VCE Mathematical Methods Past Exam Questions
Browse VCE Mathematical Methods 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 2(c)Question part (c)
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c. Find the equation of the tangent line to the graph of y = f (x) at the origin. 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Mathematical Methods examination 2 (PDF, 1.3 MB)Section B, Question 2(d)Question part (d)
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d. Find the equations of the tangent lines to the graph of y = f (x) that have a gradient of - 1 8. 2 marks
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Mathematical Methods examination 2 (PDF, 1.3 MB)Section B, Question 2(e)Question part (e)
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e. Let a, b ∈ R, where 0 < a < b.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Mathematical Methods examination 2 (PDF, 1.3 MB)Section B, Question 2(e)(i)Question part (e)(i)
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i. Show, using algebra, that the average rate of change of f over the interval [a, b] is given by 1 1 12 2 ab a b ( )( ) . 3 marks Section B
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Mathematical Methods examination 2 (PDF, 1.3 MB)Section B, Question 2(e)(ii)Question part (e)(ii)
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Estimated difficulty · Medium
ii. Hence, or otherwise, find a in terms of b such that f (a) = f (b). 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Mathematical Methods examination 2 (PDF, 1.3 MB)Section B, Question 2(f)Question part (f)
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f. Let g : R → R, g x x x k ( ) 2 , where k ∈ (0, ∞).
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Mathematical Methods examination 2 (PDF, 1.3 MB)Section B, Question 2(f)(i)Question part (f)(i)
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i. Find the x-values of the stationary points of g in terms of k. 1 mark
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ii. Find all values of k such that g is strictly decreasing for x ≥ 1. 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Mathematical Methods examination 2 (PDF, 1.3 MB)Section B, Question 2(f)(iii)Question part (f)(iii)
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iii. Let L be the straight line passing through the stationary points of g. Find the total area of the regions bounded by the graph of y = g(x) and the line L, between the stationa
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Mathematical Methods examination 2 (PDF, 1.3 MB)Section B, Question 3
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Question 3 (15 marks) Two hiking apps, app A and app B, provide information about hiking trails. Question 3 continues on the next page.
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a. For app A, the distance, in kilometres, of a randomly selected hiking trail can be modelled by a continuous random variable X with probability density function f x x x x ( ) ( )
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Mathematical Methods examination 2 (PDF, 1.3 MB)Section B, Question 3(a)(i)Question part (a)(i)
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Estimated difficulty · Easy
i. Sketch the graph of y = f (x) for 0 ≤ x ≤ 50 on the axes below. 2 marks x y 0.02 0.04 0.06 0.08 0.10 10 20 30 40 50 O
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Mathematical Methods examination 2 (PDF, 1.3 MB)How to use ClassConnect past exam questions
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