AS & A Level Mathematics (9709) — October–November 2024, Paper 51

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 · Probability (the geometric distribution)

Nicola throws an ordinary fair six-sided dice. The random variable X is the number of throws that she takes to obtain a 6. Find P(X < 8).

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Question 2 · 6 marks · Discrete random variables (probability distributions)

The random variable X takes the values −2, −1, 0, 2, 3. It is given that P(X = x) = k(x^2 + 2), where k is a positive constant. Draw up the probability distribution table for X,…

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Question 3 · 8 marks · Representation of data (cumulative frequency graphs)

The time taken, in minutes, to walk to school was recorded for 200 pupils at a certain school. These times are summarised in the following table. Time taken (t minutes) t ≤ 15 t ≤…

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Question 4 · 6 marks · Probability (tree diagrams and combined events)

Rahul has two bags, X and Y. Bag X contains 4 red marbles and 2 blue marbles. Bag Y contains 3 red marbles and 4 blue marbles. Rahul also has a coin which is biased so that the…

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Question 5 · 9 marks · The normal distribution

The weights of the green apples sold by a shop are normally distributed with mean 90 grams and standard deviation 8 grams. Find the probability that a randomly chosen green apple…

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Question 6 · 8 marks · The normal distribution (finding mean and standard deviation)

The heights of the female students at Breven college are normally distributed: - 90% of the female students have heights less than 182.7 cm. - 40% of the female students have…

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Question 7 · 9 marks · Permutations and combinations (arrangements with repeated letters and a grouping restriction)

How many different arrangements are there of the 9 letters in the word INTELLECT in which the two Ts are together?

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