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 13
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Question 13 A racing car is travelling on a straight horizontal track at a velocity of 80 m s−1 when the brakes are applied at time t = 0 seconds. From time t = 0 to the moment the
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section A, Question 14
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Report-based difficulty · DifficultAverage marks: 36% of available · official reportAnswered correctly: 36% · official report
Question 14 Consider the vectors r and § where [r|=9 and s = 2i ~ 2 + k. If the vector resolute of r in the direction of § is equal to —4i + 4 — 2k, then the scalar resolute of § i
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section A, Question 14
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Question 14 An equilateral triangle is spanned by the vectors a, b and c, as shown below. ~a ~b ~c The scalar product i a b is equivalent to A. 1 2 a B. − 1 C. a 2 D. 3 E
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section A, Question 15
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Report-based difficulty · DifficultAverage marks: 36% of available · official reportAnswered correctly: 36% · official report
Question 15 The position of a moving body is given by £(r) =sin (1)i + cos (21), where tis measured in seconds, for t= 0. The motion of the body can be described as moving along a
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section A, Question 15
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Question 15 A normal vector to the plane that contains the points (2, −1, −1), (3, 1, 1) and (−1, −1, 2) is A. 2 3 3 i j k B. − − − 2 7 10 i j k C. − − − 2 3 2 D. 2 3 2 E. 2
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section A, Question 16
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Report-based difficulty · MediumAverage marks: 43% of available · official reportAnswered correctly: 43% · official report
Question 16 Particle 1 has position vector t(£) =cos(t)i +sin(t)j + y/sin(21) k and Particle 2 has position vector 1, (7) =sin(1)i + cos(r)j + y/sin(2¢) k, where ¢ is measured in s
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section A, Question 16
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Question 16 The position vector r( ) t of a particle at time t is given by r i j ( ) t e e t t 4 , t ≥ 0. The value of t when the particle’s velocity is perpendicular to it
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Report-based difficulty · MediumAverage marks: 58% of available · official reportAnswered correctly: 58% · official report
Question 17 Consider the following parallel lines Lysrp=i+3j+k+s(i+j4k)and Ly: ry =-2i+ j+ 3k +o(i+ +k) wheres, 1 € R The shortest distance between L, and L, is A 3 B. c. VI7 D.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section A, Question 17
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Question 17 The angle at which the line with equation r i j k i j k ( ) t t 2 3 2 , t ∈ R, intersects the plane with equation 2 3 x y z is A. π 6 B. 4 C. 3 D. 3 E. 2
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Report-based difficulty · MediumAverage marks: 68% of available · official reportAnswered correctly: 68% · official report
Question 18 The point of intersection of the line r= + j— 2k +1(~2i + j + 3k), where ¢ € Rand the plane 3x — 2p + 4z = 5 is A. (-5,-1,2) B. (-1,2,1) C. (3.41) D. (-5.4,7)
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section A, Question 18
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Question 18 The shortest distance between the two parallel planes with equations 2x + 2y − z = 6 and −4x − 4y + 2z = −24 is A. 1 B. 2 C. 3 D. 4 E. 6 N H T End of Section A End of S
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Report-based difficulty · MediumAverage marks: 68% of available · official reportAnswered correctly: 68% · official report
Question 19 When conducting a hypothesis test, a type II error occurs when A. anull hypothesis is not rejected when the alternative hypothesis is true. a null hypothesis is rejecte
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