In Year 11 Foundation Mathematics, explore Algebra, number and structure; Data analysis, probability and statistics. See the learning outline, assessment information and original sample before choosing.
Confirm your cohort: The VCAA Foundation Mathematics study page (accessed 2026-10-22) links the 2023 Mathematics Study Design (updated v1.1, file dated 2025-10) as current; it is accredited from 1 January 2023 with no replacement study design published, so it is expected to apply to Units 1 and 2 in 2027, subject to VCAA Bulletin notices.
What will I learn?
Algebra, number and structure
Unit 1Data analysis, probability and statistics
Unit 1Discrete mathematics
Unit 1Space and measurement
Unit 1Algebra, number and structure
Unit 2Data analysis, probability and statistics
Unit 2Discrete mathematics
Unit 2Space and measurement
Unit 2Units 3 and 4, AOS 1 — Algebra, number and structure
Year 12 guide — check cohort versionThis area of study is the arithmetic and algebra the rest of the subject runs on. It starts with mathematical conventions and notation, order of operations, and the difference between rational numbers and the irrational numbers that turn up in measurement. From there it covers ratio, proportion, rates and percentages, including percentage increase and decrease and percentage error, and direct and indirect variation with a constant of proportionality. The algebra is practical: substituting into a supplied formula, transposing a formula to make a different variable the subject, and solving simultaneous equations both graphically and algebraically to find a break-even point. It closes on estimation and approximation — interval estimates, rounding, significant figures, leading-digit approximations, and floor and ceiling values — together with the habit of checking whether a calculated answer is plausible in its context.
Units 3 and 4, AOS 2 — Data analysis, probability and statistics
Year 12 guide — check cohort versionThe data strand runs from collecting data to being sceptical about it. It opens with the types of data — categorical, discrete numerical and continuous — and with designing a survey around a stated purpose and audience. You then build and read representations: tables, spreadsheets, the standard charts, and the contemporary displays the study design names explicitly, including pictograms, bubble charts, Mekko, radar, sunburst, heat map and stacked area charts. Summary statistics cover mean, median and mode for centre, and range, percentiles, quantile intervals, cumulative frequency and standard deviation for spread, alongside the shape of a distribution and the effect of outliers. The last part is inference: interpolation, extrapolation and prediction, long-term data and relative frequency used to talk about likelihood, and the limitations, errors and misrepresentations that make a statistic misleading.
Units 3 and 4, AOS 3 — Discrete mathematics: financial and consumer mathematics
Year 12 guide — check cohort versionDespite the 'Discrete mathematics' heading, this area of study is financial and consumer mathematics from start to finish — there is no graph theory, no networks, no matrices and no recursion in Foundation Mathematics. It covers money management: borrowing, loans and mortgages, credit and debit, debt consolidation, and comparing a mortgage against renting. Taxation and superannuation are studied at personal and business level, including income tax scales and marginal rates, and routine business transactions such as GST, invoicing and Business Activity Statements, payroll, leave entitlements and depreciation. It also asks you to compare non-bank financial products — insurance, phone and internet plans, hire purchase — and to read financial and economic data at the community, national or global level, including inflation, currency fluctuation, gender pay gaps and other indicators, and to think about financial risk over the short, medium and long term.
Units 3 and 4, AOS 4 — Space and measurement
Year 12 guide — check cohort versionSpace and measurement covers shape, size and how confident you can be in a measurement. It begins with the names and properties of two- and three-dimensional shapes and objects and the drawing conventions used for diagrams, plans, maps, models and nets, then works through transformations, symmetry, similarity and common angle properties, and the scaling calculations behind enlargement and reduction. Measurement itself covers metric units, derived quantities such as rates and density, routine non-metric measures, and reading digital and analogue instruments and scales. The calculation work is perimeter, area, surface area, volume and capacity of compound shapes and objects, including using Pythagoras' theorem and the area formulas on the supplied sheet. It ends with calibration and error: tolerance, accuracy and precision, and what an acceptable margin actually means in a manufacturing or construction context.
Units 1 and 2 — assumed knowledge (not externally examined)
Year 12 guide — check cohort versionFoundation Mathematics Units 1 and 2 are named in the study design as the assumed knowledge and skills for Units 3 and 4, and they mirror the same four areas of study at a more routine level. Area of Study 1 covers integers, fractions and decimals and their operations, ratio, proportion, percentage and rate, and estimation and reasonableness. Area of Study 2 covers collecting data and representing it in diagrams, tables and graphs, and interpreting it to communicate a finding. Area of Study 3 is personal financial and consumer mathematics — banking, bills, borrowing, rates of pay and payslips, personal taxation and superannuation, fees and interest. Area of Study 4 covers standard metric units and common derived measures, reading digital and analogue instruments, estimation strategies, and time and duration including dates, schedules and timetables.
How will I be assessed?
School arrangements: Units 1 and 2 are school-assessed against the study design. Ask for your school’s task and date outline. Original practice exams are not official assessment requirements.
