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
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Estimated difficulty · Medium
Question 6 (10 marks) A manufacturer produces a bicycle in three stages. The times taken to complete each stage, T,, T; and T hours, may be assumed to be independent and normally d
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 6
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Question 6 (10 marks) The volume of water, V mL, consumed by a student during a school day may be assumed to be normally distributed with a mean of 1000 mL and a standard deviation
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Estimated difficulty · Medium
a. i. Write down the mean and standard deviation of the sampling distribution for the average volume of water consumed by randomly selected samples of 25 students. Give your answer
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE Specialist Mathematics examination 2 (PDF, 1.17 MB)Section B, Question 6(a)Question part (a)
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a. Find the value of a. 1 mark
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Report-based difficulty · EasyAverage marks: 85% of available · official reportFull marks: 85.8% of students · official report
ii. What is the probability, correct to four decimal places, that the average volume of water consumed by a random sample of 25 students on a particular school day is more than 970
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 B, Question 6(b)Question part (b)
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Estimated difficulty · Medium
b. What is the probability that the total time taken to produce a bicycle exceeds 20 hours? Give your answer correct to four decimal places. 1 mark o ° =) S H FE he ES @ El ? E Id
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Report-based difficulty · EasyAverage marks: 88% of available · official reportFull marks: 88.1% of students · official report
b. Find a 95% confidence interval for the mean volume of water dispensed into each Wasser bottle. Give your values in millilitres, correct to one decimal place. 1 mark
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 B, Question 6(c)Question part (c)
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Report-based difficulty · EasyAverage marks: 76% of available · official reportFull marks: 76.9% of students · official report
c. The engineers decide to take 300 random samples, each containing 30 bottles, and calculate the respective 95% confidence intervals. All samples are independent. In how many of t
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 B, Question 6(c)Question part (c)
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Estimated difficulty · Easy
c. Find an approximate 99% confidence interval for the mean height of people in Australia. Give your answer in centimetres rounded to one decimal place. 1 mark
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 6(d)Question part (d)
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Estimated difficulty · Easy
d. If the manufacturer took 200 such samples, how many of the 99% confidence intervals would be expected to contain the value of the population mean? 1 mark
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 6(d)Question part (d)
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Estimated difficulty · Easy
d. What is the minimum size of the sample required to ensure that the difference between the sample mean and the mean volume dispensed is no more than 1 mL at the 95% confidence le
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE Specialist Mathematics examination 2 (PDF, 1.17 MB)Section B, Question 6(e)Question part (e)
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Estimated difficulty · Easy
e. The manufacturer wants to get a better estimate of the population mean by decreasing the width of the confidence interval found in part ¢ by at least 60%. What minimum sample si
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2025 VCE (NHT) Specialist Mathematics examination 2 (PDF, 5.7 MB)How to use ClassConnect past exam questions
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