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: 1,669 indexed questions and parts.
Section A, Question 5
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Easy
Question 5 For z ∈ C and a ∈ R, the discriminant of the quadratic equation az2 − aiz − 5 = 0 is 36. The possible solutions for z to az2 − aiz − 5 = 0 are A. 1 2 3 i or 1 6 1 3 i B.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section A, Question 6
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Medium
Question 6 The equation Arg( ) z i 2 3 defines a ray in the complex plane. Identifying complex numbers x + yi with the points (x, y), this ray lies on the line with equation y = mx
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section A, Question 7
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Easy
Question 7 Let y = f (x) be the solution to the differential equation dy dx y 1 2 with the initial condition f (0) = 1. What is the approximation for f (1) using Euler’s method, st
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section A, Question 8
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Medium
Question 8 Using the substitution u2 = x + 1, the definite integral 1 1 3 8 x x dx can be expressed as A. 1 2 1 1 2 3 u u du B. 1 C. 1 D. 1 E. 1 u u u du
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section A, Question 9
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Easy
Question 9 The length of the curve given by x t 3 1 2 tan ( ) , y = 4 sec2 (t) where t 6 3 , , is given by A. 10 2 6 3 tan( ) sec ( ) t t dt B. 100 2 4 tan ( ) sec ( ) t t dt C. 2
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section A, Question 10
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Easy
Question 10 Consider the surface of revolution formed by rotating the curve y x x a 1 1 , about the x-axis. The area of this surface is given by A. 2 1 2 1 x x dx a B. 2 1 4 x x dx
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section A, Question 10
Source index checked · not an answer check
Working not previously checked
Report-based difficulty · EasyAverage marks: 74% of available · official reportAnswered correctly: 74% · official report
Question 10 The curve defined by the parametric equations x=5ty=12t,for0<r<k is rotated about the y-axis to form a surface of revolution. The area of this surface is A 65K B. 1307
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 A, Question 11
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Medium
Question 11 If I n x x dx e n e 2 1 log where n ∈ N, then for n ≥ 2, I n is equal to A. − − n I n 3 1 B. x x n Ie n 3 3 3 log C. e I n − − D. e n I n E. e n I n − − − Section A
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section A, Question 11
Source index checked · not an answer check
Working not previously checked
Report-based difficulty · MediumAverage marks: 58% of available · official reportAnswered correctly: 58% · official report
Question 11 The velocity—time graph of a particle moving along an east-west line with velocity vm s™' at time ¢ seconds, starting from a fixed origin O, is shown below. The graph c
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 A, Question 12
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Easy
Question 12 x y O 4 3 2 1 1 2 3 4 The direction field shown above best represents the differential equation A. dy dx x y ( ) ( ) 2 2 B. dy dx 8 2 C. dy x y 4 2 D. dy 2 2 E. dy 8 4
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section A, Question 12
Source index checked · not an answer check
Working not previously checked
Report-based difficulty · MediumAverage marks: 50% of available · official reportAnswered correctly: 50% · official report
Question 12 The position, x metres, of a particle moving in a straight line from a fixed origin O at time, 7 seconds, is given by x =e“ where k> 1. The acceleration of the particle
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 A, Question 13
Source index checked · not an answer check
Working not previously checked
Report-based difficulty · EasyAverage marks: 81% of available · official reportAnswered correctly: 81% · official report
Question 13 If the angle between the vectors 2i where m & RY, is J+ 2k and 2i + mj+ 6k is cos”! (2) then the value of m, A 2 B. 3 Cc. 4 D. 5
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)How to use ClassConnect past exam questions
- Choose a target. Filter by subject, topic, year, sitting or paper.
- Attempt it first. Work under exam conditions before opening the original question.
- Review and repeat. Compare with the official source and examiner report where available; note what to practise next.
Browse without signing in. Topic matches are approximate, not official VCAA tags. Source indexing and difficulty labels do not verify a worked solution. Check current course requirements with your teacher; classconnect is not endorsed by VCAA.
Make practice count
Create a free accountSave your next step
Sign in to save worked questions to My Library. Plus members can build topic-based exam worksheets with separate answer sheets.