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
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Question 7 (4 marks) The curve defined by the parametric equations x = 8t and y = t2 − 8loge(t), where t ∈ [1, 3], is rotated about the y-axis to form a surface of revolution. Find
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Report-based difficulty · MediumAverage marks: 57.5% of available · official reportFull marks: 27% of students · official report
Question 7 (4 marks) Solve the differential equation x +2: =0, expressing v as a function of x, given that (0) = -2. o ° =) S H FE he ES @ El ? E
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Question 8 (4 marks) Prove by mathematical induction that 1 7 2 15 3 23 8 1 1 6 1 16 5 n n n n n ( ) ( )( ) for all n ∈ N. N H T
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Question 8 (4 marks) Consider the relation x*y? + xy = 2, where x, & R.
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Report-based difficulty · EasyAverage marks: 70% of available · official reportFull marks: 54% of students · official report
a. Using implicit differentiation, show that = given that 2xy # —1. 2 marks dx
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 32% of students · official report
b. Find all points on the graph of xy + xy = 2 where the slope of the tangent is equal to —1. 2 marks Id I & 2 £ 8 H ° = o [=]
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Question 9 (6 marks) In a population, the number of kangaroos, P, is modelled by the logistic differential equation dP dt P P 0 05 10 50 . , where P ∈ [100, 500) and where t is the
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Question 9 (4 marks) A car is travelling along a straight, flat road. The velocity, v km h™, of the car and its position, x kilometres, are measured from the position on the road w
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Report-based difficulty · DifficultAverage marks: 30% of available · official reportFull marks: 32% of students · official report
a. Determine, with evidence, whether the speed detection device will be activated. 1 mark
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a. Find d P dt 2 2 in terms of P. 1 mark Part of the graph of P against t is shown below. The graph contains a single point of inflection, labelled A. O 500 400 300 200 100 2 4 6 t
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Report-based difficulty · MediumAverage marks: 53.3% of available · official reportFull marks: 35% of students · official report
b. Find the acceleration of the car, in km h™%, when x = 12. Give your answer in the form £., where k < Z. 3 marks T o ° =) S H FE he ES @ El ? E
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 1 · Report: 2024 VCE Specialist Mathematics 1 external assessment report (DOCX, 556.03 KB)Question 9(b)Question part (b)
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b. In the context of the growth of the kangaroo population, what does the point of inflection at A represent? 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 1How to use ClassConnect past exam questions
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