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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Section A, Question 7
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Question 7 The definite integral cos ( )sin ( ) 3 2 0 2 x x dx can be expressed as A. u u du 4 2 1 , where u = sin(x) B. u u du 2 4 2 , where u = sin(x) C. u u du 2 4 D. u u du 3 5
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE (NHT) Specialist Mathematics examination 2Section A, Question 7
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Report-based difficulty · MediumAverage marks: 68% of available · official reportAnswered correctly: 68% · official report
Question 7 x y O −2 −1 2 1 −2 −1 1 2 The direction field for a differential equation is shown above. On a certain solution curve of this differential equation, y = 2 when x = −1. T
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Specialist Mathematics examination 2 · Report: 2023 VCE Specialist Mathematics 2 external assessment reportSection A, Question 8
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Question 8 −6 −4 −2 O 2 4 6 −2 −4 2 4 y x The direction field shown above best represents the differential equation A. dy dx = B. dy = 2 C. dy D. dy E. dy 2 2023 SPECMATH EXAM 2 (N
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Report-based difficulty · DifficultAverage marks: 37% of available · official reportAnswered correctly: 37% · official report
Question 8 Initially a spa pool is filled with 8000 litres of water that contains a quantity of dissolved chemical. It is discovered that too much chemical is contained in the spa
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Specialist Mathematics examination 2 · Report: 2023 VCE Specialist Mathematics 2 external assessment reportSection A, Question 9
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Report-based difficulty · MediumAverage marks: 65% of available · official reportAnswered correctly: 65% · official report
Question 9 The position of a particle moving in the Cartesian plane, at time t, is given by the parametric equations x t t t ( ) 6 1 and y t t 8 42 , where t ≥ 0. What is the slope
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Question 9 The length L of a curve from x = 1 to x = 5 is given by 1 1 4 4 1 5 x dx. The equation of the curve could be A. y x = 1 2 2 B. y x 1 3 C. y x 12 3 D. y x 2 E. y x 144 6
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Question 10 An inverted right circular cone of radius 1 m and height 2 m is initially full of water, as shown below. 1 m 2 m h m Water flows out through a hole at the bottom at a r
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Question 10 If I n x e dxn x ( ) 1 0 1 , where n ∈ N, then for n ≥ 1, In equals A. −1 + nIn − 1 B. nIn − 1 C. −1 − nIn − 1 D. −nIn − 1 E. (1 − x)ne x + nIn − 1
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Question 11 The position of a moving particle at time t is given by r i j ( ) cos( ) sin( ) t t t 5 2 3 1 , where 2 3 t . The graph that shows the path and the direction take
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Report-based difficulty · MediumAverage marks: 46% of available · official reportAnswered correctly: 46% · official report
Question 11 The area of the curved surface generated by revolving part of the curve with equation y = cos−1(x) from 0 2 , to (1, 0) about the y-axis can be found by evaluating A. 2
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Question 12 The position of a particle at time t seconds is given by r i j ( ) sin ( ) cos ( ) t t t 3 2 3 , where displacement components are measured in metres. The maximum
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Report-based difficulty · MediumAverage marks: 54% of available · official reportAnswered correctly: 54% · official report
Question 12 The acceleration, a m s−2, of a particle that starts from rest and moves in a straight line is described by a = 1 + v, where v m s−1 is its velocity after t seconds. Th
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