AS & A Level Mathematics (9709) — May–June 2023, Paper 53

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 · The geometric distribution (expectation)

Two fair coins are thrown at the same time repeatedly until a pair of heads is obtained. The number of throws taken is denoted by the random variable X. State the value of E(X).

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Question 2 · 5 marks · The normal distribution (normal approximation to the binomial)

Anil is a candidate in an election. He received 40% of the votes. A random sample of 120 voters is chosen. Use an approximation to find the probability that, of the 120 voters,…

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Question 3 · 7 marks · Discrete random variables (probability distributions)

The random variable X takes the values 1, 2, 3, 4. It is given that P(X = x) = kx(x + a), where k and a are constants. Given that P(X = 4) = 3P(X = 2), find the value of a and the…

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

The times taken, in minutes, to complete a cycle race by 19 cyclists from each of two clubs, the Cheetahs and the Panthers, are represented in the back-to-back stem-and-leaf…

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Question 5 · 7 marks · Probability (independence)

Jasmine throws two ordinary fair 6-sided dice at the same time and notes the numbers on the uppermost faces. The events A and B are defined as follows. A: The sum of the two…

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Question 6 · 10 marks · The normal distribution (finding an unknown standard deviation)

The mass of grapes sold per day by a large shop can be modelled by a normal distribution with mean 28 kg. On 10% of days less than 16 kg of grapes are sold. Find the standard…

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Question 7 · 9 marks · Permutations and combinations (arrangements with repeated letters and restrictions)

Find the number of different arrangements of the 10 letters in the word CASABLANCA in which the two Cs are not together.

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