AS & A Level Further Mathematics (9231) — May–June 2025, Paper 44

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

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Question 1 · 4 marks · Further Probability & Statistics - Hypothesis tests (t-test for a population mean)

A random sample of 12 observations of a normal random variable is taken. The results give unbiased estimates for the population mean and variance as 10.24 and 0.52 respectively.…

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Question 2 · 7 marks · Further Probability & Statistics - Non-parametric tests (Wilcoxon signed-rank test)

The level of sound produced by a particular type of machine was measured for a random sample of 11 such machines. The results, in suitable units, are shown below. Machine A B C D…

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Question 3 · 7 marks · Further Probability & Statistics - Chi-squared tests (contingency table test for independence)

A shop selling electrical goods has a team of three salespeople: Avril, Ben and Charlie. The manager wishes to investigate whether the salespeople are equally successful at…

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Question 4 · 9 marks · Further Probability & Statistics - Continuous random variables (probability density function)

The continuous random variable X has probability density function f given by f(x) = kx for 0 <= x < 1, f(x) = kx^2 for 1 <= x <= 2, f(x) = 0 otherwise. Show that k = 6/17. [2]

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Question 5 · 10 marks · Further Probability & Statistics - Probability generating functions

Eric has three identical coins, each of which is biased so that the probability of obtaining a head when it is thrown is 1/3. The random variable X is the number of heads obtained…

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Question 6 · 13 marks · Further Probability & Statistics - Confidence intervals (population mean, normal distribution)

Lina and Mona are two statisticians who also write songs. The 'time' of a song is the number of minutes for which it lasts. For a random sample of 10 of her songs, Lina calculates…

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