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 1(c)Question part (c)
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c. Sketch the graph of f on the axes below. Label the asymptotes with their equations and label any stationary and inflection points with their coordinates, correct to two decimal
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c. i. Find the coordinates of point A. 1 mark
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Estimated difficulty · Easy
ii. Find the coordinates of point B. 1 mark The return track from point D to point O follows an elliptical path given by x = 2cos(t) + 2, y = (e − 2)sin(t), where t 2 , .
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Report-based difficulty · EasyAverage marks: 85% of available · official reportFull marks: 81% of students · official report
d. Find the Cartesian equation of the elliptical path. 2 marks
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Estimated difficulty · Easy
d. Let g x x x x x kk ( ) 4 2 7 2 3 2 2 , where k is a real constant. For what values of k will the graph of gk have
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i. one vertical asymptote 1 mark
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ii. no vertical asymptotes? 1 mark
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Report-based difficulty · DifficultAverage marks: 20% of available · official reportFull marks: 22% of students · official report
e. Sketch the elliptical path from D to O on the diagram on page 10. 1 mark
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Estimated difficulty · Medium
e. The graph of g2 , where g x x x x x2 2 4 2 7 2 3 2 ( ) , is rotated about the x-axis from x = 0 to x = 5 to form a solid of revolution. Write down a definite integral that gives
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Estimated difficulty · Medium
f. i. Write down a definite integral in terms of t that gives the length of the elliptical path from D to O. 1 mark 2023 SPECMATH EXAM 2 12 d o n o t w r i t e i n t h i s a r e a
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ii. Find the length of the elliptical path from D to O. Give your answer in kilometres correct to three decimal places. 1 mark
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Estimated difficulty · Medium
Question 2 (11 marks) The circle given by z i 2 3 2 3 , where z ∈ C, has its centre at 2 3 , .
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