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 3(a)Question part (a)
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Report-based difficulty · EasyAverage marks: 70% of available · official reportFull marks: 71% of students · official report
a. Use integration to show that the displacement, x metres, of the particle relative to O is given by x t t k k ( ) . 2 1 mark
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Report-based difficulty · EasyAverage marks: 70% of available · official reportFull marks: 57% of students · official report
b. Find the initial acceleration, in terms of k, of the particle in m s-2. 2 marks
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Report-based difficulty · MediumAverage marks: 40% of available · official reportFull marks: 28% of students · official report
c. Another particle starts at O at the same time as the first particle and follows the same path. Its position relative to O is described by the equation s t t ( ) = . Three second
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Estimated difficulty · Medium
Question 4 (5 marks) The waiting time, T hours, to see a particular doctor at a clinic has a distribution with a probability density function f defined by f t t t t e ( ) log ( ) (
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 37% of students · official report
a. Use integration to show that E( ) T = 1 2. 3 marks
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE Specialist Mathematics examination 1 (PDF, 860.54 KB) · Report: 2025 VCE Specialist Mathematics 1 external assessment report (DOCX, 386.51 KB)Question 4(a)Question part (a)
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Estimated difficulty · Medium
a. Show that wn 2) = . 2 marks 12) B+1 Consider the complex number = =(v/3 +1) + (v3 = 1)i.
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Estimated difficulty · Easy
b. Express in polar form. 1 mark Consider the complex number w =
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 49% of students · official report
b. For random samples of 25 waiting times, it may be assumed that the sample means are approximately normally distributed. Find the probability that the average waiting time for a
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Estimated difficulty · Medium
c. Show that w=32+ 32431. 1 mark
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Estimated difficulty · Medium
d. On the complex plane, the origin, 0, and the points representing the complex numbers z and w form a triangle. Calculate the area of the triangle. 2 marks o ° =) S H FE he
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Estimated difficulty · Medium
Question 5 (5 marks) The growth of a population of bees is modelled by the logistic differential equation a _, 0 I =) where B is the number of bees after ¢ weeks. ar 500 The initia
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Question 5 (4 marks) The position vectors of particles P and Q at time t seconds are given by r i j P t t at ( ) ( ) 3 2 and r i j Q t bt t t ct t ( ) ( ) ( ) 2 2 2 , w
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