AS & A Level Further Mathematics (9231) — May–June 2024, Paper 43

6 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.

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Question 1 · 7 marks · Further Probability & Statistics - non-parametric tests (Wilcoxon rank-sum test)

A college uses two assessments, X and Y, when interviewing applicants for research posts at the college. These assessments have been used for a large number of applicants this…

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Question 2 · 7 marks · Further Probability & Statistics - confidence intervals (population mean, small sample, t-distribution)

A rowing club has a large number of members. A random sample of 12 of these members is taken and the pulse rate, x beats per minute (bpm), of each is measured after a 30-minute…

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Question 3 · 7 marks · Further Probability & Statistics - chi-squared test (contingency table, test of independence)

There are three bus companies in a city. The council is investigating whether the buses reliably arrive at their destination on time. The results from random samples of buses from…

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Question 4 · 9 marks · Further Probability & Statistics - probability generating functions (normalisation constant)

The random variable X has probability generating function GX(t) given by GX(t) = ct(1 + t)^5, where c is a constant. Find the value of c.

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Question 5 · 10 marks · Further Probability & Statistics - continuous random variables (relating pdf and cdf, sketching the pdf)

The continuous random variable X has cumulative distribution function F given by F(x) = 0 for x < 2, F(x) = (x - 2)^2 / 12 for 2 <= x < 4, F(x) = 1 - (8 - x)^2 / 24 for 4 <= x <=…

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Question 6 · 10 marks · Further Probability & Statistics - confidence intervals (difference of two population means, large samples)

Seva is investigating the lengths of the tails of adult wallabies in two regions of Australia, X and Y. He chooses a random sample of 50 adult wallabies from region X and records…

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