AS & A Level Mathematics (9709) — October–November 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 · 6 marks · Probability (conditional probability)

At a college, the students choose exactly one of tennis, hockey or netball to play. The numbers of students in Year 1 and Year 2 playing each sport are: Tennis Hockey Netball…

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Question 2 · 4 marks · Permutations and combinations

Find the number of different arrangements of the 9 letters in the word ALGEBRAIC.

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Question 3 · 6 marks · Discrete random variables (probability distributions)

A fair coin and an ordinary fair six-sided dice are thrown at the same time. The random variable X is defined as follows. - If the coin shows a tail, X is twice the score on the…

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Question 4 · 7 marks · The normal distribution

The heights, in metres, of white pine trees are normally distributed with mean 19.8 and standard deviation 2.4. In a certain forest there are 450 white pine trees. How many of…

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Question 5 · 6 marks · Permutations and combinations (selections)

In a class of 21 students, there are 10 violinists, 6 guitarists and 5 pianists. A group of 7 is to be chosen from these 21 students. The group will consist of 4 violinists, 2…

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Question 6 · 10 marks · Representation of data (stem-and-leaf diagrams)

Teams of 15 runners took part in a charity run last Saturday. The times taken, in minutes, to complete the course by the runners from the Falcons and the runners from the Kites…

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Question 7 · 11 marks · The geometric distribution

In a game, players attempt to score a goal by kicking a ball into a net. The probability that Leno scores a goal is 0.4 on any attempt, independently of all other attempts. The…

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