Higher Mathematics

Gradient from an angle, perpendicular lines, and medians/altitudes in a triangle.

Generating terms, the linear recurrence relation, and when a limit exists.

Synthetic division, the factor theorem, and the discriminant.

Building and evaluating composite functions, and finding an inverse function.

How a(x), f(x)+a, f(x+a), and f(-x) each move or reshape a graph.

The laws of logarithms, and solving exponential and logarithmic equations.

The addition formulae, double angle formulae, and solving trig equations over a range.

Writing a sin(x) + b cos(x) as a single R sin(x ± α), and using it to solve equations and find max/min values.

The rule for differentiating powers of x, and what a derivative represents.

The chain rule, and differentiating sin(x), cos(x), and expressions built from them.

Stationary points, curve sketching, and optimisation problems.

Reversing differentiation, and the standard integrals for Higher.

Evaluating a definite integral, and using it to find the area under and between curves.

Components, magnitude, the section formula, and the scalar product.