AS & A Level Mathematics (9709) — May–June 2024, Paper 53

6 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.

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Question 1 · 8 marks · Discrete random variables (probability distributions)

The numbers on the faces of a fair six-sided dice are 1, 2, 2, 3, 3, 3. The random variable X is the total score when the dice is rolled twice. Draw up the probability…

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Question 2 · 8 marks · The normal distribution

In a certain country, the heights of the adult population are normally distributed with mean 1.64 m and standard deviation 0.25 m. Find the probability that an adult chosen at…

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Question 3 · 7 marks · Probability (tree diagrams)

Box A contains 6 green balls and 3 yellow balls. Box B contains 4 green balls and x yellow balls. A ball is chosen at random from box A and placed in box B. A ball is then chosen…

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Question 4 · 8 marks · Representation of data (stem-and-leaf diagrams)

The times taken, in seconds, by 15 members of each of two swimming clubs, the Penguins and the Dolphins, to swim 50 metres are shown in the following table. Penguins 35 39 42 44…

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Question 5 · 11 marks · The geometric distribution

Salah decides to attempt the crossword puzzle in his newspaper each day. The probability that he will complete the puzzle on any given day is 0.65, independent of other days. Find…

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Question 6 · 8 marks · Permutations and combinations (arrangements with repeated letters)

How many different arrangements are there of the 9 letters in the word RECORDERS?

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