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.
Matching results: 1,669 indexed questions and parts.
Section A, Question 7
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Question 7 x y O–2 –1 1 –2 –1 1 2 The direction field above best represents the differential equation A. dy dx y x B. dy dx x y C. dy dx x y D. dy dx y x
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section A, Question 8
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Question 8 A curve is described parametrically by x = sin (t), y = sec (t), where 2 2 t . The exact value of t, where dy dx = 4 3, is A. π 6 B. 1.047 C. 3 D. tan 1 4 3 Section A
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Question 9 Using the substitution x3 - 1 = u2 , u ≥ 0, the definite integral x x dx 3 1 2 1 can be expressed as A. 2 3 1 1 1 0 7 2 u du B. 1 3 1 0 2 u C. 3 2 1 1 1 1 2 D. 2 2
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section A, Question 10
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Question 10 The curve defined by the parametric equations x = 2t - sin (2t), y = 1 - cos (2t) for 0 ≤ t ≤ π is rotated about the x-axis to form a surface of revolution. The area of
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Question 11 By separation of variables, the differential equation dy dx e x x y x y x y sin ( ) sin ( ) sin ( ) cos ( ) 2 leads to A. e y dy e x dxy x sin ( ) sin ( ) 2 B. e y dy e
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section A, Question 13
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Question 13 A particle moves along a straight line. The position of the particle from a fixed point is given by x(t) = e-t sin (t) for 0 ≤ t ≤ 3 π. The number of times the particle
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section A, Question 14
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Question 14 A particle moves in a straight line such that its acceleration, a m s-2 , is given by a = 2 + v, where v m s-1 is the velocity of the particle. At the origin, the veloc
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section A, Question 15
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Question 15 Let u i j k a 3 5 , where a ∈ R, and v i j k 2 2 . If the scalar resolute of u in the direction of v is 2, then the value of a is A. 2 5 B. 1 2 C. 5
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Question 16 Consider vectors a i j k p 4 , b i j k 2 4 and c i k 3 4 , where p is a positive integer. Given tan 3, where θ is the angle between a and b
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section A, Question 17
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Question 17 Two objects have velocities given by r i j k ( ) cos ( ) sin ( ) t t t and s ( ) i j k t t t 2 2 cos ( ) sin ( ) , where components are measured in m s-1 . Given r
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section A, Question 18
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Question 18 The angle between the planes given by x y z 2 2 and x y z 2 4 is A. π 3 B. 2 C. 3 4 D. 5 6 Section A
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Question 19 Which one of the following vector equations describes the line of intersection of the planes given by x - 2y + z = 3 and 2x + y - z = 5? A. r i j k i j k
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)How to use ClassConnect past exam questions
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