VCE Specialist Mathematics free practice questions with answers
Read question 1 and its full worked answer from paper 1 of our 20-paper VCE Specialist Mathematics set, then download the 3-page PDF. These are original practice questions, not official past papers. Page updated 3 November 2026.
(4 marks)
(a) Let z₁ = -2 + 3i and z₂ = 1 + 3i. Find z₁z₂ and z₁/z₂ in the form a + bi. [2 marks]
(b) Express z = -1 + √3i in polar form r cis(θ), where -π < θ ≤ π. [2 marks]
Question 1 (4 marks) [Complex numbers]
(a) Answer: z₁z₂ = -11 - 3i; z₁/z₂ = • z₁z₂ = (-2 + 3i)(1 + 3i) = -11 - 3i.
- z₁/z₂: multiply top and bottom by the conjugate 1 - 3i: (-2 + 3i)(1 - 3i)/((1 + 3i)(1 - 3i)) = • z₁/z₂ = (b) Answer: z = 2 cis( • r = |z| = √(-1² + √3²) = 2.
- Plot the point to find the quadrant; θ = Divide complex numbers by multiplying by the conjugate; polar form needs r = |z| and the argument from the correct quadrant.
Your sample is downloading. Liked it? VCE Specialist Mathematics Paper 1 is the full paper: Exam 1 with 10 short-answer questions (40 marks) and Exam 2 with 20 multiple-choice plus 5 extended-response questions (80 marks), 120 marks in all, with a worked solution for every question.
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Questions about this sample
What is in the VCE Specialist Mathematics free sample?
The first 3 questions from paper 1 of the set, in the real exam layout, followed by the step-by-step worked answers. It is a 3-page PDF; this page shows question 1 with its answer.
How many full VCE Specialist Mathematics papers are there?
20 original papers for Victorian Year 12 students (VCE Units 3 and 4). Each is Exam 1 with 10 short-answer questions (40 marks) and Exam 2 with 20 multiple-choice plus 5 extended-response questions (80 marks), 120 marks in all, with a worked solution for every question. Papers start at A$15.99 and download instantly as a PDF.
Are these official past papers?
No. The sample is taken from our own original practice paper and is not an official past paper or affiliated with any exam authority.