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 B, Question 1(b)Question part (b)
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Easy
b. The region bounded by the graph of y x x x 3 23 , the coordinate axes and the line x = 2 is rotated about the x-axis to form a solid of revolution.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE Specialist Mathematics examination 2 (PDF, 1.17 MB)Section B, Question 1(b)(i)Question part (b)(i)
Source index checked · not an answer check
Working not previously checked
Report-based difficulty · EasyAverage marks: 90% of available · official reportFull marks: 90.1% of students · official report
i. Write down a definite integral that, when evaluated, will give the volume of the solid of revolution. 1 mark Section B
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)Section B, Question 1(b)(i)Question part (b)(i)
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Medium
i. Using partial fractions, show that g(x) = x=1 x+l o ° =) S H FE he ES @ El ? E
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 1(b)(ii)Question part (b)(ii)
Source index checked · not an answer check
Working not previously checked
Report-based difficulty · EasyAverage marks: 81% of available · official reportFull marks: 81.5% of students · official report
ii. Find the volume of the solid of revolution correct to two decimal places. 1 mark
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)Section B, Question 1(b)(ii)Question part (b)(ii)
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Medium
ii. Show that when a = 2 the graph of y = f(x) has no stationary points. 1 mark
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 1(c)Question part (c)
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Easy
c. Sketch the graph of y = f(x) when a = ~2 on the axes below. Label all asymptotes with their equations, and label any intercepts with the coordinate axes with their values. 3 mar
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 1(c)Question part (c)
Source index checked · not an answer check
Working not previously checked
Report-based difficulty · EasyAverage marks: 73% of available · official reportFull marks: 73.5% of students · official report
c. Find the equations of the vertical asymptotes of the curve given by y x x x 3 5 23 . 1 mark
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)Section B, Question 1(c)(i)Question part (c)(i)
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Easy
i. Using f(x) =x +a+9" 2 - —- find f(x) where a is an arbitrary real constant. xX— X+ - ", B Give your answer in the form f(x) = oF where 4, Band p € R. G+) 1 mark
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 1(c)(ii)Question part (c)(ii)
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Medium
ii. Hence, verify that the graph of y = £ (x) has no points of inflection when a = ~2 anda =-1. 2 marks o ° =) S H FE he
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 1(d)Question part (d)
Source index checked · not an answer check
Working not previously checked
Estimated difficulty · Easy
d. A family of curves is given by y x x x ax ( ) 3 23 , where a ∈ R.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE Specialist Mathematics examination 2 (PDF, 1.17 MB)Section B, Question 1(d)(i)Question part (d)(i)
Source index checked · not an answer check
Working not previously checked
Report-based difficulty · EasyAverage marks: 84% of available · official reportFull marks: 84.3% of students · official report
i. Consider the case where the graph has a stationary point P. Find the y-coordinate of P in terms of a. 1 mark
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)Section B, Question 1(d)(ii)Question part (d)(ii)
Source index checked · not an answer check
Working not previously checked
Report-based difficulty · MediumAverage marks: 45% of available · official reportFull marks: 45.9% of students · official report
ii. For a given value of a, the graph has no stationary points. Find the equations of the vertical asymptotes of the graph in this case. 1 mark
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
- 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.