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.
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Section B, Question 2(b)Question part (b)
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b. Sketch the graph of the relation |z —2i| = Im(z +7) on the Argand diagram below for —3<Re(z)<3. Label the endpoints with their coordinates. 1 mark Im(z) 4 2 1 + t + + t +> Re(2)
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE (NHT) Specialist Mathematics examination 2 (PDF, 5.7 MB)Section B, Question 2(b)(ii)Question part (b)(ii)
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Report-based difficulty · EasyAverage marks: 78% of available · official reportFull marks: 78.3% of students · official report
ii. Sketch z z i z i z C : , 2 3 on the Argand plane in part a. 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE Specialist Mathematics examination 2 (PDF, 1.17 MB) · Report: 2025 VCE Specialist Mathematics 2 external assessment report (DOCX, 908.84 KB)Section B, Question 2(c)Question part (c)
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c. i. Find the points of intersection of the curves defined in part a and in part b.i, expressing your answers in the form a + ib, where a, b ∈ R. 2 marks Consider the points P and
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE Specialist Mathematics examination 2 (PDF, 1.17 MB)Section B, Question 2(c)(i)Question part (c)(i)
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i. Sketch the ray on the Argand diagram above. 1 mark = s
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE (NHT) Specialist Mathematics examination 2 (PDF, 5.7 MB)Section B, Question 2(c)(ii)Question part (c)(ii)
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Report-based difficulty · EasyAverage marks: 73% of available · official reportFull marks: 73.9% of students · official report
ii. Label these points on the Argand plane in part a. 1 mark Section B
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE Specialist Mathematics examination 2 (PDF, 1.17 MB) · Report: 2025 VCE Specialist Mathematics 2 external assessment report (DOCX, 908.84 KB)Section B, Question 2(d)Question part (d)
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Estimated difficulty · Easy
d. Sketch the graph of the relation [2 ~ 21] = Im(Z +), where z =x + iy, x,y € R, on the Argand diagram provided in part b, labelling it with its Cartesian equation. 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE (NHT) Specialist Mathematics examination 2 (PDF, 5.7 MB)Section B, Question 6(h)Question part (h)
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Report-based difficulty · MediumAverage marks: 53% of available · official reportFull marks: 53.6% of students · official report
h. Assume that, after the service, the true mean volume of water in the Apa bottles was found to be 747.5 mL and that the population standard deviation, σ, is 5 mL. At the 1% level
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE Specialist Mathematics examination 2 (PDF, 1.17 MB) · Report: 2025 VCE Specialist Mathematics 2 external assessment report (DOCX, 908.84 KB)Question 1(c)Question part (c)
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 49% of students · official report
c. Plot the solutions of (2) = 0 on the Argand diagram below. 1 mark Re(2) 4 2 £ 3 ° = o [=]
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 1 · Report: 2024 VCE Specialist Mathematics 1 external assessment report (DOCX, 556.03 KB)Question 10
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Estimated difficulty · Difficult
Question 10 (4 marks) Use integration by parts to evaluate 4 3 3 2 3 3 2 arcsin x dx . Give your answer in the form aπ + b, where a, b ∈ R. This page is blank. N H T Mensuration ar
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 1Section A, Question 5
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Report-based difficulty · EasyAverage marks: 70% of available · official reportAnswered correctly: 70% · official report
Question 5 If the point z = 1+ +/3i is represented on an Argand diagram, the point representing —= can be located by A. reflecting the point representing = in the real axis B. rota
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 A, Question 6
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Estimated difficulty · Medium
Question 6 The equation Arg( ) z i 2 3 defines a ray in the complex plane. Identifying complex numbers x + yi with the points (x, y), this ray lies on the line with equation y = mx
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section B, Question 2
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Estimated difficulty · Medium
Question 2 (11 marks) Question 2 continues on the next page. The points representing z1, z2 and z3 are shown on the Argand diagram below.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2How to use ClassConnect past exam questions
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