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 6(b)(ii)Question part (b)(ii)
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Report-based difficulty · EasyAverage marks: 80% of available · official reportFull marks: 75% of students · official report
ii. Using the p value found in part b.i, state with a reason whether the machine should be paused. 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section B, Question 6(c)Question part (c)
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c. Write down suitable null and alternative hypotheses for the statistical test. 1 mark Section B
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section B, Question 6(c)Question part (c)
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 44% of students · official report
c. Assuming that the mean volume dispensed by the machine each time is in fact 997 mL and not 1000 mL, find the probability of a type IT error for the test using nine bottles at th
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section B, Question 6(d)Question part (d)
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Estimated difficulty · Easy
d. i. Find the p value for this test correct to three decimal places. 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section B, Question 6(d)Question part (d)
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 58% of students · official report
d. Let X denote the sample mean of a random sample of nine bottles. As a quality-control measure, the machine will be paused if X <a or if X >b, where Pr(X <a)=0.01 and Pr(X >5)=0.
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section B, Question 6(d)(ii)Question part (d)(ii)
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Estimated difficulty · Easy
ii. Draw an appropriate conclusion about H0 from the p value found in part d.i. Give a reason involving p for your conclusion. 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section B, Question 6(e)Question part (e)
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Report-based difficulty · EasyAverage marks: 80% of available · official reportFull marks: 82% of students · official report
e. Find a 95% confidence interval for the population mean volume dispensed by the new machine, giving values correct to one decimal place. You may assume a population standard devi
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Specialist Mathematics examination 2 · Report: 2024 VCE Specialist Mathematics 2 external assessment report (DOCX, 980.56 KB)Section B, Question 6(e)Question part (e)
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Estimated difficulty · Easy
e. Find the largest mean concentration of sugar that could be observed from a sample of 56 bottles for the null hypothesis not to be rejected at the 1% level of significance. Give
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Section B, Question 6(f)Question part (f)
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Estimated difficulty · Medium
f. Assume that the true mean concentration of sugar from the shorter process is 0.40 grams per litre and the standard deviation is 0.12 grams per litre. A sample of 56 bottles is t
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE (NHT) Specialist Mathematics examination 2Question 1
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Question 1 (3 marks) If sin (x) = 3cos (x), find the value of sin (2x), where x 0 2 , . Instructions Answer all questions in the spaces provided. Unless otherwise specified, an exa
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE (NHT) Specialist Mathematics examination 1Question 1
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Question 1 (4 marks) Consider the function f with rule f x x x x ( ) 2 6 1 .
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Report-based difficulty · EasyAverage marks: 90% of available · official reportFull marks: 87% of students · official report
a. Show that the rule for the function f can be written as f x x x ( ) 2 4 1 . 1 mark
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Specialist Mathematics examination 1 · Report: 2023 VCE Specialist Mathematics 1 external assessment reportHow to use ClassConnect past exam questions
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