AS & A Level Mathematics (9709) — May–June 2024, Paper 52

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

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Question 1 · 5 marks · The geometric distribution

Rajesh applies once every year for a ticket to a music festival. The probability that he is successful in any particular year is 0.3, independently of other years. Find the…

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Question 2 · 5 marks · Probability (conditional / total probability with a tree diagram)

Seva has a coin which is biased so that when it is thrown the probability of obtaining a head is 1/3. He also has a bag containing 4 red marbles and 5 blue marbles. Seva throws…

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Question 3 · 6 marks · The normal distribution

The weights of oranges can be modelled by a normal distribution with mean 131 grams and standard deviation 54 grams. Oranges are classified as small, medium or large. A large…

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Question 4 · 7 marks · Representation of data (median and interquartile range)

The back-to-back stem-and-leaf diagram shows the annual salaries of 19 employees at each of two companies, Petral and Ravon (see the shared stem-and-leaf diagram, with key 2 31 5…

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Question 5 · 7 marks · Discrete random variables (probability of an outcome)

Jasmine has one $5 coin, two $2 coins and two $1 coins. She selects two of these coins at random. The random variable X is the total value, in dollars, of these two coins. Show…

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Question 6 · 10 marks · The normal approximation to the binomial distribution

The residents of Mahjing were asked to classify their local bus service: - 25% of residents classified their service as good. - 60% of residents classified their service as…

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

How many different arrangements are there of the 10 letters in the word REGENERATE?

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