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(g)(ii)Question part (g)(ii)
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ii. For what value(s) of b will the graph of f b have two straight-line asymptotes? 1 mark Section B
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 2
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Question 2 A function with domain x ∈ [0, ∞) has the following rule. f x x x x x x p x ( ) arctan , [ , ) \{ } , 2 4 3 4 0 4 4 2 For the function to be continuous on the interval [
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 2(a)Question part (a)
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a. On the Argand diagram below, sketch the circle and draw the line Im(z) = 4. Plot and label the points z0 , v and w. 2 marks Re(z) Im(z) O 2 4 6 8 2 4 6 8
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 2(c)Question part (c)
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c. Find the area of the major segment bounded by an arc of the circle and the chord connecting point v to point w. 2 marks
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 2(d)Question part (d)
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d. The tangents to the circle at points v and w intersect at a point, P, on the line Im(z) = 4. Show that the x-coordinate of P is 7. 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 2(e)Question part (e)
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e. There are two circles that pass through point P that are tangent to the circle | z - (3 + 4i) | = 2 and have their centres on the line Im(z) = 4. Find the equation of each circl
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 3
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Question 3 (10 marks) A curve is defined parametrically by dx dt = 1, x(0) = 0 and dy dt y 1, y(0) = 0, where t ≥ 0.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 3(a)Question part (a)
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a. i. Write down an expression for dy dx . 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 3(a)(ii)Question part (a)(ii)
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ii. Using integration, show that y = e x - 1. 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 3(b)Question part (b)
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b. The graph of y = e x - 1 where 0 ≤ x ≤ loge (k), for constant k > 1, is rotated about the x-axis to form a solid of revolution.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 3(b)(i)Question part (b)(i)
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i. Given that the volume of the solid of revolution is π × loge (k), use calculus to show that k satisfies the equation k2 - 4k + 3 = 0. 2 marks
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 3(b)(ii)Question part (b)(ii)
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ii. Hence, find the value of k. 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)How to use ClassConnect past exam questions
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