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 3(c)Question part (c)
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Report-based difficulty · MediumAverage marks: 46% of available · official reportFull marks: 38.9% of students · official report
c. Using Euler’s method with a step size of 15 minutes, find Q(30), the approximate quantity of salt in the tank after 30 minutes. Give your answer in kilograms, correct to two dec
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(d)Question part (d)
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Estimated difficulty · Easy
d. i. Express as a definite integral the time it would take for N to reach 7500. 1 mark
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Report-based difficulty · EasyAverage marks: 74.7% of available · official reportFull marks: 59.3% of students · official report
d. Use calculus to solve the differential equation dQ dt Q 300 150 , expressing Q in terms of t. 3 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 3(d)(ii)Question part (d)(ii)
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Estimated difficulty · Easy
ii. Find the time it would take for the number of bacteria to grow to 7500. Give your answer in minutes correct to one decimal place. 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 3(e)Question part (e)
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Report-based difficulty · EasyAverage marks: 79% of available · official reportFull marks: 79.5% of students · official report
e. What value does the quantity of salt in the tank approach as time approaches infinity? Give your answer in kilograms. 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(e)Question part (e)
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Estimated difficulty · Easy
e. Given that 400 15000 7500 the graph of N against has a non-stationary point of inflection where N = 7500. 2 marks al ( hl {1-5 to cluions 0 verify that o ° =) S H FE he This pag
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(f)Question part (f)
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 60.7% of students · official report
f. Find the time taken for the quantity of salt in the tank to reach 100 kg. 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(g)Question part (g)
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Report-based difficulty · DifficultAverage marks: 18% of available · official reportFull marks: 18.1% of students · official report
g. When the quantity of salt in the tank reaches 100 kg, the tap draining the tank is turned off. Assume that the tank does not overflow and there is no change to the inflow rate.
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 4
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Estimated difficulty · Difficult
Question 4 (10 marks) A duck swims on a lake. The duck’s position vector, relative to an origin, O, at time seconds, is given by 1p(0) = (2-5cos(1))i + (1-6sin (1) j, where 0 << 10
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Estimated difficulty · Difficult
Question 4 (10 marks) The path of a moving particle with position vector r i ( ) cos cos sin sin t t t t t 5 4 5 2 5 4 5 2 j is shown below for time t ≥ 0. All lengths are in
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Estimated difficulty · Easy
a. Find the Cartesian equation of the path of the duck. 2 marks
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Report-based difficulty · EasyAverage marks: 93% of available · official reportFull marks: 93.4% of students · official report
a. Write down the coordinates of the particle’s starting point. 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)How to use ClassConnect past exam questions
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