The laws of indices, logarithms and their laws, and solving exponential and logarithmic equations.
Solving quadratics, the discriminant, completing the square, and the relationship between roots and coefficients.
Algebraic identities and partial-fraction-style manipulation, and solving linear and quadratic inequalities.
Polynomial division, the factor and remainder theorems, and solving cubic equations.
Function notation, composite and inverse functions, and sketching and transforming graphs.
Straight lines, distance and midpoint, parallel and perpendicular gradients, and the circle.
Arithmetic and geometric sequences and series, sum formulae, and the sum to infinity.
The binomial theorem for positive integer powers, binomial coefficients, and finding specific terms.
Trig ratios and exact values, the sine and cosine rules, identities, and solving trig equations.
Differentiation from first principles and by rule, gradients, and the chain, product and quotient rules.
Stationary points, maxima and minima, the second derivative, and rates of change.
Integration as the reverse of differentiation, indefinite and definite integrals, and area under a curve.
Using calculus to link displacement, velocity and acceleration, and finding distances and key moments of motion.
Matrix operations, the identity and determinant, inverses of 2×2 matrices, and transformations.
Vector notation and arithmetic, magnitude, position vectors, and using vectors in geometry.