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 4(b)Question part (b)
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Estimated difficulty · Easy
b. i. Find all real values of k for which f (x) = k has exactly two solutions for x. 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 4(b)(ii)Question part (b)(ii)
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ii. Find all real values of k for which f (x) = k has exactly three solutions for x. 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 4(c)Question part (c)
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c. i. When the graph of y = f (x) is reflected in the x-axis, its image has two local maximum turning points. State the coordinates of these two turning points. 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 4(c)(ii)Question part (c)(ii)
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Estimated difficulty · Medium
ii. The function f has the property that when its graph is reflected in the x-axis and then reflected in the y-axis, its image can be expressed in the form y = f (x + b) + c, for s
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 4(d)Question part (d)
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Estimated difficulty · Easy
d. The graph of y = f (x) is shown again below. 1 2 3 4 −3 −4 −2 −1 1 2 3 4 5 −1 −2 −3 −4 −5 x y O ( ) y f x = Let h1 be the inverse function of f when f is restricted to have doma
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 4(d)(i)Question part (d)(i)
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Estimated difficulty · Easy
i. State the domain of h1. 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 4(d)(ii)Question part (d)(ii)
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ii. Find h1(2). 1 mark 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 4(e)Question part (e)
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Estimated difficulty · Easy
e. Let hm be the inverse function of f when f is restricted to have domain [m, m + 1] for particular values of m ∈ [0, 4].
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 4(e)(i)Question part (e)(i)
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Estimated difficulty · Medium
i. Explain why m must be an integer for the inverse function hm to exist. 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 4(e)(ii)Question part (e)(ii)
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ii. Find the value(s) of m such that h m(1) is an integer. 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 4(f)Question part (f)
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Estimated difficulty · Medium
f. Let g : (-0.8, 1.8) → R, g(x) = x3 - x2 - x + 3.
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 4(f)(i)Question part (f)(i)
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Estimated difficulty · Medium
i. Find the range of g and, hence, show that f g x ( ) is defined for all x ∈ (-0.8, 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)How to use ClassConnect past exam questions
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