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 A, Question 4
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Question 4 0 Im(z) Re(z) Q P R S T 4 3 2 1 –1 –2 –3 –4 –4 –3 –2 –1 1 2 3 4 On the Argand diagram shown above, 4 2 cis − π is represented by the point A. P B. Q C. R D.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2018 VCE (NHT) Specialist Mathematics examination 2Section A, Question 6
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Estimated difficulty · Medium
Question 6 Given that (z – 3i) is a factor of P(z) = z3 + 2z2 + 9z + 18, which one of the following statements is false? A. P(3i) = 0 B. P(–3i) = 0 C. P(z) has three linear factors
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Question 6 The complex numbers z, iz and z + iz, where z ∈ C \ {0}, are plotted in the Argand plane, forming the vertices of a triangle. The area of this triangle is given by A. z
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c. Sketch L and the graph of the relation z z = 4 on the Argand diagram below. 2 marks –5 –4 –3 –2 –1 1 2 3 4 5 –5 –4 –3 –2 –1 1 2 3 5 4 Im(z) Re(z) O The part of the line L in the
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Report-based difficulty · EasyAverage marks: 70% of available · official reportFull marks: 58% of students · official report
c. Graph the circle given by z z i + = − 1 2 on the Argand diagram below, labelling the intercepts with the vertical axis. 2 marks Re(z) Im(z) –5 –4 –3 –2 –1 1 2 3 4 5 5 4 3 2 1 –1
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Report-based difficulty · MediumAverage marks: 65% of available · official reportFull marks: 55% of students · official report
d. Draw the line given by z z − = − 1 3 on the Argand diagram in part c. Label the points of intersection with their coordinates. 2 marks
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Estimated difficulty · Easy
Question 4 The solutions to z n = 1 + i, n ∈ Z + are given by A. 2 4 2 1 2n n k n k R cis π π + ∈ , B. 2 4 2 n k k Z cis π π + C. 2 4 2n k D. 2 4 n k Z cis E. 2 4
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Estimated difficulty · Easy
Question 5 On an Argand diagram, a point that lies on the path defined by z i z − = − 2 + 4 is A. 3 1 2 , − B. − − 3 1 , C. − 3 3 D. 3 1 E. 3 3
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Estimated difficulty · Easy
b. Plot and label the roots of z z z3 2 2 3 4 0 − + = on the Argand diagram below. 3 marks Im(z) Re(z) 3 2 1 –1 –2 –3 O –3 –2 –1 1 2 3 15 2017 SPECMATH EXAM 2 (NHT) TURN OVER
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Report-based difficulty · EasyAverage marks: 70% of available · official reportFull marks: 53% of students · official report
e. Sketch the line represented by x y − − = 3 4 0 and plot the roots of z2 + 4z + 16 = 0 on the Argand diagram below. 2 marks Re(z) Im(z) –5 –4 –3 –2 –1 1 2 3 4 5 5 4 3 2 1 –1 –2 –
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Estimated difficulty · Medium
Question 6 The points corresponding to the four complex numbers given by z z z z 1 2 3 4 2 3 3 4 2 2 = = = − = − cis cis cis cis π π , , , 44 are the vertices
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Report-based difficulty · EasyAverage marks: 85% of available · official reportFull marks: 77% of students · official report
c. Sketch both the line z z i − = + − 1 2 3 and the circle z − = 1 3 on the Argand diagram below. 2 marks Im(z) Re(z) –4 –3 –2 –1 O –1 –2 –3 –4 4 3 2 1 1 2 3 4
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