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(c)(iv)Question part (c)(iv)
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 54% of students · official report
iv. State the coordinates of the yacht when the minimum speed occurs. 1 mark o ° =) S H FE = ES @ El ? E
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section B, Question 4(d)Question part (d)
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Estimated difficulty · Medium
d. i. Write down a definite integral, in terms of 7, that gives the distance travelled by : : 2 _ _4n the yacht along the path given by ty (1) over the time interval = <=. 1 mark
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Estimated difficulty · Easy
d. Find the constant speed of the drone, in m s−1 , correct to two decimal places. 1 mark
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 57% of students · official report
ii. Find the distance travelled by the yacht over this time interval. Give your answer in metres correct to one decimal place. 1 mark
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Estimated difficulty · Medium
e. The top of a tree has the position vector r i j k tree 60 25 8 . Find the minimum distance from the drone to the top of the tree. Give your answer in metres, correct to
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Report-based difficulty · DifficultAverage marks: 30% of available · official reportFull marks: 24% of students · official report
e. The position vector of a drone videoing the yacht, relative to the same origin as the yacht, 0, is given by 1p, (1) = (2 3)i + (4 —1)j + (6 — )k, where 0 < 1 < 5. Displacement c
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Estimated difficulty · Medium
Question 5 (10 marks) Consider the points A(1, 2, 3) and B(2, =5, ~1).
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Estimated difficulty · Medium
Question 5 (10 marks) Consider the three points A (−1, 1, 2), B (0, 3, 3) and C (3, 2, −1), which lie in the plane P.
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 55% of students · official report
a. Find a vector equation, in terms of the components i, j and k, for the line passing through these points. 1 mark
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Estimated difficulty · Medium
a. Show that the points A, B and C do not lie on a straight line. 2 marks
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Estimated difficulty · Easy
b. Find the Cartesian equation of the plane P. 2 marks Section B Now consider the plane Q, given by 2x − y + 3z = 1, and the line L, given by r i j k i j k ( ) t t 2
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Report-based difficulty · MediumAverage marks: 63.3% of available · official reportFull marks: 50% of students · official report
b. Consider the different line Ly: £,(1)=2i+j~3k+(~i+2j+k), rR. Find the shortest distance from L, to point A. Give your answer in the form where a, b and c are positive integers.
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