CAIE A Level 9709

Mathematics 2025 · May/June

21 Questions Q&A Available

Questions & Model Answers 21 Qs

Short Answer 3 marks

Rachel has three coins. The first coin is biased so that the probability of obtaining a head when it is thrown is . The second coin is biased so that the probability of obtaining a head when it is thrown is The third coin is fair. Rachel throws the three coins at the same time. The random variable X is the number of tails that she obtains. Draw up the probability distribution table for X.

Structured 5 marks

In Millford, 70% of the residents own a bicycle. A random sample of 160 residents is selected. Use a suitable approximation to find the probability that more than 120 of these residents own a bicycle.

Short Answer 1 mark

A bag contains 4 blue marbles and 12 red marbles. One marble is selected at random from the bag. If this marble is blue, it is replaced in the bag, but if it is red, it is not replaced. A second marble is now selected at random from the bag.

Q3(a)

Short Answer 2 marks

Find the probability that both marbles selected are the same colour .

Q3(b)

Short Answer 3 marks

Find the probability that the first marble is blue given that the second marble is red.

Short Answer 1 mark

Vehicles approaching a certain road junction from Bromley must go either left, right or straight on. Over time, it is known that 30% turn left, 25% turn right and 45% go straight on. The driver of each vehicle chooses a direction independently of all other drivers.

Q4(a)

Short Answer 2 marks

Find the probability that the next three vehicles approaching this junction from Bromley all go in different directions.

Q4(b)

Short Answer 2 marks

Find the probability that, from the vehicles approaching this junction from Bromley today, the 1st vehicle to go left is before the 9th vehicle.

Q4(c)

Short Answer 2 marks

Find the probability that, from the vehicles approaching this junction from Bromley today , the 2nd vehicle to go left is the 7th vehicle.

Short Answer 1 mark

The times taken, t minutes, by 300 students to travel to Hollowton College are recorded. The results are summarised in the table below. Time (t minutes) t10G t02G t03G t04G t06G t09G Cumulative frequency34 86 142 208 265 300

Q5(a)

Short Answer 2 marks

On the grid, draw a cumulative frequency graph to illustrate this information.

Q5(b)

Short Answer 2 marks

120 students take more than k minutes to travel to college. Use your graph to estimate the value of k .

Q5(c)

Structured 6 marks

Calculate estimates of the mean and standard deviation of the times taken to travel to college by the 300 students.

Q6(a)

Short Answer 3 marks

Find the number of dif ferent ways in which the 10 letters in the word AMALGAMATE can be arranged so that there is an M at the beginning, an M at the end and no As are together.

Q6(b)

Short Answer 1 mark

Find the number of dif ferent ways in which the 10 letters in the word AMALGAMATE can be arranged with exactly 3 letters between the two Ms. [3] Five letters are selected from the 10 letters in the word AMALGAMATE.

Q6(c)

Short Answer 3 marks

Find the number of dif ferent selections in which the five letters include at least one M and at least two As.

Short Answer 1 mark

Kestrels are birds whose adult wingspans are normally distributed with mean 74.8 cm and standard deviation 3.2 cm. A random sample of 120 adult kestrels is selected.

Q7(a)

Short Answer 1 mark

How many of these 120 adult kestrels would you expect to have wingspan between 72.4 cm and 76.3 cm? [4] The masses of adult kestrels are normally distributed with mean n kg and standard deviation v kg. It is known that 20% of adult kestrels have mass greater than 0.202 kg and 28% have mass less than 0.185 kg.

Q7(b)

Structured 5 marks

Find the value of n and the value of v.

Q10

Short Answer 1 mark

adult kestrels are selected at random.

Q10(c)

Short Answer 1 mark

Find the probability that fewer than 3 have masses greater than 0.202 kg. [3] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable ef fort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. Additional page If you use the following page to complete the answer to any question, the question number must be clearly shown.

Paper Details

Board	CAIE
Level	A Level
Subject	Mathematics
Code	`9709`
Year	2025
Session	May/June
Q&A	21 questions

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