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 1(b)Question part (b)
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Report-based difficulty · MediumAverage marks: 63.3% of available · official reportFull marks: 39% of students · official report
b. Sketch the graph of f on the axes below, labelling any asymptotes with their equations. 3 marks O 10 8 6 4 2 −2 −4 y x 5 −5 −4 −3 −2 −1 1 2 3 4 5 2023 SPECMATH EXAM 1 4 D O N O
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Estimated difficulty · Medium
Question 2 (4 marks) The time taken for Sam to vacuum the house, V hours, is normally distributed with a mean of 1 hour and a standard deviation of 0.3 hours. The time taken for Sa
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 37% of students · official report
Question 2 (3 marks) Consider the complex number z = (b − i)3, where b ∈ R+. Find b given that arg( ) z 2 .
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Estimated difficulty · Easy
a. Find the expected value of C. 1 mark
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Estimated difficulty · Medium
b. Show that the variance of C is 0.25 1 mark
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Estimated difficulty · Medium
c. Sam wants to clean the house before a friend visits at 1.00 pm. If Sam starts cleaning at 9.00 am, what is the probability that the cleaning will not be finished by 1.00 pm? Use
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Question 3 – continued Question 3 (5 marks) Part of the graph of f with rule f x x x ( ) 1 3 4 2 is shown below where x > 0. −3 −1 −2 0 1 2 3 −1 −2 −3 y
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Estimated difficulty · Easy
Question 3 (3 marks) A particle moves along a straight line. When the particle is x m from a fixed point O, its velocity, v m s−1, is given by v x x 3 2 2 1, where x ≥ 1.
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Estimated difficulty · Medium
a. i. Find the second derivative of f (x). 1 mark 7 2023 SPECMATH EXAM 1 (NHT) 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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Report-based difficulty · MediumAverage marks: 45% of available · official reportFull marks: 35% of students · official report
a. Find the acceleration of the particle, in m s−2, when x = 2. 2 marks
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ii. Hence, find the coordinates of the point of inflection. Label the point of inflection, with its coordinates, on the graph above. 2 marks
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 50% of students · official report
b. Find the value that the velocity of the particle approaches as x becomes very large. 1 mark 5 2023 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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