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 5(b)Question part (b)
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 48% of students · official report
b. After the body has been in motion for two seconds, a constant braking force, R newtons, is applied to the body parallel to the plane so that the body has constant velocity. Find
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Estimated difficulty · Medium
Question 6 – continued Question 6 (6 marks)
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Question 6 (3 marks) Relative to a fixed origin, the position of a 2 kg mass after t seconds is given by r i + j k ( ) t t t e t 32 6 3 2 2 8 , t ≥ 0, where components are
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a. Find the cosine of the acute angle between the vectors a i j k 2 3 6 and b i j k 2 2 . 2 marks 9 2022 SPECMATH EXAM 1 TURN OVER d o n o t w r i t e i n t h i s a
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b. OPQ is a semicircle of radius a with equation y a x a 2 2 ( ) . P(x, y) is a point on the semicircle OPQ, as shown below. y P(x, y) O Q a x
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i. Express the vectors OP and QP in terms of a, x, y, i and j , where i is a unit vector in the direction of the positive x-axis and j is a unit vector in the direction of
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ii. Hence, using the vector scalar (dot) product, determine whether OP is perpendicular to QP. 3 marks 2022 SPECMATH EXAM 1 10 d o n o t w r i t e i n t h i s a r e a
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Question 7 (4 marks) The path of a moving particle after t seconds is given by r i + 2tan j ( ) sec( ) ( ) t t t = 4 for t 0 2 , , where components are measured in metres.
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 34% of students · official report
Question 7 (3 marks) A curve has equation x x y cos( ) 48 . Find the gradient of the curve at the point 24 7 , . Give your answer in the form a b , where a, b ∈ Z. 11 2022 SPECMATH
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a. Find the cartesian equation of the path. 2 marks
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b. Find the speed of the particle when t 6 . 2 marks 2022 SPECMATH EXAM 1 (NHT) 8 d o n o t w r i t e i n t h i s a r e a
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Question 8 ‒ continued Question 8 (6 marks) A printer can use three types of ink cartridges: Standard, Deluxe and Elite. The Standard cartridge has a mean print run (the average nu
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