VCE Specialist Maths: the tech-free Exam 1, the 80 mark Exam 2 and the areas they test

Specialist Maths Exam 1 and Exam 2

From the VCAA examination specifications for Specialist Mathematics (from 2023), checked on 11 November 2026. The VCAA sets exam dates annually and the 2027 timetable was not available to check.

Exam 2 also allows protractors, set squares and aids for curve sketching. Both exams come with the same formula sheet, all questions are compulsory, and every outcome in Units 3 and 4 can be examined. Specialist assumes you are doing, or have done, Maths Methods Units 3 and 4.

Areas of study and SACs

The study design for Units 3 and 4 has six areas of study: discrete mathematics (logic and proof, including induction); functions, relations and graphs; algebra, number and structure (complex numbers); calculus; space and measurement (vectors, lines and planes); and data analysis, probability and statistics. The calculus area covers integration techniques, volumes, differential equations and kinematics. The two exams make up 60% of the study score, so School-assessed Coursework is the remaining 40%.

Worked examples in Exam 1 style

A power of a complex number

Find (1 + i√3)⁶. Write the number in polar form: its modulus is 2 and its argument is π/3, so it is 2 cis(π/3). Then:

Check it in the Complex Numbers calculator. By hand, always show the modulus and argument before you apply De Moivre's theorem.

Integration by parts

To find ∫ x cos x dx, take u = x and dv = cos x dx, so du = dx and v = sin x:

Differentiate your answer to check: the product rule gives sin x + x cos x − sin x = x cos x.

Motion from acceleration

A particle has acceleration a = 6t m s⁻², with velocity 2 m s⁻¹ and position 1 m at t = 0. Integrating, v = 3t² + 2 and x = t³ + 2t + 1. At t = 2 the velocity is 14 m s⁻¹ and the position is 13 m. Our Specialist Maths mechanics guide covers the rest of kinematics.

Use the daily papers as a trial

Each daily paper has 8 original questions and 25 to 35 marks, a short timed trial of 35 to 45 minutes, not a full Specialist exam. Schools set their own trials; our VCE trial exams guide explains how they count. Sit paper questions without a calculator as Exam 1 practice.

• On the Further Maths paper, sit the complex numbers and Argand diagram, roots of polynomials, proof by induction and volumes of revolution questions. Skip hyperbolic functions, Maclaurin series, polar curves, second order differential equations and matrices, which the Units 3 and 4 areas of study do not list.
• On the Mechanics paper, the variable acceleration, velocity-time graph and projectile questions fit the kinematics in the study design. The statics-style questions, such as moments, friction and pulleys, are outside it.

Exam answers

Answers and a worked mark scheme for the daily paper come with today's paper once it's marked. They are ours: the VCAA publishes its own examination reports.

Common mistakes in VCE Specialist Maths

• Using technology habits in Exam 1. Exam 1 allows none, so practise exact values by hand.
• Losing the argument. The principal argument of a complex number lies in (−π, π], so check the quadrant.
• Dropping the constant before using an initial condition. Integrate, add C, then use the given values.
• Overusing the bound reference. It helps in Exam 2 only if you can find things fast.

Read next

Australia · VCEVCE Specialist Maths formula sheet: the VCAA sheetThe VCAA VCE Specialist Mathematics formula sheet for Exams 1 and 2: every section, what is missing, the bound reference rule and worked examples.