YMA01 International A Level Mathematics: past papers

Prove a trigonometric inequality by contradiction.

Proof by contradiction about whether an expression is even.

Binomial expansion to x³ and proof by contradiction.

Partial fractions, then an exact integral giving a logarithm.

Integrate an exponential expression, and partial fractions leading to a logarithm.

Area under a parametric curve with partial fractions.

Binomial series, then a numerical approximation.

Binomial expansion with a fractional power: constants, validity and a coefficient.

Binomial expansion to x³ and proof by contradiction.

Points on an implicit curve, then the tangent.

Implicit differentiation and the gradient where the curve meets the y-axis.

Implicit differentiation and a normal.

Normal to a parametric curve, then its Cartesian equation.

Tangent to a parametric curve and where it meets the curve again.

Area under a parametric curve with partial fractions.

Volume of revolution with integration by parts, and a composite solid.

Exact volume of a solid of revolution about the x-axis.

Volume of revolution using a substitution.

Integration by the substitution u = tan x.

Integrate an exponential expression, and partial fractions leading to a logarithm.

Exact definite integral with a trigonometric substitution.

Area under a parametric curve with partial fractions.

Volume of revolution using a substitution.

Volume of revolution with integration by parts, and a composite solid.

Integration by parts between limits.

Rate of change of the radius of a melting sphere.

Rate of change for an expanding sphere, and a differential equation for water depth.

Solve a differential equation with an initial condition.

Rate of change for an expanding sphere, and a differential equation for water depth.

Separable differential equation, long-term limit and a time.

Partial fractions, then an exact integral giving a logarithm.

Rate of change for an expanding sphere, and a differential equation for water depth.

Separable differential equation, long-term limit and a time.

Lines in vector form: coordinates, an angle and points giving a set triangle area.

Position vectors and perpendicular vectors.

Vector equation of a line and unknown coordinates from an angle.

Lines in vector form: coordinates, an angle and points giving a set triangle area.

Position vectors and perpendicular vectors.

Vector equation of a line and unknown coordinates from an angle.

Lines in vector form: coordinates, an angle and points giving a set triangle area.

Vector equations of lines, a point on a line and a triangle area.

Vector equations of lines, a point on a line and a triangle area.