Questions — CAIE S1 (785 questions)

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All questions AEA AS Paper 1 AS Paper 2 AS Pure C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Extra Pure Further Mechanics Further Mechanics A AS Further Mechanics AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics Further Paper 4 Further Pure Core Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Pure with Technology Further Statistics Further Statistics A AS Further Statistics AS Further Statistics B AS Further Statistics Major Further Statistics Minor Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 H240/01 H240/02 H240/03 M1 M2 M3 M4 M5 Mechanics 1 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pure 1 S1 S2 S3 S4 SPS ASFM SPS ASFM Mechanics SPS ASFM Pure SPS ASFM Statistics SPS FM SPS FM Mechanics SPS FM Pure SPS FM Statistics SPS SM SPS SM Mechanics SPS SM Pure SPS SM Statistics Stats 1 Unit 1 Unit 2 Unit 3 Unit 4
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AQA AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Paper 1 Further Paper 2 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics M1 M2 M3 Paper 1 Paper 2 Paper 3 S1 S2 S3 CAIE FP1 FP2 Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 4 M1 M2 P1 P2 P3 S1 S2 Edexcel AEA AS Paper 1 AS Paper 2 C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 OCR AS Pure C1 C2 C3 C4 D1 D2 FD1 AS FM1 AS FP1 FP1 AS FP2 FP3 FS1 AS Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Mechanics Further Mechanics AS Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Statistics Further Statistics AS H240/01 H240/02 H240/03 M1 M2 M3 M4 Mechanics 1 PURE Pure 1 S1 S2 S3 S4 Stats 1 OCR MEI AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further Extra Pure Further Mechanics A AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Pure Core Further Pure Core AS Further Pure with Technology Further Statistics A AS Further Statistics B AS Further Statistics Major Further Statistics Minor M1 M2 M3 M4 Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 SPS SPS ASFM SPS ASFM Mechanics SPS ASFM Pure SPS ASFM Statistics SPS FM SPS FM Mechanics SPS FM Pure SPS FM Statistics SPS SM SPS SM Mechanics SPS SM Pure SPS SM Statistics WJEC Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 Unit 1 Unit 2 Unit 3 Unit 4
CAIE S1 2006 June Q6
  1. How many teams play in only 1 match?
  2. How many teams play in exactly 2 matches?
  3. Draw up a frequency table for the numbers of matches which the teams play.
  4. Calculate the mean and variance of the numbers of matches which the teams play.
CAIE S1 2015 June Q4
(ii) Given that Nikita's mother does not like her present, find the probability that the present is a scarf.
CAIE S1 2014 November Q4
  1. Draw a fully labelled tree diagram to illustrate the various choices that Sharik can make until the computer indicates that he has answered the question correctly.
  2. The random variable \(X\) is the number of attempts that Sharik makes up to and including the one that the computer indicates is correct. Draw up the probability distribution table for \(X\) and find \(\mathrm { E } ( X )\).
    (a) The time, \(X\) hours, for which people sleep in one night has a normal distribution with mean 7.15 hours and standard deviation 0.88 hours.
  3. Find the probability that a randomly chosen person sleeps for less than 8 hours in a night.
  4. Find the value of \(q\) such that \(\mathrm { P } ( X < q ) = 0.75\).
    (b) The random variable \(Y\) has the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\), where \(2 \sigma = 3 \mu\) and \(\mu \neq 0\). Find \(\mathrm { P } ( Y > 4 \mu )\).
CAIE S1 2021 November Q1
1 Each of the 180 students at a college plays exactly one of the piano, the guitar and the drums. The numbers of male and female students who play the piano, the guitar and the drums are given in the following table.
PianoGuitarDrums
Male254411
Female423820
A student at the college is chosen at random.
  1. Find the probability that the student plays the guitar.
  2. Find the probability that the student is male given that the student plays the drums.
  3. Determine whether the events 'the student plays the guitar' and 'the student is female' are independent, justifying your answer.
CAIE S1 2021 November Q2
2 A group of 6 people is to be chosen from 4 men and 11 women.
  1. In how many different ways can a group of 6 be chosen if it must contain exactly 1 man?
    Two of the 11 women are sisters Jane and Kate.
  2. In how many different ways can a group of 6 be chosen if Jane and Kate cannot both be in the group?
CAIE S1 2021 November Q3
3 A bag contains 5 yellow and 4 green marbles. Three marbles are selected at random from the bag, without replacement.
  1. Show that the probability that exactly one of the marbles is yellow is \(\frac { 5 } { 14 }\).
    The random variable \(X\) is the number of yellow marbles selected.
  2. Draw up the probability distribution table for \(X\).
  3. Find \(\mathrm { E } ( X )\).
CAIE S1 2021 November Q4
4
  1. In how many different ways can the 9 letters of the word TELESCOPE be arranged?
  2. In how many different ways can the 9 letters of the word TELESCOPE be arranged so that there are exactly two letters between the T and the C ?
