Edexcel IAL Maths questions by topic: P1 to P4, S1 and M1

The IAL Maths topics Pearson tests most

The ten topics with the most questions in recent Pearson papers, across all six units. Start here if you are short of time: these are where most marks have been.

From our own question-by-question mapping of recent Pearson papers (every unit: June 2024 to June 2025). Any topic can be examined in any series.

P1 Pure Mathematics 1 (WMA11) questions by topic

P1 is one 1 hour 30 minute written paper (75 marks), calculator permitted. Each topic page has short notes, worked examples with Edexcel-style mark schemes, the common mistakes and practice questions.

• Algebra119 practice questions · 2 worked examples · tested in 4 of the last 4 papersIndices, surds, quadratics (discriminant, completing the square), simultaneous equations, inequalities.
• Coordinate Geometry68 practice questions · 2 worked examples · tested in 3 of the last 4 papersStraight lines, gradient, midpoint, perpendicular/parallel, equation of a line, distance formula.
• Trigonometry67 practice questions · 2 worked examples · tested in 4 of the last 4 papersSine and cosine rules; area of a triangle = ½ab sin C; radian measure, arc length and sector area; graphs of sin, cos and tan and their symmetries; exact values.
• Differentiation32 practice questions · 2 worked examples · tested in 4 of the last 4 papersGradient of a tangent as a limit; differentiating xⁿ and sums of such terms; gradients, tangents and normals; the second derivative.
• Integration32 practice questions · 2 worked examples · tested in 4 of the last 4 papersIndefinite integration of xⁿ (n ≠ −1) and sums of such terms; finding the constant of integration from a point on the curve.
• Graphs and Transformations30 practice questions · 2 worked examples · tested in 4 of the last 4 papersSketching cubics, quartics and reciprocals; transformations of graphs (translations, stretches, reflections); function notation.

More for P1: P1 revision hub · P1 past papers · P1 mock exam guide · where P1 students lose marks

P2 Pure Mathematics 2 (WMA12) questions by topic

P2 is one 1 hour 30 minute written paper (75 marks), calculator permitted. Each topic page has short notes, worked examples with Edexcel-style mark schemes, the common mistakes and practice questions.

• Sequences and Series35 practice questions · 2 worked examples · tested in 4 of the last 4 papersSequences by nth term and recurrence (increasing, decreasing, periodic); arithmetic and geometric series, sum to n terms, sum to infinity (|r| < 1), Σ notation.
• Logarithms and Exponentials35 practice questions · 2 worked examples · tested in 4 of the last 4 papersaˣ and logₐx, laws of logarithms, solving aˣ = b, change of base (natural logs and eˣ are P3).
• Circles45 practice questions · 2 worked examples · tested in 4 of the last 4 papersEquation of a circle in Cartesian form, tangent-radius perpendicularity, geometric problem solving.
• Further Trigonometry46 practice questions · 2 worked examples · tested in 4 of the last 4 paperstan θ = sin θ / cos θ and sin²θ + cos²θ = 1; solving trigonometric equations in a given interval (degrees or radians), including quadratics in sin/cos/tan.
• Algebraic Methods30 practice questions · 2 worked examples · tested in 4 of the last 4 papersAlgebraic long division; factor and remainder theorems; proof by deduction, exhaustion and counter-example.
• Proof18 practice questions · 2 worked examplesProof by deduction, proof by exhaustion and disproof by counter-example, in number, algebra, inequalities and coordinate geometry (proof by contradiction is P4).
• The Binomial Expansion30 practice questions · 2 worked examples · tested in 4 of the last 4 papersBinomial expansion of (a + bx)ⁿ for positive integer n; ⁿCr notation; using expansions for approximations.
• Differentiation (stationary points)33 practice questions · 2 worked examples · tested in 4 of the last 4 papersIncreasing and decreasing functions; stationary points and their nature; optimisation problems.
• Integration (definite integrals and area)33 practice questions · 2 worked examples · tested in 4 of the last 4 papersDefinite integrals; area under a curve and between a curve and a line; the trapezium rule.

