Mathematics Methods ATAR Year 12 syllabus — for teaching from 2026
School assessment comprises Response 40%, Investigation 20% and Examination 40%. The external examination has a Calculator-free section with 5 minutes reading and 50 minutes working, and a Calculator-assumed section with 10 minutes reading and 100 minutes working. A separate changeover of up to 15 minutes permits no work. The combined 165 minutes includes reading and working, not changeover. The 2025 reference raw totals are 47 and 97 marks, weighted at 35% and 65% respectively; historical raw totals may vary. Both sections require written responses. Calculator-free permits no special items; a supervisor-supplied formula sheet is available. Calculator-assumed permits drawing instruments, templates, notes on two unfolded A4 sheets and up to three calculators, with CAS capability assumed. Follow the official instructions for the particular sitting.
Past papers on this subject span more than one syllabus. Papers written under an older one still work as practice, but the units and content areas they test have changed — the index labels every paper with the syllabus it was set under.
Syllabus for teaching from 2026 · 2026–presentEarlier syllabus — check current alignment · 2020–2025
The units and content areas, one by one
Each area below lists the concepts named in the syllabus, what the SCSA exam asks of them, and the mistake that most often costs marks.
- Unit 3 — Topic 3.1: Further differentiation and applications
- Unit 3 — Topic 3.2: Integrals
- Unit 3 — Topic 3.3: Discrete random variables
- Unit 4 — Topic 4.1: The logarithmic function
- Unit 4 — Topic 4.2: Continuous random variables and the normal distribution
- Unit 4 — Topic 4.3: Interval estimates for proportions
Area 1 of 6
Unit 3 — Topic 3.1: Further differentiation and applications
Differentiate exponential and trigonometric functions using product, quotient and chain rules. Use first and second derivatives to analyse rates, concavity, stationary points and optimisation.
What the syllabus lists under this area · 4 points
- Euler's number e, the limit (a^h - 1)/h and the derivative of e^x and Ae^(kx)
- Derivatives of sin x and cos x and their use in practical problems
- The product, quotient and chain rules and composite functions
- Second derivatives, concavity, inflection, the increments formula, curve sketching and optimisation
What the exam asks
Show the rule and working, preserve domains and units, and justify the nature of an optimum. Use the increments formula for small changes and interpret velocity and acceleration.
Where marks go missing
Trigonometric derivatives require radians. A zero second derivative is only a candidate for inflection, and local stationary-point tests do not replace endpoint comparisons in global optimisation.
Area 2 of 6
Unit 3 — Topic 3.2: Integrals
Find antiderivatives, use initial conditions, and connect definite integrals with signed area and the fundamental theorem. Apply integration to areas, accumulated change and linear motion.
What the syllabus lists under this area · 4 points
- Indefinite integrals of x^n, e^x, sin x, cos x and f(ax - b), linearity and initial conditions
- Area as a limit of sums, signed areas, additivity and linearity of definite integrals
- The signed area function and the fundamental theorem of calculus
- Areas under and between curves, total change from a rate, and linear motion
What the exam asks
Choose correct bounds, identify signs and intersections, evaluate upper minus lower and connect the integral to the requested contextual quantity.
Where marks go missing
Signed area can cancel. Distance requires speed rather than signed velocity, and a change must be added to an initial value to obtain a final value.
Area 3 of 6
Unit 3 — Topic 3.3: Discrete random variables
Represent discrete probability distributions and calculate expected value, variance and standard deviation. Model Bernoulli trials and binomial counts and examine linear transformations.
What the syllabus lists under this area · 2 points
- Discrete random variables: probability functions, expected value, variance and linear changes of scale and origin
- Bernoulli trials and the binomial distribution: probabilities, mean np and variance np(1 - p)
What the exam asks
Check probabilities sum to one, justify independence and constant success probability, translate inequalities correctly and interpret distribution summaries.
Where marks go missing
The expected value need not be an attainable outcome. Variance and standard deviation scale differently; sampling without replacement from a small population is not exactly independent.
Area 4 of 6
Unit 4 — Topic 4.1: The logarithmic function
Use logarithms as indices, apply logarithm laws and interpret transformed graphs and scales. Differentiate natural logarithmic functions and recognise integrals of the form f′/f.
What the syllabus lists under this area · 3 points
- Logarithms as indices, the log laws and solving index equations
- Graphs of y = log_a x and its translations, logarithmic scales and logarithmic models
- The natural logarithm: derivative of ln x and ln f(x), and integrals of 1/x and f'(x)/f(x)
What the exam asks
Retain positive-argument conditions, reject extraneous equation solutions, distinguish multiplicative scale changes from additive changes and interpret models within their valid domains.
Where marks go missing
There is no log-of-a-sum law. Simplification must preserve the original domain, and a mathematically allowed extrapolation is not automatically a suitable contextual prediction.
Area 5 of 6
Unit 4 — Topic 4.2: Continuous random variables and the normal distribution
Use densities and cumulative distribution functions to calculate probabilities and moments. Apply continuous and normal models, standardisation and inverse-normal calculations.
What the syllabus lists under this area · 3 points
- Probability density functions, cumulative distribution functions and probabilities as integrals
- Expected value, variance and standard deviation of continuous random variables, including uniform and triangular
- The normal distribution: features, standardisation, and probabilities and quantiles with technology
What the exam asks
Verify density conditions, integrate over the support, choose the appropriate tail and use technology accurately for probabilities and quantiles.
Where marks go missing
Density height is not probability and can exceed one. A single point has zero probability in a density model; check whether normal notation or calculator inputs use variance or standard deviation.
Area 6 of 6
Unit 4 — Topic 4.3: Interval estimates for proportions
Examine random sampling, bias and variation in sample proportions. Construct approximate confidence intervals, interpret coverage and compare confidence, sample size and margin of error.
What the syllabus lists under this area · 4 points
- Random samples, sources of bias and variability of samples from uniform, normal and Bernoulli distributions
- The sample proportion p-hat as a random variable: mean, standard deviation and approximate normality
- Confidence intervals for a proportion and the margin of error
- Sample size, confidence level and the interpretation of repeated confidence intervals by simulation
What the exam asks
State model assumptions, distinguish the fixed population proportion from a varying sample statistic, justify rounding in sample-size planning and evaluate sampling limitations.
Where marks go missing
A larger sample does not remove bias. Confidence describes repeated-sampling performance; simple normal intervals can be unreliable near zero or one.
Common questions
Are the multiple-choice revision drills the official exam format?
No. Both official sections use written-response questions. Multiple-choice drills are an additional original ATARMAxxing revision format.
Why are the raw marks different from the percentage weights?
The 2025 reference papers carry 47 and 97 raw marks, a total of 144. Their examination contributions are 35% and 65%. Raw marks and weighted percentages must not be treated as interchangeable.
What does the 165-minute duration include?
It combines 150 working minutes and 15 reading minutes across both sections. The separate changeover period of up to 15 minutes is not working time and is not included.
Do older official papers use the current syllabus?
The current saved syllabus is for teaching from 2026. The linked papers are from 2020–2025, so check individual questions and permitted materials against the current syllabus rather than assuming unchanged scope.
Does an interval estimate account for a biased survey?
The usual confidence margin describes sampling variation under the stated model. It does not automatically account for coverage, nonresponse or wording bias. Evaluate the sampling method as well as the calculation.