Synthesis and the bridge to DP

Sets · Intersection · Union · Complement · Venn diagrams (2- and 3-set) · Sample space

Experimental & theoretical probability · Compound events · Tree diagrams · Two-way tables · Conditional probability · Mutually exclusive vs independent · Testing for independence

Definition of function & relation · Domain, range, vertical line test · Function notation · [EXT] Inverse and composite functions · [EXT] Absolute-value and step functions

Solving by factorising and quadratic formula · Completing the square · Switching between forms · Quadratic graphs (vertex, axis of symmetry, roots, intercepts) · Quadratic modelling · [EXT] Inequalities · [EXT] Use of discriminant

Translations and dilations · Reflections · Algebraic and graphical forms a·f(x), f(ax), f(x)+c

Exponential shape and asymptote · Growth and decay · Depreciation and compound interest · Contextual meaning of parameters · [EXT] Index laws for rational indices · [EXT] Introduction to logarithms, log laws and log equations

Sine rule · Cosine rule · Area of a triangle · Bearings · Problem-solving · [EXT] Ambiguous case of sine rule

Radian measure · Full unit circle · Arc length, sector and segment area · Special triangles, exact values · Negative-angle, complementary-angle and Pythagorean identities · sin/cos/tan equations

Periodic behaviour · Sine and cosine functions · Fitting periodic models to data · [EXT] Set functions

Simultaneous equations (substitution, elimination, graphical, technology) · Word problems · [EXT] Systems for fitting model coefficients using technology

Algebraic simplification · Linear-equation review · Operations with algebraic fractions · Complex fractions

DP IA-style mini project — choose a question, model it, write it up; bridge to the Year 12 Exploration