Completing the square, the quadratic formula, the discriminant, solving quadratic equations and inequalities, and sketching parabolas.
Domain and range, one-one functions, composite and inverse functions, and graph transformations.
Lines, gradients, midpoints and distances, parallel and perpendicular lines, and the equation of a circle.
Radians, conversion between radians and degrees, and the arc length and sector area formulae.
Trig graphs, exact values, the identities, solving trigonometric equations, and the sine and cosine rules.
The binomial expansion, arithmetic progressions, and geometric progressions including sum to infinity.
The derivative, the power, chain, product and quotient rules, tangents and normals, and stationary points.
Integration as the reverse of differentiation, the constant of integration, definite integrals, and area under curves.
The laws of logarithms, exponential and log functions, the number e, and using logs to solve equations and linearise data.
Differentiating trig functions, implicit and parametric differentiation, and integration by substitution and by parts.
Locating roots by sign change, iterative methods, and vectors in two and three dimensions including the scalar product.
Forming and solving first-order differential equations by separating variables, and the algebra and geometry of complex numbers.
Displacement, velocity and acceleration, the constant-acceleration (suvat) equations, motion graphs, and calculus methods for variable acceleration.
Forces, resultants and equilibrium, Newton's three laws, friction, connected particles, and momentum.
Representing and summarising data, measures of location and spread, permutations and combinations, and the rules of probability.
Discrete random variables, the binomial distribution, the normal distribution, and the normal approximation to the binomial.