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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 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
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CAIE S1 2018 June Q1
4 marks Easy -1.8
1 Each of a group of 10 boys estimates the length of a piece of string. The estimates, in centimetres, are as follows. $$\begin{array} { l l l l l l l l l l } 37 & 40 & 45 & 38 & 36 & 38 & 42 & 38 & 40 & 39 \end{array}$$
  1. Find the mode.
  2. Find the median and the interquartile range.
CAIE S1 2018 June Q2
6 marks Moderate -0.3
2 In a group of students, \(\frac { 3 } { 4 }\) are male. The proportion of male students who like their curry hot is \(\frac { 3 } { 5 }\) and the proportion of female students who like their curry hot is \(\frac { 4 } { 5 }\). One student is chosen at random.
  1. Find the probability that the student chosen is either female, or likes their curry hot, or is both female and likes their curry hot.
  2. Showing your working, determine whether the events 'the student chosen is male' and 'the student chosen likes their curry hot' are independent.
CAIE S1 2018 June Q3
6 marks Moderate -0.3
3
  1. The volume of soup in Super Soup cartons has a normal distribution with mean \(\mu\) millilitres and standard deviation 9 millilitres. Tests have shown that \(10 \%\) of cartons contain less than 440 millilitres of soup. Find the value of \(\mu\).
  2. A food retailer orders 150 Super Soup cartons. Calculate the number of these cartons for which you would expect the volume of soup to be more than 1.8 standard deviations above the mean.
CAIE S1 2018 June Q4
6 marks Moderate -0.8
4 Mrs Rupal chooses 3 animals at random from 5 dogs and 2 cats. The random variable \(X\) is the number of cats chosen.
  1. Draw up the probability distribution table for \(X\).
  2. You are given that \(\mathrm { E } ( X ) = \frac { 6 } { 7 }\). Find the value of \(\operatorname { Var } ( X )\).
CAIE S1 2018 June Q5
7 marks Easy -1.2
5 The lengths, \(t\) minutes, of 242 phone calls made by a family over a period of 1 week are summarised in the frequency table below.
Length of phone
call \(( t\) minutes \()\)
\(0 < t \leqslant 1\)\(1 < t \leqslant 2\)\(2 < t \leqslant 5\)\(5 < t \leqslant 10\)\(10 < t \leqslant 30\)
Frequency1446102\(a\)40
  1. Find the value of \(a\).
  2. Calculate an estimate of the mean length of these phone calls.
  3. On the grid, draw a histogram to illustrate the data in the table. \includegraphics[max width=\textwidth, alt={}, center]{a813e127-d116-411c-88ec-2443fdbc9391-07_2002_1513_486_356}
CAIE S1 2018 June Q6
10 marks Moderate -0.8
6
  1. Find the number of ways in which all 9 letters of the word AUSTRALIA can be arranged in each of the following cases.
    1. All the vowels (A, I, U are vowels) are together.
    2. The letter T is in the central position and each end position is occupied by one of the other consonants (R, S, L).
  2. Donna has 2 necklaces, 8 rings and 4 bracelets, all different. She chooses 4 pieces of jewellery. How many possible selections can she make if she chooses at least 1 necklace and at least 1 bracelet?
CAIE S1 2018 June Q7
11 marks Standard +0.3
7 In a certain country, \(60 \%\) of mobile phones sold are made by Company \(A , 35 \%\) are made by Company \(B\) and 5\% are made by other companies.
  1. Find the probability that, out of a random sample of 13 people who buy a mobile phone, fewer than 11 choose a mobile phone made by Company \(A\).
  2. Use a suitable approximation to find the probability that, out of a random sample of 130 people who buy a mobile phone, at least 50 choose a mobile phone made by Company \(B\).
  3. A random sample of \(n\) mobile phones sold is chosen. The probability that at least one of these phones is made by Company \(B\) is more than 0.98 . Find the least possible value of \(n\).
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
CAIE S1 2018 June Q1
5 marks Moderate -0.8
1 The masses in kilograms of 50 children having a medical check-up were recorded correct to the nearest kilogram. The results are shown in the table.
