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 9(a)Question part (a)
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 45% of students · official report
a. Show that f x ( ) can be written in the form f x x x ( ) 1 1 1, for x R \{ , } 1 1 . 2 marks
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(b)Question part (b)
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 46% of students · official report
b. Consider the function with rule g x x x x x x R k x ( ) , \{ , } { } 3 2 2 1 1 1 1 , Find the value of k such that the graph of g is continuous at x = 1. 1 mark
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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
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Report-based difficulty · EasyAverage marks: 93% of available · official reportAnswered correctly: 93% · official report
Question 1 A tiger is a type of cat. Consider the following statement. ‘If I have a tiger, then I have a cat.’ The contrapositive of this statement is A. if I do not have a tiger,
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 A, Question 1
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Estimated difficulty · Medium
Question 1 Consider the statement “ifn? +5 is odd, then n is even’, where n & Z. The contrapositive of this statement is A. ifniseventhenn’ +5 is odd. B. ifn’ +5iseventhenn is even
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Report-based difficulty · MediumAverage marks: 48% of available · official reportAnswered correctly: 48% · official report
Question 2 Consider the following statement. ‘If f ( ) 0 0, then the graph of f necessarily has a point of inflection at x = 0.’ A counter-example that disproves this statement is
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Estimated difficulty · Easy
Question 2 The number of straight-line asymptotes of the graph of the function with o ° =) S H FE he rule f(x) = 25 OF ZxH3 A 0 B. | c 2 D. 3
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Report-based difficulty · MediumAverage marks: 68% of available · official reportAnswered correctly: 68% · official report
Question 3 The graph of y x a bx c 2 has an asymptote given by y x 1 4 and a y-intercept of −2. The values of a, b and c are A. a = 2, b = −2, c = −1 B. a = 2, b = 2, c = −1 C. a =
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Estimated difficulty · Easy
Question 3 PB How many integer values of a can —————— be expressed in the form —— + ——, x" +ax-21 x+b x+c where b and c are integers and B, C € R? A 2 B. 3 C. 4 D. 5
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Estimated difficulty · Medium
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. +
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Report-based difficulty · EasyAverage marks: 72% of available · official reportAnswered correctly: 72% · official report
Question 4 Consider the following algorithm used to estimate a volume of revolution. define f(x) return √x + 1 sum 🡠 0 a 🡠 1 b 🡠 3 left 🡠 a while left ≤ b volume 🡠 π(f(left))
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Report-based difficulty · MediumAverage marks: 69% of available · official reportAnswered correctly: 69% · official report
Question 5 The equation z az bz3 2 52 0 , where a, b ∈ R and z ∈ C, has a solution z = 2 − 3i. The value of ab is A. −232 B. −64 C. −8 D. 0
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