Stage 2 Essential Mathematics Subject Outline
School assessment contributes 70%: Assessment Type 1 Skills and Applications Tasks is 30% (four or five tasks under direct teacher supervision) and Assessment Type 2 Folio is 40% (two tasks, each a maximum of ten A4 pages). The externally assessed examination contributes 30% and lasts 130 minutes with no separate reading time. It is a written paper examination, not an e-exam. It is one question booklet of nine compulsory multi-part questions in three equal blocks — Topic 2 Questions 1–3 (30 marks), Topic 4 Questions 4–6 (30 marks) and Topic 5 Questions 7–9 (30 marks) — for 90 marks, with the front cover advising approximately 40 minutes per topic. There is no multiple-choice section and no formula sheet; the formulae for the surface area or volume of a pyramid, cone or sphere are printed in the question when they are needed. Students may take one unfolded A4 sheet (two sides) of handwritten notes and approved calculators, and must show working and steps of logic. The original practice papers on this site use that verified 90-mark, three-block model; the multiple-choice drills are a practice format only and are not part of the real paper.
Past papers on this subject span more than one subject outline. Papers written under an older one still work as practice, but the topics they test have changed — the index labels every paper with the subject outline it was set under.
Stage 2 Essential Mathematics Subject Outline (accredited from 2017; reissued to 2025) · 2017–2026
The topics, one by one
Each area below lists the concepts named in the subject outline, what the SACE Board exam asks of them, and the mistake that most often costs marks.
- Topic 2: Measurement (examined)
- Topic 4: Statistics (examined)
- Topic 5: Investments and loans (examined)
- Topic 1: Scales, plans, and models (school-assessed only)
- Topic 3: Business applications (school-assessed only)
- Topic 6: Open topic (school-developed)
Area 1 of 6
Topic 2: Measurement (examined)
Work in two dimensions with circles, polygons and composite shapes and in three dimensions with prisms, cylinders, cones, pyramids and spheres. Use Pythagoras' theorem and right-angled trigonometry, then the sine and cosine rules for non-right triangles. Estimate irregular areas with Simpson's rule or by decomposition, and connect volume, capacity, mass and density.
What the subject outline lists under this area · 5 points
- Subtopic 2.1: Linear measure — units, conversion, estimation, perimeter, circumference and arc length
- Subtopic 2.1: Pythagoras' theorem, right-angled trigonometry, angles of elevation and depression
- Subtopic 2.1: Sine rule and cosine rule for non-right-angled triangles (no ambiguous case)
- Subtopic 2.2: Area of regular, composite and irregular shapes, including Simpson's rule, and surface area
- Subtopic 2.3: Mass, volume, capacity and density
What the exam asks
Read a labelled diagram marked 'not drawn to scale', choose and convert units, state the formula, substitute clearly and give an answer with units and sensible rounding. 'Show that' parts fix a value you may reuse even if your own working differs. Interpretation parts ask why extra material was ordered, whether a design meets a stated limit, or how accurate an estimate is.
Where marks go missing
Simpson's rule needs an even number of equal strips and the end offsets must be included even when their length is zero. Finding an unknown angle needs trigonometry or the cosine rule, not Pythagoras' theorem, and adding a wall thickness changes a diameter by twice that thickness.
Area 2 of 6
Topic 4: Statistics (examined)
Choose and criticise sampling methods, and separate sampling, measurement, coverage and non-response error. Compare two distributions using mean, median, range, interquartile range and standard deviation, and represent them with stem-and-leaf and box-and-whisker plots. Analyse bivariate data with scatter plots, r, r² and the least squares line.
What the subject outline lists under this area · 5 points
- Subtopic 4.1: Census, population and sample; simple random, stratified, systematic and self-selected sampling
- Subtopic 4.1: Bias, sampling, measurement, coverage and non-response error, and the effect of sample size
- Subtopic 4.2: Mean, median, range, interquartile range, standard deviation and the effect of outliers
- Subtopic 4.2: Stem-and-leaf plots and box-and-whisker plots for comparing distributions
- Subtopic 4.3: Scatter plots, Pearson's r, the coefficient of determination, the least squares line, interpolation and extrapolation
What the exam asks
Complete a supplied table or plot, calculate a stratified sample size, draw and label a box plot, and then explain what the numbers mean for the situation described. Prediction parts ask for a value from the regression equation and a judgement about whether it can be trusted.
Where marks go missing
Identifying a source of bias earns only part of the mark — the impact on the results must be explained. A strong correlation is not causation, an outlier is removed only with justification, and a comparison that is unreasonable is usually unreasonable because of the sampling method or sample size, not because of a background factor such as inflation.
Area 3 of 6
Topic 5: Investments and loans (examined)
Rearrange the simple interest formula, use technology for compound interest, and adjust returns for taxation and inflation. Build future-value annuities, including superannuation, and analyse present-value annuities: repayment, outstanding balance, remaining term, total interest and the effect of paying more.
