VCE Maths Methods: the two exams, the SACs and practice questions with answers

Each daily paper has 8 original questions worth 25 to 35 marks. The Year 12 Maths Methods paper fits the calculus area of study in its rules of differentiation, tangents, stationary points, rates of change, integration and area questions; skip substitution, integration by parts, parametric and differential equation questions, which go beyond Methods. The Year 11 paper fits functions, transformations, exponentials and logarithms, polynomials and trigonometric equations; skip partial fractions and proof.

Maths Methods Exam 1 and Exam 2

Both exams come with the same formula sheet. That is the VCAA's exam specification for the study design from 2023. In 2026, Exam 1 was on Thursday 5 November and Exam 2 on Friday 6 November; results come out on Thursday 10 December 2026.

Areas of study and SACs

Units 3 and 4 have four areas of study: functions, relations and graphs; algebra, number and structure; calculus; and data analysis, probability and statistics. School-assessed Coursework is worth 40% of the study score: an application task in Unit 3, and modelling or problem-solving tasks in Unit 4. The VCAA moderates SAC marks against your school group's exam results, keeping your rank.

Maths Methods practice questions with answers

We wrote these in the style of Exam 1: do them without a calculator.

1. An exponential equation. Solve e^2x − 5e^x + 6 = 0. Answer: let u = e^x, so u² − 5u + 6 = (u − 2)(u − 3) = 0 and u = 2 or 3. Then x = log_e(2) or x = log_e(3). Both are valid, because e^x is positive in each case.

2. A tangent. Find the equation of the tangent to y = x log_e(x) at x = e. Answer: by the product rule, dy/dx = log_e(x) + 1, which is 2 at x = e. The point is (e, e), so y − e = 2(x − e), giving y = 2x − e. Check derivatives with the Derivative Calculator.

3. A probability density function. X has density f(x) = kx² for 0 ≤ x ≤ 3, and 0 elsewhere. Find k and E(X). Answer: the total area must be 1, so k × 3³ ÷ 3 = 9k = 1 and k = 1/9. Then E(X) = (1/9) × 3⁴ ÷ 4 = 9/4.

4. An inverse function. For f(x) = 2 log_e(x − 1) + 3 with x > 1, find the inverse function and its domain. Answer: swap x and y: x = 2 log_e(y − 1) + 3, so log_e(y − 1) = (x − 3) ÷ 2 and f⁻¹(x) = e^{(x − 3)/2} + 1. The range of f is all real numbers, so the inverse has domain R and range y > 1.

5. The normal distribution. The mass of a bag of rice is normally distributed with mean 500 g and standard deviation 4 g. Given that about 95% of values lie within two standard deviations of the mean, estimate the probability that a bag weighs more than 508 g. Answer: 508 g is two standard deviations above the mean. About 5% lie outside the middle 95%, split evenly, so the probability is about 0.025. Try a normal distribution question from our Probability course, then press Mark.

Use the daily papers as a Methods trial

1. Sit today's Year 12 paper to the suggested time, 35 to 45 minutes, without a calculator, as Exam 1 practice.
2. Skip the substitution, parts, parametric and differential equation questions.
3. For probability, sit the binomial, normal and conditional probability questions on the statistics paper.
4. Use VCAA past Exam 2 papers for CAS practice, since the daily papers are written for working by hand.

Common Maths Methods mistakes

• Dropping a solution when you substitute u = e^x: check each u is positive before taking logs.
• Forgetting to state the domain of an inverse function, which is the range of the original.
• Leaving out the constant in an antiderivative, or keeping it in a definite integral.
• Not checking a density function integrates to 1 before you use it.
• Relying on CAS in Exam 1 practice. Exam 1 allows no technology at all.

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