VCE Specialist Mathematics Past Exam Questions
Browse VCE Specialist Mathematics exam questions from 2015–2026, including NHT and VCE papers. Filter by topic, year and paper; open the original source.
Matching results: 77 indexed questions and parts.
Section B, Question 2(c)Question part (c)
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Report-based difficulty · EasyAverage marks: 85% of available · official reportFull marks: 74% of students · official report
c. A second circle is given by |z — (1+2i) = 2. Sketch this circle on the Argand diagram below, labelling the imaginary axis intercepts with their values. 2 marks Im(z) 4 5 > Re(z)
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section B, Question 2(d)Question part (d)
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Estimated difficulty · Easy
d. i. Sketch the ray on the Argand diagram provided in part c. 1 mark
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Estimated difficulty · Medium
f. Assume that the true mean concentration of sugar from the shorter process is 0.40 grams per litre and the standard deviation is 0.12 grams per litre. A sample of 56 bottles is t
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Question 2
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 37% of students · official report
Question 2 (3 marks) Consider the complex number z = (b − i)3, where b ∈ R+. Find b given that arg( ) z 2 .
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Specialist Mathematics examination 1 · Report: 2023 VCE Specialist Mathematics 1 external assessment reportQuestion 10(d)Question part (d)
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Report-based difficulty · DifficultAverage marks: 30% of available · official reportFull marks: 7% of students · official report
d. Find all values of t for which the position vector of the particle, r( ) t , is perpendicular to its velocity vector, r( ) t . 2 marks
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Specialist Mathematics examination 1 · Report: 2023 VCE Specialist Mathematics 1 external assessment reportSection A, Question 4
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Report-based difficulty · MediumAverage marks: 62% of available · official reportAnswered correctly: 62% · official report
Question 4 If z = − (2a + 1) + 2ai, where a is a non-zero real constant, then 4 1 a z + is equal to A. 2 4 cis B. 2 3 4 C. cis D. 2 3 cis E. cis
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Specialist Mathematics examination 2 · Report: 2023 VCE Specialist Mathematics 2 external assessment reportSection A, Question 5
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Report-based difficulty · DifficultAverage marks: 34% of available · official reportAnswered correctly: 34% · official report
Question 5 Let z be a complex number where Re(z) > 0 and Im(z) > 0. Given z = 4 and arg(z3) = − π , then z2 is equivalent to A. 4z B. −2z C. 3z D. z 2 E. −4z
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Specialist Mathematics examination 2 · Report: 2023 VCE Specialist Mathematics 2 external assessment reportSection B, Question 2
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Estimated difficulty · Medium
Question 2 (10 marks) Let w cis 2 7 .
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Estimated difficulty · Easy
b. Sketch the circle given by z i 2 3 2 3 on the Argand diagram below. Label the axes intercepts with their values. 3 marks Im(z) Re(z) 6 4 2 −2 −4 −6 −6 −4 −2 2 6 4 O 15 2023 SPEC
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE (NHT) Specialist Mathematics examination 2Section B, Question 2(c)Question part (c)
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 53% of students · official report
c. On the Argand diagram below, plot and label the points that represent all the roots of z7 − 1 = 0. 2 marks 1 −1 1 −1 O Im(z) Re(z) 13 2023 SPECMATH EXAM 2 d o n o t w r i t e i
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Specialist Mathematics examination 2 · Report: 2023 VCE Specialist Mathematics 2 external assessment reportSection B, Question 2(d)Question part (d)
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Estimated difficulty · Easy
d. i. On the Argand diagram below, sketch the ray that originates at the real root of z7 − 1 = 0 and passes through the point represented by cis 2 7 . 1 mark 1 −1 1 −1 O Im(z) Re(z
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Specialist Mathematics examination 2Section B, Question 2(f)Question part (f)
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Estimated difficulty · Easy
f. i. Express cis cis 2 7 12 in the form Acos (B π), where A, B ∈ R+. 1 mark 15 2023 SPECMATH EXAM 2 d o n o t w r i t e i n t h i s a r e a TURN OVER
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