Grade 12

Revise exponential functions, define and convert logarithms, apply log laws including product, quotient, power and change of base, solve exponential and logarithmic equations, and sketch the graph of y = logₐx.

Revise arithmetic and geometric sequences, master sigma notation, calculate arithmetic and geometric series sums, and apply the sum to infinity for convergent geometric series.

Revise simple and compound growth and decay, use logarithms to solve for n, convert between nominal and effective interest rates, and apply future value and present value annuity formulae to savings and loan problems.

Apply compound and double angle identities, prove trigonometric identities, solve trig equations, and tackle 2D and 3D problems using the sine rule, cosine rule and area rule.

Apply the Remainder and Factor Theorems, fully factorise cubic polynomials using long division, solve cubic equations and sketch cubic graphs from their factorised form.

Use the discriminant to determine the nature of roots, consolidate factorisation and the quadratic formula, solve quadratic inequalities from a sketch, tackle linear-quadratic simultaneous systems, and solve equations involving surds, exponents and algebraic fractions.

Master all circle theorems — angle at centre, angles in the same segment, angle in a semicircle, cyclic quadrilaterals, tangent theorems, and the alternate segment theorem — and apply them to riders and proofs.

Apply the distance, gradient and midpoint formulae, find the equation of a circle in standard and expanded form, determine equations of tangents at points on circles, and solve multi-step problems combining circle and line geometry.

Master limits, differentiation from first principles, rules of differentiation, equations of tangents, cubic function sketching, and optimisation using calculus.

Revise the five number summary and box and whisker diagrams, draw and interpret ogives, identify symmetric and skewed distributions, apply the 68-95-99.7 rule for the normal distribution, and analyse scatter plots with regression lines and correlation coefficients.

Apply the addition rule and complementary events, master the fundamental counting principle, calculate permutations with restrictions and repeated items, and use these counting techniques to solve combined probability problems.