What the subject outline lists under this area · 4 points
- Subtopic 5.1: Simple and compound interest on a lump sum; fixed and variable rates
- Subtopic 5.1: Taxation of interest earned and the effect of inflation
- Subtopic 5.2: Future-value annuities, the regular deposit, interest earned, superannuation and long-term assumptions
- Subtopic 5.3: Loan annuities — present value, repayment, outstanding balance, term, interest paid and interest minimisation
What the exam asks
Use the financial solver with the correct signs and state your inputs. Interest earned or paid is a difference, not a solver output. Discussion parts ask you to state an assumption, describe a realistic change to it and quantify or explain the effect on the balance.
Where marks go missing
In the examination the number of compounding periods per year always equals the number of payments per year. An inflated cost needs 1 plus the rate as a decimal, a stated account condition such as a minimum opening balance or a ban on withdrawals must be checked before a recommendation, and a question asking you to discuss is not answered by naming an option.
Area 4 of 6
Topic 1: Scales, plans, and models (school-assessed only)
Name and describe plane shapes and solids, build and read nets, and construct scale diagrams from field measurements. Recover lengths, perimeters and areas from a map, plan or model, and solve bearing problems.
What the subject outline lists under this area · 2 points
- Subtopic 1.1: Properties of plane shapes and solids, and nets
- Subtopic 1.2: Constructing and reading scale diagrams, bearings, and the accuracy of scaled measurements
What the exam asks
Assessed in skills and applications tasks and folio tasks, never in the external examination. Present a scale as a ratio, label dimensions and discuss the size of the error a scaled measurement carries.
Where marks go missing
A small error in a measured angle is magnified by distance, and a plan view cannot record a slope, so a distance read from a map is a horizontal distance, not a travelled one.
Area 5 of 6
Topic 3: Business applications (school-assessed only)
Compare premises by location, facilities and cost. Work a price through the manufacturer, wholesaler and retailer chain with discounts, GST and input tax credits, calculate depreciation by both methods, find a break-even point graphically and by marginal income, and build a profit and loss statement. Compare taxation under a sole trader and a partnership.
What the subject outline lists under this area · 3 points
- Subtopic 3.1: Planning a business premises — location, facilities and comparison of costs
- Subtopic 3.2: Costing calculations — discounts, GST and input tax credits, profit margin, depreciation, break-even analysis and profit and loss statements
- Subtopic 3.3: Business structures and taxation — sole trader and partnership comparisons
What the exam asks
Assessed in skills and applications tasks and folio tasks, never in the external examination. Put costs on a common period before comparing them, and support a recommendation with the numbers you calculated.
Where marks go missing
Series discounts are applied one after another, not added together, and the two depreciation methods give different book values in different years, so the better choice depends on the year being considered. No calculation is required for a company structure.
Area 6 of 6
Topic 6: Open topic (school-developed)
Where a school runs an open topic, it replaces either Topic 1 or Topic 3 and is written by the school for its own context, to a standard comparable with the other topics.
What the exam asks
Assessed only through school assessment types. Ask your teacher for the key questions and key concepts written for your class, because they are not published in the subject outline.
Where marks go missing
The open topic is never examined externally, so time spent on it is not preparation for the examination, although it does count toward the 70% school assessment.
Common questions
Are the practice papers official past exams?
No. They are original ATARMAxxing questions with worked responses and mark-by-mark guides. The SACE Board's own 2023, 2024 and 2025 papers and the 2021–2025 Subject Assessment Advice are linked separately. This platform is not affiliated with the SACE Board or SATAC.
Which topics can the examination actually ask about?
Only Topic 2: Measurement, Topic 4: Statistics and Topic 5: Investments and loans. The paper devotes exactly 30 marks and roughly 40 minutes to each. Topics 1, 3 and 6 are assessed in school tasks.
Is there a formula sheet?
No. You must know the area formulae for triangle, square, rectangle, parallelogram, trapezium, circle and sector, and the surface-area and volume formulae for cubes, rectangular and triangular prisms and cylinders. The outline states that where a pyramid, cone or sphere is required, the formula will be provided in the question.
What can I take in?
One unfolded A4 sheet of handwritten notes, two sides, plus approved calculators. For Essential Mathematics you are not required to clear a graphics calculator's memory, computer algebra systems are not permitted, and a scientific calculator's memory must be cleared (Information sheet 49). You record the calculator brand and model on the front cover.
What do markers say costs the most marks?
The 2025 Subject Assessment Advice singles out right-angled trigonometry to find an angle, omitting the zero end offsets in Simpson's rule, calculating interest earned or paid as a difference, identifying bias without explaining its impact, and answers given with no working. It also warns that a one-mark question containing both a correct and an incorrect response scores zero.
What if my 'show that' answer does not match?
Use the value printed in the question for the later parts. Markers follow through so that you can still show understanding, and using the given value keeps the rest of the question intact.