AS & A Level Further Mathematics (9231) — October–November 2023, 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 - hypothesis test for a population mean (t-test, small sample, unknown variance)

Maya is an athlete who competes in 1500-metre races. Last summer her practice run times had mean 4.22 minutes. Over the winter she has done some intense training to try to improve…

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Question 2 · 7 marks · Further Probability & Statistics - chi-squared test (test of independence in a contingency table)

A town council has published its plans for redeveloping the town centre and residents are being asked whether they approve or disapprove. A random sample of 250 responses has been…

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Question 3 · 8 marks · Further Probability & Statistics - hypothesis test for a mean difference (paired-sample t-test)

Scientists are studying the effects of exercise on LDL blood cholesterol levels. Over a three-month period, a large group of people exercised for 20 minutes each day. For a…

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Question 4 · 9 marks · Further Probability & Statistics - continuous random variables (probability density function, unknown constants)

As shown in the diagram, the continuous random variable X has probability density function f given by f(x) = mx for 0 <= x <= 2, f(x) = k/x^2 + c for 2 <= x <= 6, f(x) = 0…

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Question 5 · 10 marks · Further Probability & Statistics - probability generating functions (geometric distribution)

The random variable X has the geometric distribution Geo(p). Show that the probability generating function of X is pt/(1 - qt), where q = 1 - p.

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Question 6 · 10 marks · Further Probability & Statistics - non-parametric tests (Wilcoxon signed-rank test, single sample, normal approximation)

A school is conducting an experiment to see whether the distance that children can throw a ball increases in hot weather. On a cold day, all the children at the school were asked…

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October–November 2023 Paper 42 →

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