AS & A Level Mathematics (9709) — October–November 2023, 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 · 6 marks · Discrete random variables (probability distribution)

Becky sometimes works in an office and sometimes works at home. The random variable X denotes the number of days that she works at home in any given week. It is given that P(X =…

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Question 2 · 6 marks · The normal distribution

The weights of large bags of pasta produced by a company are normally distributed with mean 1.5 kg and standard deviation 0.05 kg. Find the probability that a randomly chosen…

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Question 3 · 7 marks · Probability (conditional selection, without replacement)

Tim has two bags of marbles, A and B. Bag A contains 8 white, 4 red and 3 yellow marbles. Bag B contains 6 white, 7 red and 2 yellow marbles. Tim also has an ordinary fair 6-sided…

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Question 4 · 10 marks · Representation of data (cumulative frequency graph)

The weights, x kg, of 120 students in a sports college are recorded and summarised in the cumulative frequency table provided. Draw a cumulative frequency graph to represent this…

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Question 5 · 11 marks · The geometric distribution

The probability that a driver passes an advanced driving test is 0.3 on any given attempt. Dipak keeps taking the test until he passes. The random variable X denotes the number of…

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Question 6 · 10 marks · Permutations (arrangements with grouped items)

Jai and his wife Kaz are having a party. Jai has invited five friends and each friend will bring his wife, making 12 people in total. At the beginning of the party, the 12 people…

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