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 4(b)Question part (b)
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Report-based difficulty · MediumAverage marks: 62% of available · official reportFull marks: 62.8% of students · official report
b. On the graph above, draw an arrow from the point (9, 0) to indicate the direction of motion of the particle. 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 4(b)Question part (b)
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Estimated difficulty · Medium
b. How far does the duck travel along the path in the first 5 seconds? Give your answer in metres correct to one decimal place. 2 marks o ° =) S H FE he ES @ El ? E Id I ® 2 £ 8 =
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 4(c)Question part (c)
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Estimated difficulty · Medium
c. Use integration to show that the position vector of the drone is re0=(30 0200020 fio 2 a0 30 jo ($20 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 4(c)Question part (c)
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Report-based difficulty · MediumAverage marks: 52% of available · official reportFull marks: 52.9% of students · official report
c. Find the value of t for which the particle will first return to its starting point. 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 4(d)Question part (d)
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Report-based difficulty · MediumAverage marks: 57.7% of available · official reportFull marks: 35.6% of students · official report
d. Show that the speed of the particle, in m s−1 , at time t can be expressed as 125 100 3 2 cos 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 4(d)Question part (d)
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Estimated difficulty · Easy
d. Find the values of a, b and c if the drone reaches the duck when ¢ = 10. Give your answers correct to one decimal place. 2 marks
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 4(e)Question part (e)
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Report-based difficulty · EasyAverage marks: 72% of available · official reportFull marks: 72.9% of students · official report
e. What is the maximum speed of the particle in m s−1 ? 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 4(e)Question part (e)
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Estimated difficulty · Easy
e. At what time is the duck closest to the initial position of the drone? Give your answer in seconds correct to one decimal place. 3 marks 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 4(f)Question part (f)
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Report-based difficulty · MediumAverage marks: 65% of available · official reportFull marks: 65.8% of students · official report
f. On the graph on page 18, trace the path of the particle for t ∈ [0, π]. 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 4(g)Question part (g)
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Report-based difficulty · MediumAverage marks: 68% of available · official reportFull marks: 63.7% of students · official report
g. Find the length of the path traced in part f, giving your answer in metres, correct to one decimal place. 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 5
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Estimated difficulty · Medium
Question 5 (10 marks) Consider three planes defined by the equations P1 : 2x + 9z = 8, P2 : 3x + 6y + 5z = 7 and P3 : x + 9y − 3z = 7.
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Estimated difficulty · Medium
Question 5 (10 marks) The points P (a, —4, —4), (3, -4,-2), S(5,4,-2) and T(2, 3, 2), where a € R, lic on the plane I, relative to an origin, 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)How to use ClassConnect past exam questions
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