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 2
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Estimated difficulty · Medium
Question 2 (3 marks) Given the complex numbers z i 1 3 and w = –2 – 2i, find z w 3 2 in cartesian form. 2022 SPECMATH EXAM 1 (NHT) 4 d o n o t w r i t e i n t h i s a r e a
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Report-based difficulty · EasyAverage marks: 73.3% of available · official reportFull marks: 60% of students · official report
Question 2 (3 marks) Solve the differential equation dy dx x y 4 2 given that y(2) = 0. Give your answer in the form y = f (x). 5 2022 SPECMATH EXAM 1 TURN OVER d o n o t w r i t e
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Question 3 (4 marks) The time taken by a coffee machine to dispense a cup of coffee varies normally with a mean of 10 seconds and a standard deviation of 1.5 seconds.
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Question 3 (3 marks) The region enclosed by the graph of y = x2 – 2x + 1 and the straight line that passes through the x and y intercepts of this parabola is rotated about the x-ax
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Report-based difficulty · DifficultAverage marks: 35% of available · official reportFull marks: 31% of students · official report
a. Find the probability that more than 34 seconds is needed to dispense a total of four cups of coffee. Give your answer correct to two decimal places. 2 marks b. This question has
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Report-based difficulty · MediumAverage marks: 62.5% of available · official reportFull marks: 36% of students · official report
Question 4 (4 marks) Find 3 4 12 4 2 x x x x dx ( ) . 7 2022 SPECMATH EXAM 1 TURN OVER 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 4 ‒ continued Question 4 (5 marks) A smooth plane is inclined at an angle θ to the horizontal. Two particles of mass m1 kilograms and m2 kilograms are connected by a light
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a. Given that the system is in equilibrium, express m2 in terms of m1. 2 marks
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b. The string is cut and the particle of mass m1 kilograms starts to slide down the plane. Find how far, in metres, the particle of mass m1 kilograms has slid down the plane from i
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Question 5 (3 marks) A body of mass 10 kg, which is initially at rest, slides down a smooth inclined plane, as shown in the diagram below. The plane is inclined at an angle θ to th
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Question 5 (3 marks) Find the centre and the radius of the circle defined by 3 z i z , where z ∈ C.
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Report-based difficulty · MediumAverage marks: 65% of available · official reportFull marks: 55% of students · official report
a. Find the speed of the body after the body has been in motion for two seconds. 2 marks
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