AS & A Level Further Mathematics (9231) — October–November 2024, 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 · 4 marks · Confidence intervals - population mean, normal distribution, small sample (t-distribution)

A scientist is investigating the lengths of the leaves of a certain type of plant. The scientist assumes that the lengths of the leaves of this type of plant are normally…

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Question 2 · 8 marks · Probability generating functions - mean and variance of a discrete distribution

The random variable X has probability generating function GX(t) given by GX(t) = 1/5 + p t + q t^2, where p and q are constants. Given that E(X) = 1.1, find the numerical value of…

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Question 3 · 10 marks · Chi-squared goodness of fit - estimating a binomial parameter from the sample mean

Rosie sows 5 seeds in each of 150 plant pots. The number of seeds that germinate is recorded for each pot. The results are summarised in the following table. Number of seeds that…

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Question 4 · 10 marks · Continuous random variables - cumulative distribution function from the pdf

The random variable X has probability density function f given by f(x) = (1/21)(x - 1)^2 for 2 <= x <= 5, f(x) = 0 otherwise. Find the cumulative distribution function of X. [3]

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Question 5 · 9 marks · Hypothesis tests - difference of two population means, large samples (z-test)

Dev owns a small company which produces bottles of juice. He uses two machines, X and Y, to fill empty bottles with juice. Dev is investigating the volumes of juice in the…

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Question 6 · 9 marks · Non-parametric tests - Wilcoxon signed-rank test (single sample, normal approximation)

A sports college keeps records of the times taken by students to run one lap of a running track. The population median time taken is 51.0 seconds. After a month of intensive…

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