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 1(d)(iii)Question part (d)(iii)
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Report-based difficulty · EasyAverage marks: 75% of available · official reportFull marks: 70.8% of students · official report
iii. For a given value of a, the graph will have a point of inflection at x = 2. Find the value of a. 2 marks
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
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Estimated difficulty · Medium
Question 2 (10 marks) Question 2 continues on the next page.
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(a)Question part (a)
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Estimated difficulty · Medium
a. Show that the relation |z — 2i| = Im (= + i) can be expressed in Cartesian form as 6y=x"+3, where z=x+iy, x,y € R. 1 mark Id I ® 2 £ 8 H ° = o [=] Section B
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(a)Question part (a)
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Report-based difficulty · EasyAverage marks: 88% of available · official reportFull marks: 88.3% of students · official report
a. Sketch { : , } z zz z C 4 on the Argand plane below. 1 mark Im(z) Re(z) 2 1 3 −2 −1 −3 1 −1 −2 −3 2 3 O
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(b)Question part (b)
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Estimated difficulty · Easy
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)Question part (b)
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Estimated difficulty · Medium
b. i. Show that z z i z i z C : , 2 3 may be expressed as y x = 3 . 2 marks
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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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Estimated difficulty · Easy
c. Aray from the origin O is tangential to the part of the curve where Re(z) > 0. = 3 Id I ® 2 £ 8 H ° = o [=]
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)Question part (c)
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Estimated difficulty · Easy
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
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Estimated difficulty · Easy
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(c)(ii)Question part (c)(ii)
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Estimated difficulty · Easy
ii. Find the equation of this ray in Cartesian form. 2 marks ® ° FE =
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE (NHT) Specialist Mathematics examination 2 (PDF, 5.7 MB)How to use ClassConnect past exam questions
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