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 5
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Question 5 (10 marks) Consider the three points P1 4 3 3 0 , , , P2 3 0 4 , , and P3 0 2 2 ( ) , , .
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 5(a)Question part (a)
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a. Using a vector method, find the area of the triangle with vertices P1, P2 and P3. Give your answer in the form a b c , where a, b, c ∈ Z + and c = a + 1. 3 marks
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b. The points P1, P2 and P3 lie in the plane Π1. Find the Cartesian equation of this plane. 2 marks Use the following information to answer part c and part d. Now consider the plan
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 5(c)Question part (c)
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c. i. Show that the plane Π3 given by d z x y 1 5 3 1 2 . , where d ∈ R, is parallel to the plane Π2 . 1 mark
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ii. Determine the values of d so that the minimum distance between plane Π2 and plane Π3 is 2 6 . 2 marks
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d. Consider the plane Π2, and the plane Π4 given by p2x - (p + 2)y - 5z = 1 for p ∈ R. Find the possible values of p for these two planes to be perpendicular. 2 marks Section B
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Question 6 (10 marks) In preparation for an upcoming competition, a snowboarder undertakes many descents down a competition slope. The times taken for the snowboarder to descend th
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a. Find the probability that the times taken for two descents differ by less than 5 s. Give your answer correct to four decimal places. 2 marks
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b. Find the probability that the average time of four descents differs by less than 5 s from the mean of 200 s. Give your answer correct to four decimal places. 2 marks Use the fol
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c. Write down suitable null and alternative hypotheses for the test. 1 mark
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d. i. Determine the p value for the test. Give your answer correct to four decimal places. 1 mark
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 6(d)(ii)Question part (d)(ii)
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ii. Does the application of the new wax produce a significant improvement in descent times at the 5% level of significance? Justify your answer in terms of the p value. 1 mark
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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