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(c)(iii)Question part (c)(iii)
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iii. Find the point of intersection of the ray with the curve. Express your answer in the form a + ib, where a, b € R. 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 2(d)Question part (d)
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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 2(d)Question part (d)
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d. A ray originating at point P and passing through point Q has the equation Arg ( ) z z 0 , where q is a radian measure. Write down the values of z0 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(e)Question part (e)
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e. i. The line that passes through the points z, = —1 and z, = 3 + 2i has the equation |2|=|z=(c+id)|, where c, d € R\{0}. Find the values of ¢ and d. 1 mark Find the area of the r
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(e)Question part (e)
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e. Find the area of the minor segment bounded by the chord connecting the points P and Q and the circle given by z = 3. Give your answer in the form c π + d, where c, d ∈ R. 2 mark
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Question 3 (10 marks) A tank initially contains 5 kg of salt dissolved in 3000 litres of water. Salty water that contains 0.1 kg of salt per litre of water enters the tank at a rat
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Question 3 (10 marks) Let I;(x) = [sec o) a - [seo sec(x)) ds. Question 3 continues on the next page.
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Report-based difficulty · DifficultAverage marks: 20% of available · official reportFull marks: 20.4% of students · official report
a. By considering concentration, explain whether the quantity of salt in the tank increases with time. 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 3(a)Question part (a)
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a. Use integration by parts to find an expression for /(x) involving sec(x), tan(x) and I(x), where I(x) = Jsee (x)) dx. 3 marks o ° =) S H FE he Id I ® 2 £ 8 = [=] The graph of y
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 3(b)Question part (b)
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Report-based difficulty · MediumAverage marks: 61% of available · official reportFull marks: 61.5% of students · official report
b. Let Q denote the quantity of salt, in kilograms, in the tank at time t minutes. Show that Q satisfies the differential equation dQ dt Q 300 150 . 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 3(b)Question part (b)
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b. Using V(x)= af Lo, where y= 1,(x), find the volume of fluid needed to dv completely fill the dish. Give your answer in cubic centimetres correct to one decimal place. 2 marks Se
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c. What maximum value will N approach? 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)How to use ClassConnect past exam questions
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