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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Question 1
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Question 1 (3 marks) An object is moving in a straight line with constant positive acceleration. At time t seconds, its velocity is v m s−1 and its displacement is d metres. When t
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a. Show that the initial velocity of the object is 3 m s−1 . 1 mark
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b. After how many seconds is the object’s displacement 28 m? 2 marks Instructions • Answer all questions in the spaces provided. • Write your responses in English. • Unless otherwi
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Question 2 (3 marks) Prove by mathematical induction that the number given by n2 + 5n is even for all n ∈ N.
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Question 3 (3 marks) Determine the x-coordinate(s) of any point(s) of inflection of the graph of f (x) = x5 + x4 − x.
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a. Consider the differential equation 2 0 2 d y dx dy dx y . Two solutions of the differential equation have the form y = e mx, where m ∈ R. Show that m 1 2 or m = 1. 2 marks
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b. The graphs of the two solutions of the differential equation are shown on the Cartesian plane below. –2 – 1 1 2 x 1 2 3 y O x = 1 The shaded region shown above is bounded by the
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Question 5 (4 marks) Evaluate x x x dx 2 0 3 2 1 .
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Question 6 (3 marks) The masses of a particular variety of cherry tomato may be assumed to be normally distributed with a population standard deviation of 6 grams. A sample of size
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a. Write down the sample mean. 1 mark
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b. Calculate n, the sample size. 2 marks
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Question 7 (3 marks) A curve is described by the parametric equations x t t 2 2 1 and y t t 1 , where t ∈ R \{0}.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 1 (PDF, 633.42 KB)How to use ClassConnect past exam questions
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