HSC maths: Standard, Advanced and Extension courses, the 2027 exams and practice questions

Each daily paper has 8 original questions worth 25 to 35 marks. The Year 12 Maths Advanced paper fits Advanced calculus; its substitution, integration by parts, parametric and differential equation questions are for Extension students. The Year 11 paper revises functions, trigonometry, logarithms and sequences; its binomial expansion and polynomial questions are Extension 1, and partial fractions and proof go further. The statistics paper suits Standard 2 and Advanced, with binomial questions for Extension 1; skip hypothesis testing, which no HSC maths course covers.

HSC maths exams in 2027

Every exam gives you a reference sheet and allows NESA-approved calculators; the rest of each paper is written answers. These are NESA's exam specifications for the 2024 syllabuses. The Standard 1 exam is optional; if you want Standard 1 to count toward an ATAR, sit it, because UAC can use that exam mark. The 2027 HSC written exams run from Wednesday 13 October to Friday 5 November 2027, and each course's date comes out with the timetable on Friday 30 April 2027.

As in every HSC course, your mark is half exam and half moderated school assessment. In Advanced, school assessment weights knowledge and understanding and working mathematically at 50% each, and your school sets the tasks. Band 6 is 90 to 100 in the 2 unit courses; Extension courses use bands E1 to E4.

What's in Year 12 HSC maths

• Mathematics Advanced: further graph transformations and modelling, sequences and series, differential calculus, integral calculus, applications of calculus, random variables, and financial mathematics.
• Mathematics Standard 2: algebraic relationships, investment and loans, annuities, trigonometry, ratios and rates, network flow, critical path analysis, bivariate data, relative frequency and probability, and the normal distribution.
• Mathematics Extension 1: proof by mathematical induction, vectors, inverse trigonometric functions, further calculus skills and applications, and the binomial distribution and the sampling distribution of the mean.

These are the 2024 syllabus focus areas. If you are revising from older notes or past papers, watch for content that has moved between courses: NESA lists additions, exclusions and relocations as part of the change.

HSC maths practice questions with answers

We wrote these for this page. Each says which course it is for.

1. Stationary points (Advanced). Find and classify the stationary points of f(x) = x³ − 3x² − 9x + 2. Answer: set f′(x) = 3x² − 6x − 9 = 3(x + 1)(x − 3) equal to zero: the stationary points are at x = −1 and x = 3. Since f″(x) = 6x − 6 equals −12 at x = −1, (−1, 7) is a local maximum; it equals +12 at x = 3, so (3, −25) is a local minimum.

Here x is the input and y is f(x). Check derivatives with the Derivative Calculator.

2. A definite integral (Advanced). Evaluate the integral of 3x² + 2 from x = 0 to x = 2. Answer: the primitive is x³ + 2x, so the value is (8 + 4) − 0 = 12. The Integral Calculator shows the area.

3. Annuities (Advanced and Standard 2). Mia deposits $200 at the start of every month into an account paying 0.5% interest per month. How much is there after 3 years? Answer: the deposits form a geometric series with ratio 1.005 over 36 months: FV = 200 × 1.005 × (1.005³⁶ − 1) ÷ 0.005 = $7906.56. She paid in $7200, so $706.56 is interest.

4. The normal distribution (Standard 2 and Advanced). Exam scores are normally distributed with mean 65 and standard deviation 8. Ravi scores 81. Find his z-score and roughly what percentage scored higher. Answer: z = (81 − 65) ÷ 8 = 2. About 95% of scores lie within 2 standard deviations of the mean, so about 5% lie outside, half of them above: about 2.5% scored higher. Try a normal distribution question from our Probability course, then press Mark.

5. The binomial distribution (Extension 1). A free throw goes in with probability 0.3. In 5 independent throws, what is the probability of exactly 2 going in? Answer: P(X = 2) = ⁵C₂ × 0.3² × 0.7³ = 10 × 0.09 × 0.343 = 0.3087.

Use the daily papers as an HSC maths trial

1. Advanced: sit the Year 12 paper to the suggested time, 35 to 45 minutes, skipping the Extension questions listed above.
2. Standard 2: sit the statistics paper, skipping hypothesis testing and binomial questions.
3. Extension 1 and 2: treat the substitution, parts, parametric and differential equation questions as extra practice, checking each against your syllabus, and sit the binomial questions on the statistics paper.
4. Mark each paper, note the focus area of every lost mark, and use NESA's past HSC papers for full-length timing, checking each question against the 2024 syllabus.

Common HSC maths mistakes

• Not justifying the nature of a stationary point. Show the second derivative or a table of gradients.
• Forgetting the extra factor of (1 + r) when deposits are made at the start of each period.
• Leaving the calculator in degrees when a calculus question uses radians.
• Using the binomial formula when trials aren't independent or the probability changes.
• Learning from old past papers without checking the new syllabus. Some content has moved between courses.

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