YMA01 International A Level Mathematics: past papers
158 papers from 2014 to 2025, with 170 questions sorted by syllabus topic.
Algebra and functions WMA13 · 7 questions
Modulus graphs and equations3
A modulus function: vertex, an inequality and the range of k for two intersections.
Sketch transformed modulus graphs and solve a modulus equation.
Modulus graph, a modulus inequality and a transformation.
Functions, domain and range3
Composite functions, range, an inverse and solving f⁻¹(x) = f(x).
Intercept and stationary point of a logarithmic curve, then a range after a transformation.
Inverse functions, show a function is increasing, and the range of a composite.
Composite functions3
Composite functions, range, an inverse and solving f⁻¹(x) = f(x).
Inverse and composite of a rational function, then transformations of a point.
Inverse functions, show a function is increasing, and the range of a composite.
Modulus inequalities2
A modulus function: vertex, an inequality and the range of k for two intersections.
Modulus graph, a modulus inequality and a transformation.
One-one and inverse functions3
Composite functions, range, an inverse and solving f⁻¹(x) = f(x).
Inverse and composite of a rational function, then transformations of a point.
Inverse functions, show a function is increasing, and the range of a composite.
Transformations of graphs3
Inverse and composite of a rational function, then transformations of a point.
Sketch transformed modulus graphs and solve a modulus equation.
Modulus graph, a modulus inequality and a transformation.
Trigonometry WMA13 · 5 questions
Reciprocal functions and their identities1
Solve trigonometric equations in radians and degrees.
Compound-angle formulae3
Prove a tangent identity, then solve an equation in an interval.
Solve trigonometric equations in radians and degrees.
Compound angle identities and a trigonometric equation.
Double-angle formulae3
Prove a tangent identity, then solve an equation in an interval.
Solve trigonometric equations in radians and degrees.
Trigonometric identities, R-form, and the maximum value.
The R-form (harmonic form)2
Write a sine–cosine combination as R cos(x + α), then its minimum.
Trigonometric identities, R-form, and the maximum value.
Exponentials and logarithms WMA13 · 5 questions
The functions eˣ and ln x1
An exponential cooling model: initial value, asymptote, a time and a rate.
Exponential models and linear forms5
Turn a straight-line log–log graph into a power law.
Cooling model: find constants and when the cooling rate takes a value.
A logarithmic model: initial value and time to reach a target.
An exponential cooling model: initial value, asymptote, a time and a rate.
Log graph of a model, showing N = abᵗ.
Differentiation WMA13 · 10 questions
Derivatives of eˣ, ln x and trigonometric functions4
Cooling model: find constants and when the cooling rate takes a value.
Intercepts of a trigonometric curve, a second derivative, and a normal and tangent.
Intercept and stationary point of a logarithmic curve, then a range after a transformation.
Differentiate a trigonometric curve, show a gradient form and find an exact point.
The product and quotient rules3
Show a rational form of f(x) and differentiate it.
Where a rational function is increasing.
A projectile model: exact root, maximum and iteration.
The chain rule2
Differentiate a trigonometric curve, show a gradient form and find an exact point.
A curve given by an equation in x and y: gradient, normal and a triangle area.
Stationary points and tangents6
A stationary point, an iteration formula and a root to 3 decimal places.
Intercepts of a trigonometric curve, a second derivative, and a normal and tangent.
Where a rational function is increasing.
Intercept and stationary point of a logarithmic curve, then a range after a transformation.
A normal by differentiation and an area by integration.
A curve given by an equation in x and y: gradient, normal and a triangle area.
Integration WMA13 · 4 questions
Integrating eˣ, 1/x and trigonometric functions2
A trigonometric integral and an algebraic integral.
A normal by differentiation and an area by integration.
Integrating (ax + b)ⁿ1
A trigonometric integral and an algebraic integral.
Exact definite integrals and logarithms2
Find constants in a split fraction, then integrate to a logarithm.
Rewrite a rational function and integrate to a logarithm.
Numerical methods WMA13 · 3 questions
Locating roots: sketches and sign changes2
A stationary point, an iteration formula and a root to 3 decimal places.
Locate a root of a trigonometric function and use an iteration.
Fixed-point iteration3
A stationary point, an iteration formula and a root to 3 decimal places.
Locate a root of a trigonometric function and use an iteration.
A projectile model: exact root, maximum and iteration.