CAIE S1 2021 November Q5
5 In a certain region, the probability that any given day in October is wet is 0.16 , independently of other days.
  1. Find the probability that, in a 10-day period in October, fewer than 3 days will be wet.
  2. Find the probability that the first wet day in October is 8 October.
  3. For 4 randomly chosen years, find the probability that in exactly 1 of these years the first wet day in October is 8 October.
CAIE S1 2021 November Q6
6 The times taken, in minutes, to complete a particular task by employees at a large company are normally distributed with mean 32.2 and standard deviation 9.6.
  1. Find the probability that a randomly chosen employee takes more than 28.6 minutes to complete the task.
  2. \(20 \%\) of employees take longer than \(t\) minutes to complete the task. Find the value of \(t\).
  3. Find the probability that the time taken to complete the task by a randomly chosen employee differs from the mean by less than 15.0 minutes.
CAIE S1 2021 November Q8
8
*
\end{tabular} & MATHEMATICS & 9709/52
\hline 0 & Paper 5 Probability \& Statistics 1 & October/November 2021
\hline \(\infty\) & & 1 hour 15 minutes
\hline & You must answer on the question paper. &
\hline & You will need: List of formulae (MF19) &
\hline \end{tabular} \end{center} \section*{INSTRUCTIONS}
  • Answer all questions.
  • Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
  • Write your name, centre number and candidate number in the boxes at the top of the page.
  • Write your answer to each question in the space provided.
  • Do not use an erasable pen or correction fluid.
  • Do not write on any bar codes.
  • If additional space is needed, you should use the lined page at the end of this booklet; the question number or numbers must be clearly shown.
  • You should use a calculator where appropriate.
  • You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.
  • Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
\section*{INFORMATION}
  • The total mark for this paper is 50.
  • The number of marks for each question or part question is shown in brackets [ ].
1 Each of the 180 students at a college plays exactly one of the piano, the guitar and the drums. The numbers of male and female students who play the piano, the guitar and the drums are given in the following table.
PianoGuitarDrums
Male254411
Female423820
A student at the college is chosen at random.
  1. Find the probability that the student plays the guitar.
  2. Find the probability that the student is male given that the student plays the drums.
  3. Determine whether the events 'the student plays the guitar' and 'the student is female' are independent, justifying your answer.
    2 A group of 6 people is to be chosen from 4 men and 11 women.
  4. In how many different ways can a group of 6 be chosen if it must contain exactly 1 man?
    Two of the 11 women are sisters Jane and Kate.
  5. In how many different ways can a group of 6 be chosen if Jane and Kate cannot both be in the group?
    3 A bag contains 5 yellow and 4 green marbles. Three marbles are selected at random from the bag, without replacement.
  6. Show that the probability that exactly one of the marbles is yellow is \(\frac { 5 } { 14 }\).
    The random variable \(X\) is the number of yellow marbles selected.
  7. Draw up the probability distribution table for \(X\).
  8. Find \(\mathrm { E } ( X )\).
    4
  9. In how many different ways can the 9 letters of the word TELESCOPE be arranged?
  10. In how many different ways can the 9 letters of the word TELESCOPE be arranged so that there are exactly two letters between the T and the C ?
    5 In a certain region, the probability that any given day in October is wet is 0.16 , independently of other days.
  11. Find the probability that, in a 10-day period in October, fewer than 3 days will be wet.
  12. Find the probability that the first wet day in October is 8 October.
  13. For 4 randomly chosen years, find the probability that in exactly 1 of these years the first wet day in October is 8 October.
    6 The times taken, in minutes, to complete a particular task by employees at a large company are normally distributed with mean 32.2 and standard deviation 9.6.
  14. Find the probability that a randomly chosen employee takes more than 28.6 minutes to complete the task.
  15. \(20 \%\) of employees take longer than \(t\) minutes to complete the task. Find the value of \(t\).
  16. Find the probability that the time taken to complete the task by a randomly chosen employee differs from the mean by less than 15.0 minutes.
    7 The distances, \(x \mathrm {~m}\), travelled to school by 140 children were recorded. The results are summarised in the table below.
    Distance, \(x \mathrm {~m}\)\(x \leqslant 200\)\(x \leqslant 300\)\(x \leqslant 500\)\(x \leqslant 900\)\(x \leqslant 1200\)\(x \leqslant 1600\)
    Cumulative frequency164688122134140
  17. On the grid, draw a cumulative frequency graph to represent these results.
    \includegraphics[max width=\textwidth, alt={}, center]{93ff111b-0267-4b4b-a41c-64c3307115af-10_1593_1593_701_306}
  18. Use your graph to estimate the interquartile range of the distances.
  19. Calculate estimates of the mean and standard deviation of the distances.
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.