AS & A Level Mathematics (9709) — May–June 2025, Paper 51

6 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.

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Question 1 · 3 marks · The normal distribution

The masses of the bags of rice made by a company are normally distributed with mean mu kg and standard deviation 0.14 kg. The probability that the mass of a randomly chosen bag of…

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Question 2 · 7 marks · Permutations and combinations

Find the number of different arrangements of the 8 letters in the word KANGAROO in which the two As are together and the two Os are not together.

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Question 3 · 12 marks · Representation of data

Last Sunday, teams of runners took part in a charity event. The time taken, in seconds, to run 50 m was recorded, correct to 1 decimal place, for each runner. The times recorded…

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Question 4 · 12 marks · The normal distribution

Every Saturday, a particular community holds a 'Puzzle' event to raise money for a new Leisure Centre. Competitors attempt to solve a puzzle as quickly as possible. Last Saturday,…

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Question 5 · 7 marks · Permutations and combinations

In a group of 20 musicians, there are 9 guitarists, 6 pianists and 5 drummers. 6 musicians are selected from these 20 to perform at a concert. Find the number of different ways in…

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Question 6 · 9 marks · Probability

A bag contains 10 marbles, of which 4 are red and 6 are blue. Four marbles are selected from the bag at random, without replacement. The random variable X denotes the number of…

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