AS & A Level Mathematics (9709) — May–June 2025, Paper 55

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

Two fair 6-sided dice with faces labelled 1, 2, 3, 4, 5, 6 are thrown. The two scores are noted. The random variable X is defined as follows. - If the two scores are equal, X = 0…

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Question 2 · 7 marks · The normal distribution

The heights of trees in a certain forest are classified as tall, medium or small. The heights can be modelled by a normal distribution with mean 20 m and standard deviation 5 m.…

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Question 3 · 8 marks · The normal distribution (normal approximation to the binomial)

In a certain large school, on average, two pupils in five have music lessons. A random sample of 80 pupils from this school is chosen. Use an approximation to find the probability…

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Question 4 · 9 marks · Probability (tree diagrams)

Students applying to Drydale College take an entrance test. A student is either accepted or rejected or required to take another test with probabilities 0.3, 0.2 and 0.5…

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Question 5 · 10 marks · Representation of data (stem-and-leaf diagrams)

The Smarts and the Teasers are two quiz teams that each contain 11 members. Both complete a puzzle and the following table gives the times taken, in minutes, by the members of…

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Question 6 · 10 marks · Permutations and combinations (probability)

A darts club has 12 members made up of 7 men and 5 women. Every Monday, a team of 4 is chosen at random to represent the club in a competition. Find the probability that, on a…

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