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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Report-based difficulty · MediumAverage marks: 45% of available · official reportAnswered correctly: 45% · official report
Question 13 A tourist in a hot air balloon, which is rising vertically at 2.5 m s−1, accidentally drops a phone over the side when the phone is 80 metres above the ground. Assuming
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 13
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Estimated difficulty · Medium
Question 13 The vector resolute of a i j k 4 3d d , where d ∈ R , in the direction of a non-zero vector b is 2 2 i j k − − . The value of d is A. −1 B. − 1 5 C. 1 3
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Report-based difficulty · MediumAverage marks: 48% of available · official reportAnswered correctly: 48% · official report
Question 14 Let a i j , b i j and c i j k 2 3 . If n is a unit vector such that a.n = 0 and b.n = 0, then c.n is equal to A. 2 B. 3 C. 4 D. 5 E. 6
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Estimated difficulty · Medium
Question 14 The angle between the vector i j k + + 2 and the positive direction of the z-axis is A. π 4 B. 3 C. cos 1 4 6 D. cos 1 1 E. cos TURN OVER 9 2023 SPECMATH EXAM 2 (
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Estimated difficulty · Easy
Question 15 Two masses of 4 kg and M kg are connected by a light inextensible string over a smooth pulley. The 4 kg mass rests on a smooth horizontal surface. Initially the system
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Estimated difficulty · Medium
Question 15 If the sum of two unit vectors is a unit vector, then the magnitude of the difference of the two vectors is A. 0 B. 1 2 C. 2 D. 3 E. 5
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Report-based difficulty · DifficultAverage marks: 32% of available · official reportAnswered correctly: 32% · official report
Question 16 A student throws a ball for his dog to retrieve. The position vector of the ball, relative to an origin O at ground level t seconds after release, is given by r
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Estimated difficulty · Easy
Question 16 A mass of 5 kg sitting at rest on a smooth horizontal surface is acted on by a horizontal force of 10 N. How far, in metres, will the mass move from its original positi
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Report-based difficulty · EasyAverage marks: 73% of available · official reportAnswered correctly: 73% · official report
Question 17 Consider the vectors a i j k , b i j k 3 4 and c i j k 2 7 , where α, β, γ ∈ R. If a b c , then A. α = −2, β = −1, γ = −5 B. α = −1, β = 2
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Estimated difficulty · Medium
Question 17 A particle of mass m kilograms moving in a horizontal straight line is acted on by a horizontal variable force. The velocity of the particle when it is x metres from a
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Estimated difficulty · Medium
Question 18 Each night, a student typically spends 100 minutes on mathematics homework and 40 minutes reading. The standard deviations of the times spent on mathematics and reading
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Report-based difficulty · EasyAverage marks: 74% of available · official reportAnswered correctly: 74% · official report
Question 18 What value of k, where k ∈ R, will make the following planes perpendicular? Π1 : 2x − ky + 3z = 1 Π2 : 2kx + 3y − 2z = 4 A. 2 B. 4 C. 6 D. 8 E. 10
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