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 15(e)Question part (e)
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Estimated difficulty · Easy
7 2023 MATHMETH EXAM 2 (NHT) TURN OVER d o n o t w r i t e i n t h i s a r e a
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Report-based difficulty · MediumAverage marks: 69% of available · official reportAnswered correctly: 69% · official report
Question 16 Let f (x) = e x − 1. Given that the product function f (x) × g(x) = e(x − 1)2 , the rule for the function g is A. g(x) = e x − 1 B. g(x) = e(x − 2)(x − 1) C. g(x) = e(x
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Mathematical Methods 2 examination · Report: 2023 VCE Mathematical Methods 2 external assessment reportSection A, Question 16
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Question 16 Let f R f x x :[ , ] , ( ) 1 3 3 1 and g R g x x : , , ( ) 3 3 2 The largest domain for which g ( f (x)) is defined is A. 1 3 , B. 1 3 3 1 3 , C. 3 3 , D. , E. [ , ] −1
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE (NHT) Mathematical Methods examination 2Section A, Question 17
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Question 17 The function f (x) = x2 + kx + 2 has more than one solution when A. k 2 2, B. k 2 2 2 2 , C. k , , 2 2 2 2 D. k , , 2 2 2 2 E. k , , 2 2 2 2
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Report-based difficulty · DifficultAverage marks: 28% of available · official reportAnswered correctly: 28% · official report
Question 17 A cylinder of height h and radius r is formed from a thin rectangular sheet of metal of length x and width y, by cutting along the dashed lines shown below. x y h r The
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Mathematical Methods 2 examination · Report: 2023 VCE Mathematical Methods 2 external assessment reportSection A, Question 18
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Question 18 An investment firm models a particular financial investment using the equation V = b(1 + a)t, where V represents the value of the investment after t years and a and b a
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Report-based difficulty · DifficultAverage marks: 29% of available · official reportAnswered correctly: 29% · official report
Question 18 Consider the function f : [−a π, aπ] → R, f (x) = sin(ax), where a is a positive integer. The number of local minima in the graph of y = f (x) is always equal to A. 2 B
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Mathematical Methods 2 examination · Report: 2023 VCE Mathematical Methods 2 external assessment reportSection A, Question 19
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Question 19 The graph of y = loge(x − k), for k ∈ R, has a tangent with a maximum horizontal axis intercept of A. x = 1 B. x = k C. x = e D. x = 1 + k E. x = e + k 2023 MATHMETH EX
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Report-based difficulty · DifficultAverage marks: 32% of available · official reportAnswered correctly: 32% · official report
Question 19 Find all values of k, such that the equation x k x k 2 2 4 3 4 9 4 0 ( ) has two real solutions for x, one positive and one negative. A. k 3 4 B. k 3 C. k > 3 D. 3 k E.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Mathematical Methods 2 examination · Report: 2023 VCE Mathematical Methods 2 external assessment reportSection A, Question 20
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Question 20 The graph of y f x 2 1 ( ) is shown below. O y x −1 If all axes are to the same scale as the graph above, the graph of y = f (x) is best represented by x O A. B. C. D.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE (NHT) Mathematical Methods examination 2Section A, Question 20
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Report-based difficulty · DifficultAverage marks: 30% of available · official reportAnswered correctly: 30% · official report
Question 20 Let f x x e ( ) log 1 2 . Let g(x) = sin(x) where x ∈ (−∞, 5). The largest interval of x values for which ( f ⸰ g)(x) and (g ⸰ f )(x) both exist is A. 1 2 5 4 B. 1 C. 4
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Mathematical Methods 2 examination · Report: 2023 VCE Mathematical Methods 2 external assessment reportSection A, Question 20(c)Question part (c)
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Estimated difficulty · Easy
9 2023 MATHMETH EXAM 2 (NHT) d o n o t w r i t e i n t h i s a r e a TURN OVER CONTINUES OVER PAGE 2023 MATHMETH EXAM 2 (NHT) 10 D O N O T W R I T E I N T H I S A R E A
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