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 B, Question 2(f)Question part (f)
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Estimated difficulty · Easy
f. i. Express cis cis 2 7 12 in the form Acos (B π), where A, B ∈ R+. 1 mark 15 2023 SPECMATH EXAM 2 d o n o t w r i t e i n t h i s a r e a TURN OVER
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ii. Given that w cis 2 7 satisfies (z − 1)(z6 + z5 + z4 + z3 + z2 + z + 1) = 0, use De Moivre’s theorem to show that cos cos cos 2 4 6 1 . 2 marks
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Question 3 (10 marks) The velocity–time graph below shows the velocity of an express lift as it travels from the ground floor to the top floor of a city building. The displacement
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Question 3 (10 marks) The curve given by y2 = x − 1, where 2 ≤ x ≤ 5, is rotated about the x-axis to form a solid of revolution.
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a. Show that the maximum acceleration of the lift during the first 4 seconds occurs when t = 2 and that the magnitude of this acceleration is 4 ms−2. 2 marks 17 2023 SPECMATH EXAM
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a. i. Write down the definite integral, in terms of x, for the volume of this solid of revolution. 1 mark
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ii. Find the volume of the solid of revolution. 1 mark
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b. i. Express the curved surface area of the solid in the form Ax B dx a b , where a, b, A, B are all positive integers. 2 marks
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b. Given that the lift travels 96 m from the ground floor to the top floor, find T. 3 marks
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Estimated difficulty · Medium
ii. Hence or otherwise, find the curved surface area of the solid correct to three decimal places. 1 mark The total surface area of the solid consists of the curved surface area pl
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c. Find a relation that gives the velocity of the lift, v, in terms of t for the last 4 seconds of motion. 2 marks
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 38% of students · official report
c. Find the efficiency ratio of the solid of revolution correct to two decimal places. 2 marks 2023 SPECMATH EXAM 2 16 d o n o t w r i t e i n t h i s a r e a
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 reportHow to use ClassConnect past exam questions
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