Euclid's Division Lemma, HCF & LCM by prime factorisation, irrationality proofs, and decimal expansion rules.

Degree and types, zeroes and their geometric meaning, the zero-coefficient relationships, and the Division Algorithm.

Graphical interpretation, consistency conditions, and the substitution, elimination and cross-multiplication methods.

Factorisation, completing the square, the quadratic formula, and the discriminant's role in the nature of roots.

The nth term formula, the sum of n terms formula, and the exam shortcuts that come from recognising an AP quickly.

The Basic Proportionality Theorem, similarity criteria (AA, SSS, SAS), areas of similar triangles, and Pythagoras.

The distance, section, and midpoint formulas, plus finding the area of a triangle and checking for collinearity.

All six trigonometric ratios, the standard angle table, the three Pythagorean identities, and complementary angles.

Angle of elevation and depression, and how to turn a heights-and-distances word problem into a solvable right triangle.

The tangent-perpendicular-to-radius theorem, equal tangent lengths from an external point, and circumscribed quadrilaterals.

Every solid-shape formula (cube to frustum), combination of solids, and melting-and-recasting problems.

Mean of grouped data by three methods, the mode and median formulas, and the empirical relationship between them.

The classical probability formula, the complement rule, and correctly counting outcomes for dice, coins and cards.