AS & A Level Mathematics (9709) — May–June 2024, 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 (mean from summarised/coded data)

A summary of 20 values of x gives Σ(x − 30) = 439 and Σ(x − 30)^2 = 12405. A summary of another 25 values of x gives Σ(x − 30) = 470 and Σ(x − 30)^2 = 11346. Find the mean of all…

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Question 2 · 7 marks · The normal distribution

The lengths of the tails of adult raccoons of a certain species are normally distributed with mean 28 cm and standard deviation 3.3 cm. Find the probability that a randomly chosen…

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Question 3 · 6 marks · Representation of data (histograms)

The heights, in cm, of 200 adults in Barimba are summarised in the following table. Height (h cm) 130 ≤ h < 150 150 ≤ h < 160 160 ≤ h < 170 170 ≤ h < 175 175 ≤ h < 195 --- --- ---…

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Question 4 · 6 marks · Probability (complementary events / repeated independent trials)

A game for two players is played using a fair 4-sided dice with sides numbered 1, 2, 3 and 4. One turn consists of throwing the dice repeatedly up to a maximum of three times.…

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Question 5 · 10 marks · The binomial distribution

In a certain area in the Arctic the probability that it snows on any given day is 0.7, independent of all other days. Find the probability that in a week (7 days) it snows on at…

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Question 6 · 7 marks · Probability distributions

Harry has three coins: - One coin is biased so that the probability of obtaining a head when it is thrown is 1/3. - The second coin is biased so that the probability of obtaining…

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Question 7 · 10 marks · Permutations and combinations (arrangements with repeated items)

The eight digits 1, 2, 2, 3, 4, 4, 4, 5 are arranged in a line. How many different arrangements are there of these 8 digits?

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