More for P2: P2 revision hub · P2 past papers · P2 mock exam guide · where P2 students lose marks

P3 Pure Mathematics 3 (WMA13) questions by topic

P3 is one 1 hour 30 minute written paper (75 marks), calculator permitted. Each topic page has short notes, worked examples with Edexcel-style mark schemes, the common mistakes and practice questions.

• Functions35 practice questions · 2 worked examples · tested in 4 of the last 4 papersDomain, range, composite and inverse functions; the modulus function y = |f(x)| and y = f(|x|); combinations of transformations.
• Numerical Methods39 practice questions · 2 worked examples · tested in 3 of the last 4 papersLocating roots of f(x) = 0 by a change of sign; approximate solutions using iteration xₙ₊₁ = g(xₙ), including cobweb/staircase diagrams. (Newton–Raphson is Further Pure 1, not P3.)
• Further Differentiation35 practice questions · 2 worked examples · tested in 4 of the last 4 papersChain, product and quotient rules; differentiating eˣ, ln x, sin x, cos x, tan x (and sec, cosec, cot); dy/dx = 1/(dx/dy).
• Further Integration35 practice questions · 2 worked examples · tested in 2 of the last 4 papersIntegrating eˣ, 1/x, sin x and cos x, including f(ax + b) forms (substitution and parts are P4).
• Algebraic Methods30 practice questions · 2 worked examples · tested in 4 of the last 4 papersSimplifying rational expressions (factorising, cancelling, algebraic division).
• Trigonometric Functions30 practice questions · 2 worked examples · tested in 3 of the last 4 paperssec, cosec and cot; arcsin, arccos, arctan and their domains/ranges; sec²θ = 1 + tan²θ and cosec²θ = 1 + cot²θ.
• Trigonometric Addition Formulae34 practice questions · 2 worked examples · tested in 4 of the last 4 papersAddition and double-angle formulae; a cos θ + b sin θ in the form R cos(θ ± α) or R sin(θ ± α).
• Exponentials and Logarithms30 practice questions · 2 worked examples · tested in 4 of the last 4 paperseˣ and ln x as inverse functions; exponential growth/decay; log-linear graphs for y = axⁿ and y = kbˣ.

More for P3: P3 revision hub · P3 past papers · P3 mock exam guide · where P3 students lose marks

P4 Pure Mathematics 4 (WMA14) questions by topic

P4 is one 1 hour 30 minute written paper (75 marks), calculator permitted. Each topic page has short notes, worked examples with Edexcel-style mark schemes, the common mistakes and practice questions.

• Vectors57 practice questions · 2 worked examples · tested in 4 of the last 4 papersVectors in 2D and 3D; magnitude, unit vectors, scalar product and angles; vector equation of a line; intersecting, parallel and skew lines.
• Partial Fractions43 practice questions · 2 worked examplesPartial fractions with distinct linear and repeated linear factors in the denominator (improper fractions by division first). Irreducible-quadratic denominators are not on the IAL specification.
• Parametric Equations15 practice questions · 2 worked examples · tested in 4 of the last 4 papersParametric equations of curves; converting between parametric and Cartesian forms; parametric differentiation; tangents and normals.
• Differential Equations13 practice questions · 2 worked examples · tested in 2 of the last 4 papersFirst-order separable differential equations, forming DEs from context, general and particular solutions.
• Proof13 practice questions · 2 worked examples · tested in 3 of the last 4 papersProof by contradiction (e.g. irrationality of √2, infinitely many primes).
• The Binomial Expansion30 practice questions · 2 worked examples · tested in 4 of the last 4 papersExpanding (a + bx)ⁿ for any rational n; validity |bx/a| < 1; using partial fractions with expansions.
• Coordinate Geometry (parametric)30 practice questions · 2 worked examplesParametric curves and conversion to Cartesian form.
• Differentiation30 practice questions · 2 worked examples · tested in 4 of the last 4 papersImplicit and parametric differentiation; connected rates of change.
• Integration30 practice questions · 2 worked examples · tested in 4 of the last 4 papersIntegration by substitution, by parts and using partial fractions; trig identities in integration; volumes of revolution about the x-axis.

