VCE Specialist Mathematics (Year 11)

VCE Specialist Mathematics (Year 11) on VCE Vault: 18 lessons written for Year 11 (VCE, Victorian Certificate of Education), each with worked examples, practice questions and Aari, an AI tutor. The first 4 lessons are free; the whole subject is a one-off A$12.99.

VCE Specialist Mathematics (Year 11) study notes: 80 pages covering 18 topics (PDF, A$9.99).

Lessons

Arithmetic and Number

• Arithmetic and Geometric Sequences (free) — Identify, describe and use arithmetic and geometric sequences and their general terms and partial sums.
• Real and Rational Numbers — Structure and Proof — Classify and manipulate real numbers; prove properties of rational and irrational numbers using direct proof and contradiction.
• Probability — Conditional and Bayes — Apply conditional probability and Bayes' theorem to solve probability problems.

Algebra and Structure

• Logic, Proof and Mathematical Reasoning (free) — Use propositional logic, construct proofs by direct and indirect methods, and apply mathematical induction.
• Vectors — Introduction and Operations (free) — Represent vectors geometrically and algebraically; perform vector addition, subtraction and scalar multiplication; find the magnitude and direction of a vector.
• Matrices — Operations and Applications — Perform matrix operations and use matrices to solve systems of linear equations.
• Polynomial Functions and Factor Theorem — Factor polynomials using the factor theorem and sketch cubic and quartic functions.
• Complex Numbers — i, the Complex Plane and Solving Quadratics — Perform arithmetic with complex numbers in Cartesian form, represent them on an Argand diagram, and solve quadratic equations that have no real solutions.
• Specialist Mathematics — Exam Skills — Apply Specialist Mathematics reasoning and proof techniques in exam contexts.

Extension — not in the 2023–2027 study design

• Circle Geometry — Theorems and Proofs (free) — State and apply circle theorems to find unknown angles, and write formal proofs using circle properties.

Discrete Mathematics

• Combinatorics — Counting Principles — Apply the multiplication principle, permutations and combinations to count arrangements.

Graphs of Linear and Non-Linear Relations

• Coordinate Geometry — Circles and Conics — Derive and apply the equations of circles, ellipses and hyperbolas.

Geometry, Measurement and Trigonometry

• Trigonometry — Compound Angles and Exact Values — Apply compound angle formulas and find exact trigonometric values.
• Transformations of the Plane — Matrices for Reflections, Rotations, Dilations and Shears — Represent linear transformations of the plane with 2 × 2 matrices, compose transformations in the correct order, and use determinants to describe changes in area and orientation.

Shared with Methods Units 1–2

• Introduction to Differential Calculus — Apply differentiation rules to find gradients and equations of tangents and normals.
• Applications of Differentiation — Use calculus to find stationary points, sketch curves, and solve optimisation problems.
• Introduction to Integration — Find anti-derivatives and evaluate definite integrals to calculate areas.

Data Analysis, Probability and Statistics

• Simulation, Sampling and the Distribution of Sample Means — Use simulation to estimate probabilities, distinguish populations from samples, and describe how the distribution of sample means behaves as sample size increases.