Pure Mathematics

Construct and understand the structure of mathematical proof, including deduction, exhaustion, counterexample, and contradiction.

Solve inequalities, manipulate surds and indices, and use proportional relationships.

Understand polynomials, function notation, composite, inverse and modulus functions, and modelling.

Apply graph transformations and use stationary points of inflection when curve sketching.

Work with curves, circles and parametric equations.

Understand sequences, arithmetic and geometric series, sigma notation, and modelling with sequences.

Exact values, inverse trigonometric functions, radians, small-angle approximations, secant/cosecant/cotangent.

Understand exponential functions and logarithms, solve equations, and reduce relationships to linear form.

Differentiation, its applications, integration techniques and differential equations.

Locate roots by sign change; fixed-point iteration; Newton–Raphson; trapezium rule.