1. Algebra and Surds | Simplifying expressions involving surds, rationalising denominators, solving equations with surd components.

2. Coordinate Geometry and Circles | Determining equations of straight lines and circles, calculating perpendicular gradients, center and radius from expanded form.

3. Calculus – Differentiation and Tangents | Differentiating polynomial functions, finding gradients of tangents, determining coordinates of points on curves using derivative values.

4. Integration and Area | Performing definite integration of algebraic expressions, calculating area between curves and the x-axis, applying limits to integrals.

5. Binomial Expansion and Logarithmic Functions | Expanding expressions using the binomial theorem for fractional powers, applying logarithmic laws to simplify and solve exponential equations.

6. Trigonometry and Proof | Proving trigonometric identities, solving trigonometric equations within a given interval, and justifying mathematical results through algebraic reasoning.