AS & A Level Mathematics (9709) — May–June 2023, Paper 51

7 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 · Representation of data (variance and standard deviation)

A summary of 50 values of x gives Σ(x − q) = 700 and Σ(x − q)^2 = 14235, where q is a constant. Find the standard deviation of these values of x.

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Question 2 · 5 marks · Permutations and combinations (selections)

Find the number of ways in which a committee of 6 people can be chosen from 6 men and 8 women if it must include 3 men and 3 women.

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Question 3 · 6 marks · Permutations and combinations (arrangements with repeated letters)

Find the number of different arrangements of the 8 letters in the word COCOONED.

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Question 4 · 9 marks · The normal distribution (calculating probabilities and expected frequencies)

A mathematical puzzle is given to a large number of students. The times taken to complete the puzzle are normally distributed with mean 14.6 minutes and standard deviation 5.2…

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Question 5 · 7 marks · Representation of data (histograms)

The populations of 150 villages in the UK, to the nearest hundred, are summarised in the table. Population 100 – 800 900 – 1200 1300 – 2000 2100 – 3200 3300 – 4800 --- --- --- ---…

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Question 6 · 11 marks · The binomial distribution

Eli has four fair 4-sided dice with sides labelled 1, 2, 3, 4. He throws all four dice at the same time. The random variable X denotes the number of 2s obtained. Show that P(X =…

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Question 7 · 8 marks · Probability (independent events / complementary probability)

A children's wildlife magazine is published every Monday. For the next 12 weeks it will include a model animal as a free gift. There are five different models: tiger, leopard,…

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