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 3(d)Question part (d)
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d. A 60 kg student stands in the lift. Find, in newtons, the minimum and maximum reaction forces that the floor of the lift exerts on the student during the journey from the ground
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 24% of students · official report
d. Another solid of revolution is formed by rotating the curve given by y2 = x − 1 about the x-axis for 2 ≤ x ≤ k, where k ∈ R. This solid has a volume of 24 π. Find the efficiency
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Estimated difficulty · Medium
Question 4 (10 marks) A fish farmer releases 200 fish into a pond that originally contained no fish. The fish population, P, grows according to the logistic model, dP dt P P 1 1000
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Question 4 (11 marks) Larry goes for a morning swim in a river that flows into the ocean. He swims once around a closed path. His position vector, r L ( ) t , relative to an orig
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a. Find the Cartesian equation of the closed path using r L ( ) t above. 1 mark
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 48% of students · official report
a. The above logistic differential equation can be expressed as A P B P dP dt 1 1000 , where A, B ∈ R. Find the values of A and B. 1 mark One form of the solution for P is P De t 1
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 57% of students · official report
b. Find the value of D. 1 mark The farmer releases a batch of n fish into a second pond, pond 2, which originally contained no fish. The population, Q, of fish in pond 2 can be mod
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Estimated difficulty · Medium
b. The graph of the closed path is shown on the set of axes below. Label Larry’s starting point with its coordinates and show the direction in which he swims. 2 marks 100 80 60 40
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Report-based difficulty · EasyAverage marks: 80% of available · official reportFull marks: 79% of students · official report
c. Find the value of n. 1 mark
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Estimated difficulty · Easy
c. i. Find the distance that Larry travels when he swims once around the closed path. Give your answer in metres, correct to two decimal places. 1 mark 19 2023 SPECMATH EXAM 2 (NHT
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Estimated difficulty · Easy
ii. Find Larry’s average speed when he swims once around the closed path. Give your answer in metres per minute, correct to one decimal place. 1 mark
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Report-based difficulty · EasyAverage marks: 90% of available · official reportFull marks: 85% of students · official report
d. Find the value of Q when t = 6. Give your answer correct to the nearest integer. 1 mark 2023 SPECMATH EXAM 2 18 d o n o t w r i t e i n t h i s a r e a
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