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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Section B, Question 5(a)Question part (a)
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Estimated difficulty · Easy
a. Given OP = mOQ + nOT, where m, n € R, find the value of a. 2 marks
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 5(a)Question part (a)
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Report-based difficulty · EasyAverage marks: 73% of available · official reportFull marks: 73.5% of students · official report
a. Find the point of intersection of the three planes. 1 mark
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Estimated difficulty · Easy
b. i. Find the vector cross product OT x 0S. 1 mark
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b. i. Find a vector that gives the direction of the line of intersection of the planes P2 and P3. 2 marks
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Estimated difficulty · Easy
ii. Find the Cartesian equation of the plane IT;. Express your answer in the form Ax + By + z = C, where 4, B, C e R. 2 marks
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Report-based difficulty · MediumAverage marks: 51% of available · official reportFull marks: 51.2% of students · official report
ii. Find a set of parametric equations that give the coordinates of the points that lie on this line of intersection. 1 mark Section B
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Estimated difficulty · Medium
c. Asecond plane IT, has the equation i’ + uy + 3z = 13, where u € R. Given that the vector ST is parallel to this plane, find the possible values of u. 2 marks o ° =) S H FE he
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Report-based difficulty · EasyAverage marks: 71% of available · official reportFull marks: 65.0% of students · official report
c. Find the shortest distance from the point (1, 1, 2) to the plane P3. 2 marks
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Estimated difficulty · Easy
d. What is the shortest distance from point Q to the line that passes through the points Sand 7? IN c Give your answer in the form where b, ¢ € Z. 3 marks Id I ® 2 £ 8 H ° = o [=]
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Estimated difficulty · Easy
d. Consider a family of planes, Ψ, with equation 6x + 27z = m, where m ∈ N.
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Report-based difficulty · MediumAverage marks: 67% of available · official reportFull marks: 67.9% of students · official report
i. Show that the plane P1 is parallel to each member of Ψ. 1 mark
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Report-based difficulty · MediumAverage marks: 45.3% of available · official reportFull marks: 33.8% of students · official report
ii. Find all values of m for which the shortest distance between plane P1 and the plane of the form 6x + 27z = m is 23 3 85 . 3 marks
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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