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 7(b)Question part (b)
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Estimated difficulty · Easy
b. The acceleration of the toy car is positive for twice the amount of time that the acceleration of the toy car is negative. Id I & 2 £ 8 H ° = o [=]
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i. Show that it takes 9 seconds for the toy car to reach line F from line O. 1 mark
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ii. Show that the equation for the velocity of the toy car when it has negative acceleration is given by v= 26 — 4z. 1 mark
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iii. Show that the displacement of the toy car, from line O, when it reaches line F, is 30 m. 1 mark o ° =) S H FE he ES @ El ? E
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c. A toy train moves with a constant velocity on an adjacent, parallel track such that the toy car and the toy train are at line O at the same time, and both arrive at line Fat tim
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Question 8 (4 marks) Consider the curve shown below. The parametric equations for this curve are = 4cos’(6) and y = 4sin’(6), where 0 & Jo 1] . xis to form a surface of revolution.
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Question 8 (5 marks) Consider the function with rule f z z z ( ) 4 2 6 25, where z C ∈ .
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Report-based difficulty · EasyAverage marks: 80% of available · official reportFull marks: 84% of students · official report
a. Consider z i 1 1 2 . Plot and label z1 and z1 on the Argand plane below. 1 mark Im(z) Re(z) 2 4 −2 −4 2 −2 −4 4 O
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Report-based difficulty · EasyAverage marks: 70% of available · official reportFull marks: 61% of students · official report
b. Given that 1 + 2i is a solution of f z ( ) = 0, find a quadratic factor of f z ( ). 2 marks
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Report-based difficulty · MediumAverage marks: 55% of available · official reportFull marks: 42% of students · official report
c. Hence, find all remaining solutions of f z ( ) = 0. 2 marks
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Question 9 (6 marks) Let f R R : \{ , } 1 1 , f x x x x x ( ) 3 2 2 1 .
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a. Show that Jarean ) d= arctan (vx ) = dx. 1 mark Hh 1+x 3
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE (NHT) Specialist Mathematics examination 1 (PDF, 2.74 MB)How to use ClassConnect past exam questions
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