Needs verification: Year 12 guide (VCE Mathematics Study Design (from 2023) — Foundation Mathematics): Units 3 and 4 are assessed 60 per cent by School-assessed Coursework — three mathematical investigations across the two units, weighted 40 per cent in Unit 3 and 20 per cent in Unit 4 — and 40 per cent by one end-of-year written examination. That examination is a single paper worth 80 marks: 15 minutes reading time and 2 hours writing time, with no technology-free and technology-active split. Section A is 20 compulsory multiple-choice questions worth 1 mark each, answered on the Multiple-Choice Answer Sheet; a correct answer scores 1, an incorrect answer scores 0, and nothing is deducted for a wrong guess. Section B is 12 compulsory questions worth exactly 5 marks each, split into two to five labelled parts and written in the spaces in the Question and Answer Book. You are allowed one scientific calculator — not a CAS or graphics calculator — and one bound reference that may be annotated, and a VCAA formula sheet is supplied. Two rules run through every assessment report so far: show working on anything worth more than one mark, because answer-only responses cannot earn a partial mark, and round only at the final step and only as instructed. Confirm the syllabus and assessment schedule for your own completion year.
Progression and companion subjects
No complete companion or exclusion review is attached to this profile. Check the official course-entry conditions, language eligibility and your school’s sequence before enrolling. Links between resource hubs show related learning; they do not establish a compulsory prerequisite.
Will I find it hard?
Difficulty depends on your experience, interests, teaching and assessment. These are our reflection prompts, not an official difficulty rating.
- How do you feel about explaining a method and working through unfamiliar multi-step problems?
- Try the sample without looking at a worked answer, then check the steps you need to practise.
Does it scale up or down?
Foundation Mathematics, 2025. The 2025 VTAC report gives rounded historical scaled study scores at seven published raw study scores. The table includes courses with individually published figures. At a raw study score of 30, the published scaled score was 20 (down 10). Direction can differ at other raw scores. Historical cohort data cannot predict your result or a future scaling direction.
| Scaled score at raw 20 | Scaled score at raw 25 | Scaled score at raw 30 | Scaled score at raw 35 | Scaled score at raw 40 | Scaled score at raw 45 | Scaled score at raw 50 |
|---|---|---|---|---|---|---|
| 12 | 16 | 20 | 26 | 32 | 40 | 50 |
Scaling is not a measure of difficulty or a guaranteed bonus. Prioritise content you can engage with and required subjects for courses you are considering.
Try a little of the subject
Number, estimation and rates
Every practical calculation in Foundation Mathematics starts with numbers written in one of several forms: integers, fractions, decimals, percentages, ratios and rates. Being fluent means you can move between these forms quickly and choose the one that makes a problem easiest. An integer is a whole number that may be positive, negative or zero, such as −7, 0 or 215. Negative integers appear whenever we measure below a reference point, for example temperatures below freezing, an overdrawn bank balance or a depth below sea level. A fraction describes part of a whole: the denominator tells you how many equal parts the whole is split into and the numerator tells you how many of those parts you have. A decimal is a fraction whose denominator is a power of ten, and a percentage is a fraction out of 100. So 3/4 = 0.75 = 75%. To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percentage, multiply by 100. To convert a percentage to a fraction, write it over 100 and simplify, for example 35% = 35/100 = 7/20. When adding or subtracting fractions you need a common denominator; when multiplying you multiply numerators together and denominators together; when dividing you multiply by the reciprocal of the second fraction. Mixed numbers such as 2½ are usually easier to handle if you first convert them to improper fractions (5/2). Percentages are used constantly in everyday life: discounts, GST, interest, test scores and survey results. Three standard calculations are worth memorising. To find a percentage of an amount, convert the percentage to a decimal and multiply. To express one quantity as a percentage of another, divide and multiply by 100. To increase or decrease by a percentage, multiply by a single multiplier: increasing by
Original practice question: A $64 item is increased by 15%. What is the new price?
Show the worked answer
B
This is ATARMAxxing’s original sample learning material. It is not an official assessment task or a prediction of your school’s workload.
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Sources, versions and verification dates
Profile source metadata last checked: 2026-10-22. A source check is not an endorsement by the authority or confirmation that a future course version is unchanged.
- VCAA - VCE Foundation Mathematics study page — VCAA; 2026-10-22. Published version Current study design page (2023 Mathematics Study Design). Confirm applicability to your cohort.
- VCE Mathematics Study Design 2023 (Foundation Mathematics Units 1-4), updated version 1.1 — VCAA; 2026-10-22. Published version Accredited from 1 January 2023; updated version 1.1. Confirm applicability to your cohort.
- ATARMAxxing VCE Mathematics Study Design (from 2023) — Foundation Mathematics guide — ATARMAxxing; 2026-09-05. Original existing study guide, not an independent official verification or a forecast of a future syllabus.
- VTAC 2025 scaling report: Foundation Mathematics — VTAC; 2026-11-12. The 2025 VTAC report gives rounded historical scaled study scores at seven published raw study scores. The table includes courses with individually published figures.