Mass (kg)\(10 - 14\)\(15 - 19\)\(20 - 24\)\(25 - 34\)\(35 - 59\)
Frequency61214108
  1. Find which class interval contains the lower quartile.
  2. On the grid, draw a histogram to illustrate the data in the table. \includegraphics[max width=\textwidth, alt={}, center]{dd75fa20-fead-48d6-aff4-c5e733769f9f-02_1397_1397_1187_415}
CAIE S1 2018 June Q2
6 marks Standard +0.3
2 The random variable \(X\) has the distribution \(\mathrm { N } \left( - 3 , \sigma ^ { 2 } \right)\). The probability that a randomly chosen value of \(X\) is positive is 0.25 .
  1. Find the value of \(\sigma\).
  2. Find the probability that, of 8 random values of \(X\), fewer than 2 will be positive.
CAIE S1 2018 June Q3
6 marks Moderate -0.3
3 The members of a swimming club are classified either as 'Advanced swimmers' or 'Beginners'. The proportion of members who are male is \(x\), and the proportion of males who are Beginners is 0.7 . The proportion of females who are Advanced swimmers is 0.55 . This information is shown in the tree diagram. \includegraphics[max width=\textwidth, alt={}, center]{dd75fa20-fead-48d6-aff4-c5e733769f9f-04_435_974_482_587} For a randomly chosen member, the probability of being an Advanced swimmer is the same as the probability of being a Beginner.
  1. Find \(x\).
  2. Given that a randomly chosen member is an Advanced swimmer, find the probability that the member is male.
CAIE S1 2018 June Q4
7 marks Moderate -0.3
4 Farfield Travel and Lacket Travel are two travel companies which arrange tours abroad. The numbers of holidays arranged in a certain week are recorded in the table below, together with the means and standard deviations of the prices.
Number of
holidays
Mean price
\(( \\) )\(
Standard
deviation \)( \\( )\)
Farfield Travel301500230
Lacket Travel212400160
  1. Calculate the mean price of all 51 holidays.
  2. The prices of individual holidays with Farfield Travel are denoted by \(\\) x _ { F }\( and the prices of individual holidays with Lacket Travel are denoted by \)\\( x _ { L }\). By first finding \(\Sigma x _ { F } ^ { 2 }\) and \(\Sigma x _ { L } ^ { 2 }\), find the standard deviation of the prices of all 51 holidays.
CAIE S1 2018 June Q5
8 marks Moderate -0.3
5 A game is played with 3 coins, \(A , B\) and \(C\). Coins \(A\) and \(B\) are biased so that the probability of obtaining a head is 0.4 for coin \(A\) and 0.75 for coin \(B\). Coin \(C\) is not biased. The 3 coins are thrown once.
  1. Draw up the probability distribution table for the number of heads obtained.
  2. Hence calculate the mean and variance of the number of heads obtained.
CAIE S1 2018 June Q6
8 marks Standard +0.3
6 The diameters of apples in an orchard have a normal distribution with mean 5.7 cm and standard deviation 0.8 cm . Apples with diameters between 4.1 cm and 5 cm can be used as toffee apples.
  1. Find the probability that an apple selected at random can be used as a toffee apple.
  2. 250 apples are chosen at random. Use a suitable approximation to find the probability that fewer than 50 can be used as toffee apples.
CAIE S1 2018 June Q7
10 marks Standard +0.3
7 Find the number of ways the 9 letters of the word SEVENTEEN can be arranged in each of the following cases.
  1. One of the letter Es is in the centre with 4 letters on either side.
  2. No E is next to another E.
    5 letters are chosen from the 9 letters of the word SEVENTEEN.
  3. Find the number of possible selections which contain exactly 2 Es and exactly 2 Ns.
  4. Find the number of possible selections which contain at least 2 Es.
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
CAIE S1 2019 June Q1
4 marks Easy -1.2
1 The times, \(t\) seconds, taken to swim 100 m were recorded for a group of 9 swimmers and were found to be as follows. $$\begin{array} { l l l l l l l l l } 95 & 126 & 117 & 135 & 120 & 125 & 114 & 119 & 136 \end{array}$$
  1. Find the values of \(\Sigma ( t - 120 )\) and \(\Sigma ( t - 120 ) ^ { 2 }\).
  2. Using your values found in part (i), calculate the variance of \(t\).
CAIE S1 2019 June Q2
3 marks Moderate -0.8
2 Jameel has 5 plums and 3 apricots in a box. Rosa has \(x\) plums and 6 apricots in a box. One fruit is chosen at random from Jameel's box and one fruit is chosen at random from Rosa's box. The probability that both fruits chosen are plums is \(\frac { 1 } { 4 }\). Write down an equation in \(x\) and hence find \(x\). [3]
CAIE S1 2019 June Q3
4 marks Moderate -0.3
3 A fair six-sided die is thrown twice and the scores are noted. Event \(X\) is defined as 'The total of the two scores is 4'. Event \(Y\) is defined as 'The first score is 2 or 5'. Are events \(X\) and \(Y\) independent? Justify your answer.
