VCE Specialist Mathematics Past Exam Questions
Browse VCE Specialist Mathematics exam questions from 2015–2026, including NHT and VCE papers. Filter by topic, year and paper; open the original source.
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Question 6(b)Question part (b)
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Report-based difficulty · MediumAverage marks: 45% of available · official reportFull marks: 40% of students · official report
b. Josie’s waiting time for a train on each work day is independent of her waiting time for a train on any other work day. The probability that, for 12 randomly chosen work days, J
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Specialist Mathematics examination 1 · Report: 2023 VCE Specialist Mathematics 1 external assessment reportQuestion 7
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Question 7 (5 marks) A particle falls from rest such that its acceleration, in ms−2, is given by a = g − 2v, where v is the velocity of the particle, in ms−1, at time t seconds.
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Report-based difficulty · MediumAverage marks: 55% of available · official reportFull marks: 31% of students · official report
Question 7 (4 marks) The curve defined by the parametric equations x t y t 2 4 1 3 , , where 0 ≤ t ≤ 2, is rotated about the x-axis to form an open hollow surface of revolution. Fi
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a. Solve a suitable differential equation to show that v g e t 2 1 2 . 4 marks
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b. Write down the limiting (terminal) velocity of the particle in ms−1. 1 mark 2023 SPECMATH EXAM 1 (NHT) 12 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: 52.5% of available · official reportFull marks: 21% of students · official report
Question 8 (4 marks) A function f has the rule f (x) = x e2x. Use mathematical induction to prove that f x x n en n n x ( ) ( ) 2 2 1 2 for n ∈ Z +, where f (n) (x) represents the
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Estimated difficulty · Medium
Question 8 – continued Question 8 (4 marks)
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a. Show that dy dx x = sec( ), given that y x x e log sec( ) tan( ) . 2 marks 13 2023 SPECMATH EXAM 1 (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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b. Part of the curve with equation y x 1 1 cos( ) is shown below. 3 π x y O Find the shaded area, which is bounded by the curve, the x-axis and the line x 3 . 2 marks 2023 SPECMATH
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Question 9 (5 marks) The position vectors of two cyclists, A and B, after t seconds are given by r i j A t a t a ( ) ( ) 6 7 2 3 and r i j B t a t a ( ) ( ) 5 4 6 2 2 r
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Question 9 (6 marks) A plane contains the points A(1, 3, −2), B(−1, −2, 4) and C(a, −1, 5), where a is a real constant. The plane has a y-axis intercept of 2 at the point D.
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a. Find a quadratic equation in the form f (a) = 0 that, when solved, gives the value of a. A solution to this equation is not required. 2 marks
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE (NHT) Specialist Mathematics examination 1How to use ClassConnect past exam questions
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