The laws of indices, fractional and negative powers, and how to simplify and rationalise surds — the algebra everything else is built on.
Sketching parabolas, completing the square, the quadratic formula and the discriminant — the most-tested topic on P1.
Solving simultaneous equations (including a line meeting a curve), and linear and quadratic inequalities with the right set notation.
Recognising the standard curves and transforming them — translations, stretches and reflections of y = f(x).
Distance, midpoint and gradient; the equation of a straight line; and the conditions for parallel and perpendicular lines.
The sine and cosine rules, the area of a triangle, radian measure with arcs and sectors, the trig graphs, identities and solving equations.
The gradient function and power rule, tangents and normals, and finding and classifying stationary points.
Integrating powers of x, the constant of integration, definite integrals and finding the area under a curve.