AS & A Level Further Mathematics (9231) — May–June 2025, Paper 42

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 · Hypothesis testing - difference of population means (large samples, unequal variances)

The manager of a hardware store is interested in whether there is a difference in the amount spent per customer on weekdays ($x) compared to weekends ($y). Random samples of 120…

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Question 2 · 12 marks · Continuous random variables - probability density functions

As shown in the diagram, the continuous random variable X has probability density function f given by f(x) = a for 0 <= x <= 5, f(x) = b - cx for 5 <= x <= 8, f(x) = 0 otherwise,…

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Question 3 · 8 marks · Chi-squared tests - goodness of fit (binomial model)

Eggs in a supermarket are sold in boxes of six. A supermarket manager wishes to model the number of broken eggs in the boxes sold in the store. A random sample of 2000 boxes is…

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Question 4 · 7 marks · Confidence intervals - difference of two means (normal, common unknown variance, t-distribution)

A researcher is interested in whether there is a difference between two schools in students' aptitude for English. She randomly chooses 10 students from school X and 8 students of…

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Question 5 · 10 marks · Non-parametric tests - Wilcoxon matched-pairs signed-rank test

Two jigsaw puzzles have the same number of pieces with identical shapes but have different pictures printed on them. One puzzle has a seaside picture and the other has a cartoon…

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Question 6 · 6 marks · Probability generating functions

Y is a discrete random variable which takes the values 0, 2, 4, ... . The probability generating function of Y is given by GY(t) = k / (1 - a t^2). Find k in terms of a. [1]

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