Mathematics Advanced: should I choose it?

What will I learn?

How will I be assessed?

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?

Mathematics Advanced, 2025. UAC Table A3 reports separate means for reported HSC marks and scaled marks per unit, with candidature for each course in 2025. These are cohort statistics. They do not supply individual raw exam marks or a conversion between the two columns. Historical cohort data cannot predict your result or a future scaling direction.

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

Working with functions: algebra, linear, quadratic and reciprocal functions

Almost every later topic in Mathematics Advanced depends on fluent algebra, so this section gathers the core techniques: index laws, surds and the three methods for solving quadratic equations. Treat these as tools you should be able to use quickly and accurately without a calculator. Index laws. For a base a > 0 and any real indices m and n: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, (ab)ⁿ = aⁿbⁿ and a⁰ = 1. A negative index means a reciprocal, a⁻ⁿ = 1/aⁿ, and a fractional index means a root, a^(1/n) = ⁿ√a and a^(m/n) = (ⁿ√a)ᵐ. When evaluating a fractional power by hand, take the root first so the numbers stay small: 27^(2/3) = (∛27)² = 3² = 9. When simplifying expressions with different bases, rewrite each base as a power of a common prime where possible. Expanding and factorising. Expanding uses the distributive law; useful patterns are (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b² and (a + b)(a − b) = a² − b². Factorising reverses this. Always look for a common factor first, then a difference of two squares, then a quadratic trinomial, and for four terms try grouping in pairs. Sums and differences of cubes are also useful: a³ ± b³ = (a ± b)(a² ∓ ab + b²). Surds. A surd is an irrational root such as √2 or ∛5. Simplify by extracting the largest square factor: √72 = √36 × √2 = 6√2. Like surds can be added (3√2 + 5√2 = 8√2), and products follow √a × √b = √(ab). Expand surd expressions exactly as you would algebraic brackets. To rationalise a denominator of the form √a, multiply top and bottom by √a. For a binomial denominator such as a + √b, multiply by its conjugate a − √b, because (a + √b)(a − √b) = a² − b is rational. Solving quadratics. Write the equation as ax² + bx + c = 0 first. Then choose a method: factorise if the roots look rational; complete the sq

Original practice question: Evaluate 8^(2/3) × 4^(−1/2).

This is ATARMAxxing’s original sample learning material. It is not an official assessment task or a prediction of your school’s workload.

Explore the resources

Open the Mathematics Advanced subject hub and free preview (opens in a new tab)

• Mathematics Advanced — HSC Year 12 (opens in a new tab)

Core subject information and planning are free. Full study resources are optional.