AS & A Level Mathematics (9709) — October–November 2023, 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 · Discrete random variables (probability distribution, expectation)

A competitor in a throwing event has three attempts to throw a ball as far as possible. The random variable X denotes the number of throws that exceed 30 metres. The probability…

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Question 2 · 5 marks · The geometric distribution

George has a fair 5-sided spinner with sides labelled 1, 2, 3, 4, 5. He spins the spinner and notes the number on the side on which the spinner lands. Find the probability that it…

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Question 3 · 5 marks · The normal distribution (normal approximation to the binomial)

A factory produces a certain type of electrical component. It is known that 15% of the components produced are faulty. A random sample of 200 components is chosen. Use an…

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

The heights, in cm, of the 11 players in each of two teams, the Aces and the Jets, are shown in the table provided. Draw a back-to-back stem-and-leaf diagram to represent this…

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Question 5 · 8 marks · The normal distribution

The heights of the members of a club are normally distributed with mean 166 cm and standard deviation 10 cm. Find the probability that a randomly chosen member of the club has…

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Question 6 · 9 marks · Probability (tree diagrams)

Freddie has two bags of marbles. Bag X contains 7 red marbles and 3 blue marbles. Bag Y contains 4 red marbles and 1 blue marble. Freddie chooses one of the bags at random. A…

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Question 7 · 10 marks · Permutations and combinations

Find the number of different arrangements of the 9 letters in the word ANDROMEDA in which no consonant is next to another consonant. (The letters D, M, N and R are consonants and…

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