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.
Question 11
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Question 11 (4 marks) Consider the two planes 2x + y + z = 4 and px + (p + 1)y + 2z = 1, where p ∈ R. Given that the acute angle between the two planes is 60°, find all possible va
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 1 (PDF, 633.42 KB)Section A, Question 6
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Question 6 Consider the Argand diagram below. –2 –1 1 2 Re(z) Im(z) π 6 O 1 2 The shaded region is best described by A. z z z z : : ( ) 1 2 3 2 arg B. z z z z : : ( ) 1 2 6 3 C. z
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 2(a)Question part (a)
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a. On the Argand diagram below, sketch the circle and draw the line Im(z) = 4. Plot and label the points z0 , v and w. 2 marks Re(z) Im(z) O 2 4 6 8 2 4 6 8
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Section B, Question 6(e)Question part (e)
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e. The wax manufacturer claims that descent times will be reduced by at least 2% with the application of the new wax. Assuming the mean descent time of 200 s is in fact reduced by
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2026 VCE (NHT) Specialist Mathematics examination 2 (PDF, 1.24 MB)Question 4(a)Question part (a)
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a. Show that wn 2) = . 2 marks 12) B+1 Consider the complex number = =(v/3 +1) + (v3 = 1)i.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE (NHT) Specialist Mathematics examination 1 (PDF, 2.74 MB)Question 4(b)Question part (b)
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b. Express in polar form. 1 mark Consider the complex number w =
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE (NHT) Specialist Mathematics examination 1 (PDF, 2.74 MB)Question 4(d)Question part (d)
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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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Report-based difficulty · EasyAverage marks: 80% of available · official reportFull marks: 84% of students · official report
a. Consider z i 1 1 2 . Plot and label z1 and z1 on the Argand plane below. 1 mark Im(z) Re(z) 2 4 −2 −4 2 −2 −4 4 O
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 9(c)Question part (c)
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Report-based difficulty · DifficultAverage marks: 33.3% of available · official reportFull marks: 16% of students · official report
c. Sketch the graph of y f x = ( ) on the axes below. Label the asymptotes with their equations. 3 marks y x 2 4 −2 −4 2 −2 −4 4 O Specialist Mathematics
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)Section A, Question 4
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Question 4 i Consider the complex numbers z and w, where w=—1++/3i, [zw] = 2v/2 and Arg(zw) = “5 The value of Arg(2*) is A. 1 _r B. 1 Ld C. Nn 3 D. +
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE (NHT) Specialist Mathematics examination 2 (PDF, 5.7 MB)Section A, Question 5
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Estimated difficulty · Easy
Question 5 Im(z) 4 Id I ® 2 £ 8 H ° = o [=] The equation of the ray on the Argand plane above is A Arg(z-2+430 = B. Arg(z+2-3i)= c. arg(z+2-3)= 2 D. Arg(z-2+3i r Section A
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE (NHT) Specialist Mathematics examination 2 (PDF, 5.7 MB)Section B, Question 2(a)Question part (a)
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Report-based difficulty · EasyAverage marks: 88% of available · official reportFull marks: 88.3% of students · official report
a. Sketch { : , } z zz z C 4 on the Argand plane below. 1 mark Im(z) Re(z) 2 1 3 −2 −1 −3 1 −1 −2 −3 2 3 O
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE Specialist Mathematics examination 2 (PDF, 1.17 MB) · Report: 2025 VCE Specialist Mathematics 2 external assessment report (DOCX, 908.84 KB)How to use ClassConnect past exam questions
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