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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c. i. Express the length of the curve given by y = e x - 1 for 0 ≤ x ≤ loge (5) in the form a e dtbt t 1 2 . 2 marks
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ii. Find the length of the curve given by y = e x - 1 for 0 ≤ x ≤ loge (5). Give your answer correct to one decimal place. 1 mark
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d. The curve given by y = e x - 1 for 0 ≤ x ≤ loge (5) is now rotated about the y-axis to form a surface 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(d)(i)Question part (d)(i)
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i. Write down a definite integral that, when evaluated, will give the area of this surface. 1 mark
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ii. Find the area of this surface correct to one decimal place. 1 mark Section B
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Question 4 (10 marks) Vectors D i j k 1 ( ) ( ) ( ) t t t t 2 1 3 1 5 and D i j k 2 ( ) ( ) ( ) t t t t 5 10 2 3 10 are the respective position vectors of two drone
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a. i. Find the speed of Drone 1. Give your answer in kilometres per hour, correct to one decimal place. 1 mark
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ii. Find the angle between vector D1 ( ) t and vector D2 ( ) t when t = 2. Give your answer in degrees, correct to one decimal place. 2 marks
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b. Determine the shortest distance between Drone 1 and Drone 2, and the time when this occurs. Give the distance in kilometres and the time in hours, each correct to three decimal
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c. i. Find the cross product D D 3 ( ) ( ) t t × 4 . 1 mark
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ii. Evaluate this cross product when t = 1 and explain what this result means in terms of the locations of Drone 3 and Drone 4. 1 mark
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Estimated difficulty · Medium
d. At time t = 1 2, Drone 4 begins to malfunction so that its position is given by the new position vector d i j k 4 ( ) ( ) sin ( ) cos ( ) ( ) t t t t t 1 1 . Using this
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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