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.
Matching results: 1,902 indexed questions and parts.
Question 6
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Question 6 (2 marks) Let X be a normal random variable. Let a and b be real numbers, where a < b. If Pr (X < a) = m and Pr (X < b) = n, find, in terms of m and n, Pr (X > a | X < b
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Question 7 (3 marks) Let f R : ( , ) 0 12 → , f x x ( ) 12 . A rectangle is inscribed on the graph of y = f (x) so that it has a vertex at the origin and the diagonally opposite ve
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a. Show that the area of the rectangle can be expressed as A k k k ( ) 12 2 3 . 1 mark
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b. Determine the value of k that maximises the area of the rectangle. 2 marks
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Question 8 (6 marks) Let f R R : → , f x x e ( ) log ( ) 1 2 . The graph of y = f (x) is shown below. x y 1 2 3 −3 −2 −1 1 2 3 −1 −2 −3 O ( ) y f x = Let g R R : → , g x f x ( ) (
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a. Determine the coordinates of the points of intersection of the graphs of y = f (x) and y = g (x). 3 marks
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b. Sketch the graph of y = g (x) on the axes on page 10. Label the coordinates of the y-intercept. 2 marks
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c. The point 2 3 , log ( ) e lies on the graph of y = f (x). The graph of y = f (x) has the following sequence of transformations applied: 1. a dilation by a factor of 1 2 from the
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Question 9 (9 marks) Let f R R : → , f x e e x ( ) 2 2 .
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a. Show that f x e e x ' ( ) 4 2 . 1 mark
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b. The graph of y = f (x) has exactly one stationary point.
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i. Find the coordinates of this stationary point. 2 marks
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