AS & A Level Further Mathematics (9231) — May–June 2025, 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 · 6 marks · Further Probability & Statistics - chi-squared goodness of fit test

A person's eye colour may be categorised as "brown", "blue" or "other". A scientist claims that these eye colours are uniformly distributed and hence are equally likely to occur…

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Question 2 · 7 marks · Further Probability & Statistics - confidence interval for difference of two means

A farmer is investigating whether using a new fertiliser will increase the yield of tomato plants. The farmer selects 40 tomato plants at random and gives them the new fertiliser.…

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Question 3 · 10 marks · Further Probability & Statistics - continuous random variables (probability density function)

A continuous random variable X has probability density function f given by f(x) = kx for 0 <= x < 1, f(x) = k(8 - x) for 1 <= x <= 8, f(x) = 0 otherwise, where k is a constant.…

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Question 4 · 8 marks · Further Probability & Statistics - Wilcoxon rank-sum test

A researcher claims that older people take longer to react to a sudden loud noise than younger people. To investigate this, the researcher randomly selects 6 people over 50 years…

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Question 5 · 8 marks · Further Probability & Statistics - paired-sample t-test

A doctor is investigating the concentration of blood glucose in patients at risk of developing type 2 diabetes, where blood glucose is measured in appropriate units. The doctor…

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Question 6 · 11 marks · Further Probability & Statistics - probability generating functions

A bag contains 7 red balls and 3 blue balls. Kieran selects 2 balls at random, without replacement. The number of red balls selected by Kieran is denoted by X, and the number of…

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