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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Question 5(a)Question part (a)
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Estimated difficulty · Medium
a. Use integration to show that (= Clog, | —>5 |. 4 marks 3 1000 - 2B Id I & 2 £ 8 H ° = o [=]
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Report-based difficulty · EasyAverage marks: 90% of available · official reportFull marks: 94% of students · official report
a. Show that for collision to occur when t = 1, the value of c is -4. 1 mark When the particles collide, their velocities are at right angles to each other.
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b. Find the value of / for which the population is increasing most rapidly. 1 mark
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 30% of students · official report
b. Find the two possible values of a for collision to occur when t = 1. 2 marks
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Report-based difficulty · DifficultAverage marks: 20% of available · official reportFull marks: 25% of students · official report
c. When the particles collide at t = 1, the magnitudes of their accelerations are equal. Find the values of a and b for collision to occur when t = 1. 1 mark
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Question 6 (4 marks) Consider the lines Z and L, with respective equations £()=1—2j+4k+1(i+3j Kk) and r,(s) = 3] — 3k + 5(2i + j + 4k), where s, 1 € R.
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Report-based difficulty · MediumAverage marks: 62.5% of available · official reportFull marks: 38% of students · official report
Question 6 (4 marks) Find the volume of the solid of revolution formed when the area between the curve y x x arctan( ) 1 2 and the x-axis from x = 1 to x = 3 is rotated about the x
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 6(a)Question part (a)
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a. Show that L, and L, are skew, that is they do not intersect and they are not parallel. 2 marks [=] o 3 S
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b. Find the shortest distance between L, and L,. 2 marks EH 3 5 Id I & 2 £ 8 H ° = o [=]
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Estimated difficulty · Difficult
Question 7 (6 marks) A toy car travels along a straight, horizontal track. At time 7 = 0 seconds, the toy car starts from rest at line O and accelerates with positive constant acce
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Report-based difficulty · MediumAverage marks: 65% of available · official reportFull marks: 29% of students · official report
Question 7 (4 marks) Use mathematical induction to prove that ( ) i n n n i n 1 1 6 2 9 132 2 1 for n N ∈ , where ( ) i 1 2 = 2 3 4 12 2 2 2 + + + + + ( ) n .
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 7(a)Question part (a)
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a. Sketch the velocity-time graph of the toy car on the axes below. 1 mark 10
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE (NHT) Specialist Mathematics examination 1 (PDF, 2.74 MB)How to use ClassConnect past exam questions
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