VCE Mathematical Methods Past Exam Questions
Browse VCE Mathematical Methods 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 5(b)Question part (b)
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Estimated difficulty · Medium
b. Let Z be the standard normal random variable such that Z N ∼ ( , ) 0 1 and Pr( ) . Z 1 0 84 . Using a normal approximation of P̂, estimate the probability that in a sample of 10
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Estimated difficulty · Easy
c. In the town, 100 people were randomly selected and surveyed, with 60 people indicating that they were unhappy with the roads.
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Report-based difficulty · MediumAverage marks: 65% of available · official reportFull marks: 44% of students · official report
i. Determine an approximate 95% confidence interval for the proportion of people in the town who are unhappy with the roads. Use = = 2 for this confidence interval 1 mark 2 marks o
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Report-based difficulty · MediumAverage marks: 40% of available · official reportFull marks: 33% of students · official report
ii. A new sample of # people results in the same sample proportion. 2 Find the smallest value of # to achieve a standard deviation of 0 for the sample proportion. 1 mark
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Report-based difficulty · DifficultAverage marks: 37.5% of available · official reportFull marks: 9% of students · official report
Question 6 (4 marks) Solve 2log; (x — 4) + log; (x) = 2 for x. ° e 2 £ iS 8 3 = [=]
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Report-based difficulty · DifficultAverage marks: 37.5% of available · official reportFull marks: 9% of students · official report
Question 6, formatting amend Write your student number in the boxes above. Letter Mathematical Methods
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Estimated difficulty · Medium
Question 6 (4 marks) Part of the graph of g x x ( ) sin 2 5 6 2 is shown below. 6 π 3 2 π 2 −0.5 0.5 1 1.5 2.5 O x y
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Estimated difficulty · Easy
a. Using the trapezium rule approximation method and three trapeziums of equal width, estimate the area bounded by the graph of y = g(x), the x-axis and the lines x 6 and x 2 3 . 2
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b. Let h : , 6 2 3 → R, h(x) = kg(x), where k ∈ R. Using calculus, find k, such that h is a probability density function. 2 marks N H T
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Question 7 (3 marks) Let X be a discrete random variable with a probability mass function of Pr( ) X x x = = 2 3 , where x ∈ Z +.
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Question 7 (9 marks) Part of the graph of f:[~7,7]— R, f(x) = xsin (x) is shown below. 7
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 30% of students · official report
a. Use the trapezium rule with a step size of 3 to determine an approximation of the total area between the graph of y = f(x) and the x-axis over the interval x €[0, 7]. 3 marks o
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2024 VCE Mathematical Methods 1 examination · Report: 2024 VCE Mathematical Methods 1 external assessment report (DOCX, 452.28 KB)How to use ClassConnect past exam questions
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