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(b)Question part (b)
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 44% of students · official report
b. The line segment from z, = | + 2i to z, = 4 is the diameter of a circle. Find the equation of this circle in the form is the centre of the circle and r is the radius. 2 marks o
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section B, Question 2(c)Question part (c)
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Report-based difficulty · EasyAverage marks: 85% of available · official reportFull marks: 74% of students · official report
c. A second circle is given by |z — (1+2i) = 2. Sketch this circle on the Argand diagram below, labelling the imaginary axis intercepts with their values. 2 marks Im(z) 4 5 > Re(z)
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section B, Question 2(c)Question part (c)
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Estimated difficulty · Easy
c. Express z3 in the form a + bi, where a, b ∈ R. 1 mark Section B
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Estimated difficulty · Easy
d. Plot the point that represents z4 . 1 mark Im(z) Re(z) −4 −2 2 4
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Estimated difficulty · Easy
d. i. Sketch the ray on the Argand diagram provided in part c. 1 mark
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 56% of students · official report
ii. Find the equation of the ray in the form Arg(z — z) = 0 where z, & Cand 0 is measured in radians in terms of 7. 1 mark
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Report-based difficulty · MediumAverage marks: 65% of available · official reportFull marks: 52% of students · official report
e. Find the area of the minor segment formed by the intersection of the ray and the circle. 2 marks Section B
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Estimated difficulty · Easy
e. For what values of n will Arg (z n) = 0 where z n = (1 − i)n, n ∈ Z +? 2 marks Let L be the line defined by L z z z a bi z C a b R : : ( ) , , and . L passes through the points
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Estimated difficulty · Easy
f. Find the values of a and b. 1 mark N H T
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Estimated difficulty · Easy
g. Find the area of the minor segment bounded by the circle z z = 10 and the line L. Give your answer correct to two decimal places. 3 marks Section B This page is blank. N H T
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Estimated difficulty · Medium
Question 3 (10 marks) A pollutant, at time 7 = 0 days, begins to enter a pond of still, unpolluted water at a rate of dav 8 dr 240+ 50 where ¥ is the volume of pollutant, in cubic
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Estimated difficulty · Difficult
Question 3 (10 marks) In a computer simulation, a speeding motorcycle, travelling along a straight, flat road at a constant velocity of 20 m s−1, passes a stationary highway patrol
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2How to use ClassConnect past exam questions
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