VCE Vault

VCE General Mathematics (Year 12)

VCE General Mathematics (Year 12) on VCE Vault: 21 lessons written for Year 12 (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$14.99.

VCE General Mathematics past exams 2023–2025: 284 questions matched to these lessons.

VCE General Mathematics (Year 12) study notes: 83 pages covering 21 topics (PDF, A$9.99).

Lessons

Data Analysis

  • Investigating Data Distributions (free) — Classify variables, choose suitable displays and describe a distribution using shape, outliers, centre and spread.
  • The Normal Distribution and z-Scores (free) — Apply the 68–95–99.7% rule and standardised scores to compare and interpret values from normal distributions.
  • Associations Between Two Variables (free) — Identify explanatory and response variables and investigate associations using two-way tables, segmented bar charts and parallel boxplots.
  • Scatterplots and Correlation (free) — Describe the association in a scatterplot and interpret Pearson's correlation coefficient r, distinguishing association from causation.
  • Least Squares Regression — Find and interpret the least squares regression line, and use it to make predictions while recognising extrapolation.
  • Residuals and the Coefficient of Determination — Calculate residuals, use residual plots to test linearity and interpret the coefficient of determination r².
  • Data Transformations — Linearising Relationships — Apply log, reciprocal and squared transformations to linearise non-linear data and use the transformed model to predict.
  • Time Series — Features and Smoothing — Describe features of a time series plot and smooth data using moving means (including centring) and median smoothing.
  • Seasonal Indices and Forecasting — Calculate and interpret seasonal indices, deseasonalise and reseasonalise data, and forecast with a trend line.

Recursion and Financial Modelling

  • Recurrence Relations — Linear and Geometric Growth — Use first-order recurrence relations to model linear growth and decay, geometric growth and decay, and combined models.
  • Depreciation — Flat Rate, Reducing Balance and Unit Cost — Model depreciation of assets using flat-rate, reducing-balance and unit-cost methods.
  • Compound Interest and Effective Interest Rates — Model compound interest with different compounding periods and compare options using effective annual interest rates.
  • Reducing Balance Loans and the Finance Solver — Model reducing balance loans with recurrence relations, amortisation tables and a CAS finance solver.
  • Annuities, Perpetuities and Annuity Investments — Model annuities, perpetuities and annuity investments, and distinguish between them.

Matrices

  • Matrices — Types, Operations and Inverses — Recognise types of matrices, perform matrix operations, find 2×2 inverses and solve simultaneous equations; use communication and dominance matrices.
  • Transition Matrices and Steady State — Set up and use transition matrices to model changing states over time, including long-term (steady-state) behaviour.

Networks and Decision Mathematics

  • Graphs — Euler, Hamilton and Planar Graphs — Use graph terminology, identify Euler trails and circuits and Hamiltonian paths and cycles, and apply Euler's formula to planar graphs.
  • Trees, Minimum Spanning Trees and Shortest Paths — Identify trees, find minimum spanning trees using Prim's algorithm and find shortest paths using Dijkstra's algorithm or inspection.
  • Flow Networks, Matching and the Hungarian Algorithm — Find maximum flow using the minimum cut and solve allocation problems using bipartite graphs and the Hungarian algorithm.
  • Project Scheduling — Critical Path Analysis and Crashing — Construct activity networks, find earliest and latest start times, float and the critical path, and analyse crashing.

Exam Preparation

  • General Maths Exam Technique — Exam 1 and Exam 2 — Apply efficient strategies for the multiple-choice and extended-response General Maths exams, including CAS use and bound-reference preparation.