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(e)Question part (e)
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Estimated difficulty · Easy
e. Let m, n ∈ R and g(x) = mf −1 (nx) be a function describing a transformation of the inverse f −1. Find the values of m and n, given that g(x) describes the tile edge joining (−4
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f. Find the area of one of the tiles. An example is shaded in Figure 2. 2 marks
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Estimated difficulty · Medium
g. Using the derivatives of f and g at x = − 4, show that the angle at the left corner of the shaded tile, at the point (−4, 0), is 90°. 2 marks N H T
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Estimated difficulty · Easy
h. The family of functions defined by y = g(x − 8k), k ∈ Z gives an infinite set of edges in Timothy’s tiling pattern, three of which are shown in bold on Figure 3. y x 10 8 6 4 2
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Estimated difficulty · Medium
Question 5 (11 marks) The graph below shows the compositions g = f and = g, where f(x) = sin(x) and 2x) = sin(2x). o H oO 2 Question 5 continues on the next page.
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Estimated difficulty · Medium
Question 5 continues on the next page. Question 5 (12 marks) Let f : R → R, f (x) = e−ex.
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Estimated difficulty · Easy
a. I The graph of y = (g = /)(x) has a local maximum whose x-value lies in the 5 « interval | 0,7 5 2 = Find the coordinates of this local maximum, correct to one decimal place. 1
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Estimated difficulty · Medium
a. Show that the rule and domain for f −1, the inverse function of f, is f x e x e 1 1 ( ) log ( ) where x ∈ (0, ∞) 2 marks
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 63% of students · official report
ii. State the range of g = / where x € [0,27] 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)Section B, Question 5(b)Question part (b)
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Estimated difficulty · Easy
b. The graphs of f and f −1 are shown below. Their unique intersection point 1 1 e e , is also labelled. 1 1 f −1 f 1 O 1 x y Find the exact area of the shaded region t
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b. i. Find the derivative of /* g. 1 mark Section B
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Estimated difficulty · Easy
c. Consider the function g1(x) = e ax, where a e = 1 .
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