The laws of indices including negative and fractional powers, and simplifying and rationalising surds.
Solving quadratics, completing the square, the discriminant, and quadratic graphs.
Linear and quadratic inequalities, and representing solutions.
Solving linear simultaneous equations and one linear with one quadratic.
Sketching standard curves and applying transformations to y = f(x).
Gradients, equations of lines, parallel and perpendicular lines, distance and midpoint.
The equation of a circle, finding the centre and radius, and tangents and chords.
Trig ratios and exact values, the sine and cosine rules, and the area of a triangle.
The key identities, solving trig equations in a range, and using the graphs.
Differentiation from first principles and by rule, gradients, tangents and normals.
Increasing and decreasing functions, stationary points, and optimisation.
Indefinite and definite integration, the constant of integration, and area under a curve.