YMA01 International A Level Mathematics: past papers
158 papers from 2014 to 2025, with 170 questions sorted by syllabus topic.
Algebra and functions WMA11 · 20 questions
Indices and surds6
Write expressions with fractional and negative powers in the form kxⁿ.
Calculus with an expression in powers of x.
Work with indices, rewrite an equation by substitution and solve the quadratic.
Index laws and a surd equation, rationalising the answer.
Write an expression using indices, then differentiate.
Expand surds, rationalise a denominator and a proof.
Quadratics, simultaneous equations and inequalities11
A quadratic in x³, then the range of k giving no real roots.
Work with indices, rewrite an equation by substitution and solve the quadratic.
Sketch a curve with an asymptote, then the range of a constant for two intersections.
Complete the square, a maximum point, trigonometric graph features and a region by inequalities.
Where two quadratic curves meet, and the condition for one meeting point.
A line meeting a quadratic, and a region described with inequalities.
Sketch a cubic and find when an equation has distinct roots.
Solve a quadratic inequality.
Perimeter and area of a rectangle leading to simultaneous equations.
Complete the square and sketch the quadratic.
A region bounded by lines, described with inequalities.
Curve sketching and transformations7
Find a cubic from given facts, sketch curves and find where they meet.
Describe graph transformations and find an exact intersection.
Find a function from its derivative and a point, then transform a point.
Sketch a curve with an asymptote, then the range of a constant for two intersections.
Sketch transformations of y = f(x) with intercepts.
Sketch a cubic and find when an equation has distinct roots.
Complete the square and sketch the quadratic.
Coordinate geometry in the (x, y) plane WMA11 · 5 questions
Gradient, length, midpoint and equations of lines3
A perpendicular line, where two lines meet, and a distance to the origin.
Line through two points, a point at a given distance and a triangle area.
A region bounded by lines, described with inequalities.
Parallel and perpendicular lines3
A perpendicular line, where two lines meet, and a distance to the origin.
Gradients and the equation of a perpendicular line through a point.
A quadratic curve, gradients and perpendicular lines.
Trigonometry WMA11 · 9 questions
Sine rule, cosine rule and area3
Sector and triangle in radians: an angle, then area and perimeter.
Angles, areas and arc lengths in radians for a badge design, and its perimeter.
Sector area, trigonometry in radians and a composite area.
Radians, arcs and sectors1
Sector and triangle in radians: an angle, then area and perimeter.
Graphs and transformations4
Points on a cosine graph and the number of solutions of trigonometric equations.
Complete the square, a maximum point, trigonometric graph features and a region by inequalities.
Trigonometric graph: maximum point and shifts of sin x.
Trigonometric graphs and their transformations.
Arc length and sector area3
Angles, areas and arc lengths in radians for a badge design, and its perimeter.
Sector area, trigonometry in radians and a composite area.
Arc length, sector area and the perimeter and area of a garden plan.
Graphs of sine, cosine and tangent3
Points on a cosine graph and the number of solutions of trigonometric equations.
Trigonometric graph: maximum point and shifts of sin x.
Trigonometric graphs and their transformations.
Segments, chords and composite shapes5
Sector and triangle in radians: an angle, then area and perimeter.
Angles, areas and arc lengths in radians for a badge design, and its perimeter.
Sector area, trigonometry in radians and a composite area.
Area of a circle segment and a related rate of change.
Arc length, sector area and the perimeter and area of a garden plan.
Differentiation WMA11 · 8 questions
Gradients and the power rule1
A quadratic curve, gradients and perpendicular lines.
Differentiating powers of x3
Differentiate a power curve and find where the gradient takes a given value.
Differentiate a curve and use a tangent condition to find a constant.
Write an expression using indices, then differentiate.
Gradients, rates of change and second derivatives2
A tangent from a derivative with an unknown, a second derivative, then integrate to find f(x).
First and second derivatives of a cubic and an unknown constant.
Tangents and normals4
A tangent from a derivative with an unknown, a second derivative, then integrate to find f(x).
Differentiate a curve and use a tangent condition to find a constant.
Normal at a point, then integrate f′(x).
A tangent, then integrate to find f(x).
Integration WMA11 · 6 questions
Integrating powers of x2
Integrate an expanded expression in powers of x and simplify.
Integrate powers of x.
Finding a curve from its gradient4
A tangent from a derivative with an unknown, a second derivative, then integrate to find f(x).
Find a function from its derivative and a point, then transform a point.
Normal at a point, then integrate f′(x).
A tangent, then integrate to find f(x).