Unit 3 · Semester 1
15 weeks · 3 syllabus topics · 4 assessment tasks
Live
3.1.1 – 3.1.15 · Weeks 1–5
Module 3.1 · Complex Numbers
Cartesian and polar form, complex arithmetic, modulus and argument, de Moivre's theorem, roots of unity, factor & remainder theorem with conjugate roots.
- Wk 1–2 Cartesian forms · Modulus, argument, polar form · de Moivre's theorem (live)
- Wk 3 The complex plane · Operations geometrically · Subsets of the plane (live)
- Wk 4–5 Roots of unity & complex roots · Factor / remainder theorem · Conjugate roots Task 1 · Wk 5
Live
3.2.1 – 3.2.8 · Weeks 6–9
Module 3.2 · Functions and Sketching Graphs
Composition and inverses, one-to-one functions; absolute value, reciprocal and rational function graphs.
- Wk 6–7 Functions · existence and composition · inverses · graphical properties of one-to-one functions (live)
- Wk 8–9 Sketching · absolute value · reciprocal · simple rational functions (live) Task 2 · Wk 9
Live
3.3.1 – 3.3.21 · Weeks 10–14
Module 3.3 · Vectors in 3D & Systems of Linear Equations
Algebra of 3D vectors, vector and Cartesian equations, vector calculus and motion; elimination methods and the geometry of linear systems.
- Wk 10 Algebra of vectors in three dimensions · simple proofs (live)
- Wk 11–13 Vector and Cartesian equations · curves, spheres, planes · vector calculus and motion (live) Task 3 · Wk 13
- Wk 14 Systems of linear equations · elimination · three cases · geometric interpretation (live)
- Wk 15 Semester 1 examination Task 4
Unit 4 · Semester 2
15 weeks · 3 syllabus topics · 4 assessment tasks
Live
4.3.1 – 4.3.7 · Weeks 1–4
Module 4.3 · Statistical Inference
Distribution of sample means, the central limit theorem, confidence intervals for population means.
- Wk 1–2 Sample means · simulation · approximate normality for large samples (live)
- Wk 3–4 Interval estimates for the population mean · simulation and known parameters (live) Task 5 · Wk 4
Live
4.1.1 – 4.1.7 · Weeks 5–9
Module 4.1 · Integration and Applications
Trig identities, substitution, partial fractions; natural log via integration; areas between curves and volumes of solids.
- Wk 5–6 Integration techniques · trig identities · substitutions · partial fractions · ln from integration (live)
- Wk 7–9 Applications · areas between curves · volumes of solids · numerical integration (live) Task 6 · Wk 8/9
Live
4.2.1 – 4.2.7 · Weeks 10–14
Module 4.2 · Rates of Change, DEs & Motion
Implicit differentiation, related rates, differential equations including the logistic equation and slope fields; modelling straight-line motion and simple harmonic motion.
- Wk 10–12 Implicit differentiation · related rates · DEs · slope fields · logistic equation (live) Task 7 · Wk 12
- Wk 13–14 Modelling motion · straight-line motion · simple harmonic motion (live)
- Wk 15 Semester 2 examination Task 8
Past Paper Revision
Atomised practice for every released past paper. Use after teaching the syllabus topic.
Topics · Year 9 → ATAR Specialist
Each topic fully atomised from Y9 entry to exam-level capstones drawn from real ATAR Specialist papers.