Grade 12

The elegant proof that links the Theorem of Pythagoras to similar triangles — a guaranteed exam question.

Master Compound Angles, Double Angles, General Solutions, Identities, and 2D/3D Problems — worth 40–50 marks in Paper 2.

Master similar triangles — understand the theorem, prove similarity correctly, use ratios for calculations, and tackle the ‘product proof’ strategy with fully worked examples.

Master the Proportionality Theorem from first principles — understand what it means, how to write ratios correctly, apply the theorem and its converse, use the Midpoint Theorem, and solve exam problems with fully worked examples.

Master the Sine Rule, Cosine Rule, Area Rule, and the common-side strategy for solving 2D and 3D problems.

Master the difference between nominal and effective interest rates — understand why they differ, derive the conversion formula, convert in both directions, and compare financial options with fully worked examples.

Master all the compound and double angle formulas — the engine behind every Grade 12 trig question.

Master the strategy for finding maximum and minimum values in real-world problems — with full worked examples.

Master the complete method for sketching cubic graphs — intercepts, turning points, inflection, and concavity.

Master finding the equation of a tangent line at any point on a curve — one of the most examined calculus topics.