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 A, Question 20
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Estimated difficulty · Easy
Question 20 Let f : R → R, f (x) = x2 (1 − x2) and g : [0, 1] → R, g(x) = f (x − a). Find all real values of a, such that g(0) is the absolute maximum value of g. A. a 2 2 B. a , C
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Estimated difficulty · Medium
Question 1 (12 marks) Consider the function /: R = R, f(x) = (x+1)(x + @)(x—2)(x —2a) where a € R. Question 1 continues on the next page.
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Question 1 (10 marks) Consider the function f : R → R, f (x) = x3 − px, where p ∈ R. Part of the graph of f is shown below, when p = 3. O y x
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Report-based difficulty · EasyAverage marks: 90% of available · official reportFull marks: 85% of students · official report
a. State, in terms of a where required, the values of x for which f(x) = 0 1 mark
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a. Find the values of the x-intercepts of f, when p = 3. 1 mark
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b. Use the derivative f ′ to find the coordinates of the turning points of f, when p = 3. 2 marks Section B
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Estimated difficulty · Easy
b. Find the values of @ for which the graph of Section B
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Report-based difficulty · MediumAverage marks: 40% of available · official reportFull marks: 10% of students · official report
i. exactly three x-intercepts. 2 marks
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Estimated difficulty · Easy
ii. exactly four x-intercepts. 1 mark
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Estimated difficulty · Easy
c. Letg be the function g: R — R, g(x) = (x+1)*(x=2)?, which is the function f where a = 1.
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Estimated difficulty · Easy
c. i. Find the value of p for which f would have exactly one stationary point. 1 mark
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Report-based difficulty · EasyAverage marks: 100% of available · official reportFull marks: 95% of students · official report
i. Find g(x). 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Mathematical Methods 2 examination · Report: 2024 VCE Mathematical Methods 2 external assessment report (DOCX, 860.29 KB)How to use ClassConnect past exam questions
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