YMA01 International A Level Mathematics: past papers
158 papers from 2014 to 2025, with 170 questions sorted by syllabus topic.
Proof WMA12 · 3 questions
Deduction, exhaustion and counterexample3
Proof by exhaustion about divisibility.
Counterexample about irrational numbers, and a proof about even numbers and multiples of 4.
Prove an inequality and give a counterexample.
Algebra and functions WMA12 · 3 questions
Polynomials: division, factor and remainder theorems3
Factor and remainder theorems, then polynomial division.
Factor and remainder theorems on a cubic, then factorise fully.
Remainder and factor theorems, factorise a cubic and count real roots.
Coordinate geometry in the (x, y) plane WMA12 · 3 questions
The equation of a circle3
Circle from a diameter, then the point nearest the x-axis.
A line through a midpoint and the centre, then the equation of the circle.
Circle centre and radius, and two circles that do not meet.
Tangents, chords and intersections2
A line through a midpoint and the centre, then the equation of the circle.
Circle centre and radius, and two circles that do not meet.
Sequences and series WMA12 · 8 questions
Binomial expansion3
Binomial expansion terms, then a coefficient to find an unknown.
Binomial expansion and choosing x for an approximation.
Binomial expansion and a coefficient in a product.
Arithmetic progressions3
Geometric series sum and a bound on a term, and the greatest sum of an arithmetic series.
Number of terms and sum of an arithmetic series.
Arithmetic series: first term, difference and smallest n for a sum.
Geometric progressions3
Geometric series sum and a bound on a term, and the greatest sum of an arithmetic series.
Common ratio and first term of a geometric series from partial and infinite sums.
Geometric models and when two models are equal.
Sum to infinity1
Common ratio and first term of a geometric series from partial and infinite sums.
Exponentials and logarithms WMA12 · 3 questions
Laws of logarithms2
Trapezium rule for a logarithmic function, and log laws to find a constant.
Solve a logarithmic equation using the laws of logarithms.
Exponential equations and inequalities1
Solve a logarithmic equation and find where exponential curves meet exactly.
Logarithmic equations2
Solve a logarithmic equation and find where exponential curves meet exactly.
Solve a logarithmic equation using the laws of logarithms.
Trigonometry WMA12 · 3 questions
Trigonometric identities3
Solve a tan equation in radians and a trigonometric equation in degrees.
Prove a trigonometric identity and solve an equation in an interval.
Solve a trigonometric equation and a sinusoidal temperature model.
Solving trigonometric equations3
Solve a tan equation in radians and a trigonometric equation in degrees.
Prove a trigonometric identity and solve an equation in an interval.
Solve a trigonometric equation and a sinusoidal temperature model.
Differentiation WMA12 · 5 questions
Stationary points and increasing functions2
Turning point, an x-intercept and the area of a region under a curve.
Stationary point, then an equal-area condition.
Optimisation and rates of change3
Model the surface area of a container and minimise it.
Optimise the dimensions of an open water tank with calculus.
Area of a circle segment and a related rate of change.
Integration WMA12 · 6 questions
The trapezium rule3
Trapezium rule, then use it to estimate related integrals.
Trapezium rule for a logarithmic function, and log laws to find a constant.
Sketch an exponential curve and use the trapezium rule.
Areas under and between curves3
Area between a curve and a line segment.
Turning point, an x-intercept and the area of a region under a curve.
Stationary point, then an equal-area condition.