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
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Question 5 (6 marks) Consider a continuous random variable X with probability density function f given by f x x c d x d ( ) 2 0 elsewhere where c, d ∈ R and c ≥ 1.
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a. Find d in terms of c. 3 marks
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Report-based difficulty · EasyAverage marks: 70% of available · official reportFull marks: 66% of students · official report
a. Evaluate sin( ) x dx 0 3 . 1 mark
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Report-based difficulty · MediumAverage marks: 60% of available · official reportFull marks: 35% of students · official report
b. Hence, or otherwise, find all values of k such that sin( ) cos( ) x dx x dx k 0 3 2 , where −3 π < k < 2 π. 3 marks 7 2023 MATHMETH EXAM 1 TURN OVER d o n o t w r i t e i n t h
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Estimated difficulty · Easy
b. Given that E( ) X = 1 24 , find the values of c and d. 3 marks 7 2023 MATHMETH EXAM 1 (NHT) TURN OVER d o n o t w r i t e i n t h i s a r e a CONTINUES OVER PAGE 2023 MATHMETH E
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Estimated difficulty · Medium
Question 6 (4 marks) Let P̂ be the random variable that represents the sample proportion of households in a given suburb that have solar panels installed. From a sample of randomly
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Estimated difficulty · Medium
Question 6 – continued Question 6 (6 marks) Consider the function f, where f D R f x x : , ( ) 3 2 1, where D is the maximal domain of f .
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a. State D, the maximal domain of f. 1 mark
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Report-based difficulty · MediumAverage marks: 50% of available · official reportFull marks: 52% of students · official report
a. Find the value of p̂ that was used to obtain this approximate 95% confidence interval. 1 mark Use z = 2 to approximate the 95% confidence interval.
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Estimated difficulty · Easy
b. Sketch the graph of y = f (x). Label any asymptotes with their equation and the axial intercepts with their coordinates. 3 marks O y x −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 5 4 3 2 1 −1
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Report-based difficulty · DifficultAverage marks: 35% of available · official reportFull marks: 26% of students · official report
b. Find the size of the sample from which this 95% confidence interval was obtained. 2 marks
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Report-based difficulty · DifficultAverage marks: 20% of available · official reportFull marks: 23% of students · official report
c. A larger sample of households is selected, with a sample size four times the original sample. The sample proportion of households having solar panels installed is found to be th
Search excerpt only. Open the original question for exact equations and diagrams.Source: 2023 VCE Mathematical Methods 1 examination · Report: 2023 VCE Mathematical Methods 1 external assessment reportHow to use ClassConnect past exam questions
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