , giving three ordinates at $x = 0, 1, 2$ . The trapezium rule formula adds the two end ordinates once and all interior ordinates twice, then multiplies by $\frac{h}{2}$ .

\text{Estimate} = \frac{1}{2} \times 1 \times (0 + 4 + 2 \times 1) = \frac{1}{2}(6) = 3

Final answer: $3$ .

Sources & how we know this

Pearson Edexcel A-Level Mathematics (9MA0) specification — Pearson Edexcel (2017)