A-Level Maths Help
Every chapter of the A-Level Maths specification — Pure, Statistics, Mechanics — with worked examples and an embedded calculator where useful.
A-Level Maths post-2017 is linear and split across Pure (~⅔) and Applied (Statistics + Mechanics, ~⅓). The four boards (Edexcel/Pearson, AQA, OCR, MEI) cover the same content with slightly different question styles.
- Algebraic fractionsSimplify, add, multiply rational expressions.
- Partial fractionsDecompose into sum of simpler fractions. Y13.
- Binomial expansion(a+b)n, including rational n. Y13.
- Sequences and seriesArithmetic, geometric; sigma notation; sum to n.
- Exponentials and logarithmsex, ln, change of base, models.
- Coordinate geometryStraight-line equations, intersections, parallel/perp.
- Equation of a circle(x-a)² + (y-b)² = r².
- Parametric equationsx = f(t), y = g(t). Y13.
- Trig identitiessin²+cos²=1; tan = sin/cos; reciprocal.
- Solving trig equations0° ≤ x < 360° or 0 ≤ x < 2π.
- R-formula (a sin + b cos)Convert a sin x + b cos x to R sin(x + α).
- Double-angle formulaesin 2x = 2 sin x cos x; cos 2x; tan 2x.
- DifferentiationFrom first principles, polynomial, with rules.
- Product rule(uv)' = u'v + uv'.
- Quotient rule(u/v)' = (u'v − uv')/v².
- Chain rule(f(g(x)))' = f'(g)·g'.
- IntegrationPower rule; definite integrals as area.
- Integration by parts∫u dv = uv − ∫v du. Y13.
- Integration by substitutionReverse chain rule. Y13.
- Numerical methodsNewton-Raphson; trapezium rule. Y13.
- Vectors (A-Level)2D and 3D; magnitude; scalar product. Y12-13.
- ProofBy deduction, contradiction, exhaustion. Y13.
- SamplingRandom, systematic, stratified, opportunity, quota.
- Probability (A-Level)Conditional, independence, tree diagrams, Venn.
- Discrete distributionsRandom variables; expected value E(X); Var(X).
- Binomial distributionX ~ B(n, p). P(X = r) = nCr p^r q^(n-r).
- Normal distributionX ~ N(μ, σ²). Z-scores, probabilities.
- Hypothesis testingH0, H1, p-value, significance.
- Correlation and regressionPearson r; regression line y on x.
- Z-scoresStandardise: z = (x − μ)/σ.
- SUVAT (constant acceleration)Five kinematics equations.
- Kinematics graphsDisplacement-time, velocity-time graphs.
- Calculus methods (kinematics)v = ds/dt, a = dv/dt, s = ∫v dt.
- Newton's laws of motionF = ma, action-reaction, inertia.
- Forces in equilibriumResolving in two directions; resultant zero.
- FrictionF ≤ μR; static vs kinetic. Y13.
- Connected particlesPulleys, lifts, cars and trailers.
- Projectiles2D motion under gravity. Y13.
- MomentsM = Fd; equilibrium of rigid bodies. Y13.
- Momentum and impulsep = mv; impulse I = Ft; conservation. Y13.