CAIE S1 2019 June Q4
6 marks Moderate -0.8
4 The Mathematics and English A-level marks of 1400 pupils all taking the same examinations are shown in the cumulative frequency graphs below. Both examinations are marked out of 100 . \includegraphics[max width=\textwidth, alt={}, center]{be6c6525-a20c-42d0-8fef-1cd254baaa76-06_1682_1246_404_445} Use suitable data from these graphs to compare the central tendency and spread of the marks in Mathematics and English.
CAIE S1 2019 June Q5
7 marks Moderate -0.3
5 In a certain country the probability that a child owns a bicycle is 0.65 .
  1. A random sample of 15 children from this country is chosen. Find the probability that more than 12 own a bicycle.
  2. A random sample of 250 children from this country is chosen. Use a suitable approximation to find the probability that fewer than 179 own a bicycle.
CAIE S1 2019 June Q6
7 marks Moderate -0.8
6 At a funfair, Amy pays \(\\) 1$ for two attempts to make a bell ring by shooting at it with a water pistol.
  • If she makes the bell ring on her first attempt, she receives \(\\) 3\( and stops playing. This means that overall she has gained \)\\( 2\).
  • If she makes the bell ring on her second attempt, she receives \(\\) 1.50\( and stops playing. This means that overall she has gained \)\\( 0.50\).
  • If she does not make the bell ring in the two attempts, she has lost her original \(\\) 1$.
The probability that Amy makes the bell ring on any attempt is 0.2 , independently of other attempts.
  1. Show that the probability that Amy loses her original \(\\) 1$ is 0.64 .
  2. Complete the probability distribution table for the amount that Amy gains.
    Amy's gain (\$)
    Probability0.64
  3. Calculate Amy's expected gain.
CAIE S1 2019 June Q7
10 marks Moderate -0.3
7 The weight of adult female giraffes has a normal distribution with mean 830 kg and standard deviation 120 kg .
  1. There are 430 adult female giraffes in a particular game reserve. Find the number of these adult female giraffes which can be expected to weigh less than 700 kg .
  2. Given that \(90 \%\) of adult female giraffes weigh between \(( 830 - w ) \mathrm { kg }\) and \(( 830 + w ) \mathrm { kg }\), find the value of \(w\).
    The weight of adult male giraffes has a normal distribution with mean 1190 kg and standard deviation \(\sigma \mathrm { kg }\).
  3. Given that \(83.4 \%\) of adult male giraffes weigh more than 950 kg , find the value of \(\sigma\).
CAIE S1 2019 June Q8
9 marks Moderate -0.3
8 Freddie has 6 toy cars and 3 toy buses, all different. He chooses 4 toys to take on holiday with him.
  1. In how many different ways can Freddie choose 4 toys?
  2. How many of these choices will include both his favourite car and his favourite bus?
    Freddie arranges these 9 toys in a line.
  3. Find the number of possible arrangements if the buses are all next to each other.
  4. Find the number of possible arrangements if there is a car at each end of the line and no buses are next to each other.
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
CAIE S1 2019 June Q1
4 marks Moderate -0.3
1 Two ordinary fair dice are thrown and the numbers obtained are noted. Event \(S\) is 'The sum of the numbers is even'. Event \(T\) is 'The sum of the numbers is either less than 6 or a multiple of 4 or both'. Showing your working, determine whether the events \(S\) and \(T\) are independent.
CAIE S1 2019 June Q2
4 marks Easy -1.2
2 The volume of ink in a certain type of ink cartridge has a normal distribution with mean 30 ml and standard deviation 1.5 ml . People in an office use a total of 8 cartridges of this ink per month. Find the expected number of cartridges per month that contain less than 28.9 ml of this ink.
CAIE S1 2019 June Q3
6 marks Moderate -0.3
3 The probability that Janice will buy an item online in any week is 0.35 . Janice does not buy more than one item online in any week.
  1. Find the probability that, in a 10 -week period, Janice buys at most 7 items online.
  2. The probability that Janice buys at least one item online in a period of \(n\) weeks is greater than 0.99 . Find the smallest possible value of \(n\).