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.
Matching results: 77 indexed questions and parts.
Section B, Question 2(f)(ii)Question part (f)(ii)
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ii. Given that w cis 2 7 satisfies (z − 1)(z6 + z5 + z4 + z3 + z2 + z + 1) = 0, use De Moivre’s theorem to show that cos cos cos 2 4 6 1 . 2 marks
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Report-based difficulty · EasyAverage marks: 100% of available · official reportFull marks: 100% of students · official report
h. The frequency curves for the sampling distributions associated with H0 and H1 are shown below. Label the critical sample mean on the diagram and shade the region that represents
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Estimated difficulty · Medium
Question 2 (3 marks) Given the complex numbers z i 1 3 and w = –2 – 2i, find z w 3 2 in cartesian form. 2022 SPECMATH EXAM 1 (NHT) 4 d o n o t w r i t e i n t h i s a r e a
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Question 7 Which one of the following could represent the solutions to z5 = 6 + 30i on an Argand diagram? –2 Im(z) Re(z) 4 2 –2 –4 4 2 10 5 –5 –10 10 5 –10 –5 –4 –4 –2 2 4 6 –6 –6
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Question 2 (9 marks) Two complex numbers u and v are given by u = a + i and v b i 2 , where a, b ∈ R.
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a. Sketch Arg z z 0 on the Argand plane below, given that the ray passes through the origin. 1 mark Im(z) 2 1 2 1 –2 –1 –1 –2 Re(z) O
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Report-based difficulty · EasyAverage marks: 70% of available · official reportFull marks: 60% of students · official report
b. Plot and label the points representing u i 3 and v i 2 2 on the Argand diagram below. 2 marks 2 –1 –2 Im(z) Re(z) O –1 –2 1 2 1
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Report-based difficulty · MediumAverage marks: 40% of available · official reportFull marks: 25% of students · official report
c. The ray given by Arg(z) = θ passes through the midpoint of the line interval that joins the points u i 3 and v i 2 2 . Find, in radians, the value of θ and plot this ray on the
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Question 5 The complex number z = b + i, where b ∈ R, has the property Arg (z7) = Arg (z). A possible value of b is A. − 3 B. 0 C. 1 3 D. 1 E. 3
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Question 6 If z is a non-zero complex number, then cos arg( ) z is equal to A. Re( ) z z B. Re( ) z zz C. Im( ) z z| | D. sin Im( ) z E. Re( ) z z| |2
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Question 2 (9 marks) Points O, U and W in the complex plane represent complex numbers 0, u and w respectively, where Arg (u) = θ. When plotted on an Argand diagram, the points are
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Report-based difficulty · MediumAverage marks: 45% of available · official reportFull marks: 31% of students · official report
b. Sketch the ray given by Arg z z 4 5 6 on the Argand diagram below. 2 marks O –4 –3 –2 –1 1 2 3 4 4 3 2 1 –1 –2 –3 –4 Im(z) Re(z)
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