VCE Vault

VCE Foundation Mathematics (Year 12)

VCE Foundation Mathematics (Year 12) on VCE Vault: 23 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.

Lessons

Number and Arithmetic

  • Integers, Fractions and Decimals (free) — Convert confidently between integers, fractions, decimals and percentages and apply them to everyday money and measurement problems.
  • Ratios and Proportions (free) — Use ratios to share quantities, scale measurements and interpret maps and recipes.
  • Percentages and Rates (free) — Calculate percentage increases and decreases, add and remove GST, and interpret rates in everyday contexts.
  • Formulas and Expressions (free) — Substitute values into given formulas and evaluate expressions following the order of operations.
  • Solving Equations — Translate word problems into equations and solve for the unknown by keeping both sides balanced.
  • Estimation and Approximation — Estimate calculations mentally by rounding, and find upper and lower bounds for measurements.

Data and Statistics

  • Collecting and Organising Data — Classify data as categorical or numerical (discrete or continuous), choose appropriate sampling methods, and build frequency tables.
  • Displaying Data: Charts and Graphs — Choose appropriate charts for different data types, and read values accurately from pie charts, bar charts and line graphs.
  • Mean, Median and Mode — Calculate the mean, median and mode of a data set, and choose the most appropriate measure of centre when outliers are present.
  • Spread and Variation — Measure spread using range and IQR, and identify outliers using the 1.5 × IQR rule.
  • Comparing Data Sets — Compare two data sets using parallel box plots or stem plots, referencing both centre and spread.
  • Interpreting Data and Statistics — Identify misleading graphs, explain why they mislead, and distinguish correlation from causation.

Financial Mathematics

  • Banking, Bills and Credit — Calculate simple interest, bill totals with fixed + variable charges, and credit card interest on an outstanding balance.
  • Income, Pay Rates and Payslips — Calculate gross and net pay, including overtime at time-and-a-half or double time, and read a payslip accurately.
  • Taxation and GST — Calculate GST on goods, taxable income after deductions, and progressive income tax using marginal brackets.
  • Superannuation — Calculate employer superannuation contributions from ordinary time earnings at the current Super Guarantee rate.
  • Loans, Fees and Interest — Calculate the total cost of a loan including repayments, fees and interest, and compare two loan options fairly.
  • Budgeting and Money Management — Build a budget, identify surplus vs deficit, and recommend adjustments to reach a savings goal.

Measurement and Geometry

  • Metric Units and Conversions — Convert between metric units for length, mass, volume, area and volume — including the squared and cubed conversion factors.
  • Length, Area and Volume — Calculate area of common 2D shapes and volume of prisms and cylinders, and convert between volume and capacity.
  • Time, Schedules and Timetables — Convert between 12-hour and 24-hour time, calculate elapsed time, and read transport timetables.
  • Maps, Directions and Scale — Use scale to convert between map distance and real distance, and describe directions using compass bearings.
  • Shapes and Geometric Reasoning — Apply Pythagoras' theorem in right-angled triangles and use angle rules for triangles, straight lines and parallel lines.