CAIE A Level 9709

Mathematics 2024 · May/June

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24 Questions Q&A Available
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This CAIE A Level Mathematics paper is strongly focused on probability and statistics, with additional work on permutations and combinations, discrete random variables, and normal distribution. Students can expect structured calculation questions rather than multiple-choice, often with several parts that build from a basic probability or data-handling idea into a fuller reasoning task, such as conditional probability, expected value, variance, box-and-whisker plots, and approximations to the binomial distribution.…

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Questions & Model Answers 24 Qs

Q2
Short Answer 1 mark
Seva has a coin which is biased so that when it is thrown the probability of obtaining a head is . He also has a bag containing 4 red marbles and 5 blue marbles. Seva throws the coin. If he obtains a head, he selects one marble from the bag at random. If he obtains a tail, he selects two marbles from the bag at random and without replacement.
Q2(a)
Short Answer 3 marks
Find the probability that Seva selects at least one red marble.
Q2(b)
Short Answer 2 marks
Find the probability that Seva obtains a head given that he selects no red marbles.
Q3
Short Answer 1 mark
The weights of oranges can be modelled by a normal distribution with mean 131 grams and standard deviation 54 grams. Oranges are classified as small, medium or large. A large orange weighs at least 184 grams and 20% of oranges are classified as small.
Q3(a)
Short Answer 3 marks
Find the percentage of oranges that are classified as large.
Q3(b)
Short Answer 3 marks
Find the greatest possible weight of a small orange.
Q4
Short Answer 1 mark
The back-to-back stem-and-leaf diagram shows the annual salaries of 19 employees at each of two companies, Petral and Ravon. Petral Ravon 3003026 9982213115 554032002 753330489 103411346 83679 Key: 2 | 31 | 5 means $31 200 for a Petral employee and $31 500 for a Ravon employee.
Q4(a)
Short Answer 1 mark
Find the median and the interquartile range of the salaries of the Petral employees. [3] The median salary of the Ravon employees is $33 800, the lower quartile is $32 000 and the upper quartile is $34 400.
Q4(b)
Short Answer 3 marks
Represent the data shown in the back-to-back stem-and-leaf diagram by a pair of box-and-whisker plots in a single diagram.
Q4(c)
Short Answer 1 mark
Comment on whether the mean or the median would be a better representation of the data for the employees at Petral.
Q5
Short Answer 1 mark
Jasmine has one $5 coin, two $2 coins and two $1 coins. She selects two of these coins at random. The random variable X is the total value, in dollars, of these two coins.
Q5(a)
Short Answer 1 mark
Show that () .X702P== .
Q5(b)
Short Answer 3 marks
Draw up the probability distribution table for X.
Q5(c)
Short Answer 3 marks
Find the value of ()XarV .
Q6
Short Answer 1 mark
The residents of Mahjing were asked to classify their local bus service:
Q6(a)
Structured 5 marks
A random sample of 110 residents of Mahjing is chosen. Use a suitable approximation to find the probability that fewer than 22 residents classified their bus service as good.
Q6(b)
Short Answer 3 marks
For a random sample of 10 residents of Mahjing, find the probability that fewer than 8 classified their bus service as good or satisfactory.
Q6(c)
Short Answer 2 marks
Three residents of Mahjing are selected at random. Find the probability that one resident classified the bus service as good, one as satisfactory and one as poor.
Q7(a)
Short Answer 1 mark
How many different arrangements are there of the 10 letters in the word REGENERATE?
Q7(b)
Structured 4 marks
How many different arrangements are there of the 10 letters in the word REGENERATE in which the 4 Es are together and the 2 Rs have exactly 3 letters in between them?
Q7(c)
Short Answer 1 mark
Find the probability that a randomly chosen arrangement of the 10 letters in the word REGENERATE is one in which the consonants (G, N, R, R, T) and vowels (A, E, E, E, E) alternate, so that no two consonants are next to each other and no two vowels are next to each other. [5] Additional page If you use the following lined page to complete the answer
Q7(c)(s)
Short Answer 1 mark
to any question
Q7(c)(s)
Short Answer 1 mark
, the question number
Q7(c)(s)
Short Answer 1 mark
must be clearly shown. Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort 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.
Paper Details
Board CAIE
Level A Level
Subject Mathematics
Code 9709
Year 2024
Session May/June
Q&A 24 questions
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