More for P4: P4 revision hub · P4 past papers · P4 mock exam guide · where P4 students lose marks

S1 Statistics 1 (WST01) questions by topic

S1 is one 1 hour 30 minute written paper (75 marks), calculator permitted. Each topic page has short notes, worked examples with Edexcel-style mark schemes, the common mistakes and practice questions.

• Data and Summary Statistics70 practice questions · 2 worked examplesTypes of data (qualitative/quantitative, discrete/continuous); mean, median, mode, quartiles and percentiles; variance and standard deviation; coding; outliers. (Sampling methods are not in IAL S1.)
• Representation of Data35 practice questions · 2 worked examples · tested in 4 of the last 4 papersHistograms (frequency density), stem-and-leaf, box plots, cumulative frequency, outliers, skewness; comparing distributions.
• Probability35 practice questions · 2 worked examples · tested in 4 of the last 4 papersVenn diagrams, tree diagrams, mutually exclusive vs independent events, conditional probability P(A|B).
• Correlation and Regression35 practice questions · 2 worked examples · tested in 4 of the last 4 papersProduct-moment correlation coefficient (PMCC), scatterplots, least-squares regression line y on x.
• Discrete Random Variables35 practice questions · 2 worked examples · tested in 4 of the last 4 papersProbability distributions of discrete random variables, expectation E(X), variance Var(X), cumulative distribution functions.
• Normal Distribution13 practice questions · tested in 4 of the last 4 papersThe normal distribution N(μ, σ²); standardising with Z; using tables for probabilities and inverse problems; finding μ and/or σ.
• Measures of Location and Spread30 practice questions · 2 worked examples · tested in 4 of the last 4 papersMean, median, mode, quartiles and percentiles (incl. interpolation), variance and standard deviation; coding.

More for S1: S1 revision hub · S1 past papers · S1 mock exam guide · where S1 students lose marks

M1 Mechanics 1 (WME01) questions by topic

M1 is one 1 hour 30 minute written paper (75 marks), calculator permitted. Each topic page has short notes, worked examples with Edexcel-style mark schemes, the common mistakes and practice questions.

• Kinematics37 practice questions · 2 worked examples · tested in 4 of the last 4 papersConstant-acceleration (suvat) formulae; vertical motion under gravity; displacement-time and velocity-time graphs (variable acceleration and projectiles are M2).
• Forces and Newton's Laws45 practice questions · 2 worked examples · tested in 3 of the last 4 papersNewton's three laws, resolving forces on inclines, connected particles (pulleys), friction with coefficient μ.
• Moments43 practice questions · 2 worked examples · tested in 4 of the last 4 papersMoment of a force; equilibrium of a rod under parallel coplanar forces, including non-uniform rods and rods on the point of tilting.
• Vectors (Mechanics context)63 practice questions · 3 worked examples · tested in 4 of the last 4 papersPosition, velocity and force vectors in i, j form; magnitude and direction; r = r₀ + vt for constant velocity; resultant forces.
• Dynamics of a Particle30 practice questions · 2 worked examples · tested in 4 of the last 4 papersF = ma in a straight line; connected particles over pulleys; tow-bars; lifts.
• Statics of a Particle30 practice questions · 2 worked examples · tested in 4 of the last 4 papersResolving forces; equilibrium of a particle; friction and limiting equilibrium (F ≤ μR).
• Momentum and Impulse30 practice questions · 2 worked examples · tested in 4 of the last 4 papersMomentum, impulse = change in momentum, conservation of momentum in direct collisions.

More for M1: M1 revision hub · M1 past papers · M1 mock exam guide · where M1 students lose marks

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