Date | May 2019 | Marks available | 1 | Reference code | 19M.1.SL.TZ2.T_11 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 2 |
Command term | Write down | Question number | T_11 | Adapted from | N/A |
Question
Consider the following sets:
The universal set U consists of all positive integers less than 15;
A is the set of all numbers which are multiples of 3;
B is the set of all even numbers.
Write down the elements that belong to A∩B.
Write down the elements that belong to A∩B′.
Write down n(A∩B′).
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
A = {3, 6, 9, 12} AND B = {2, 4, 6, 8, 10, 12, 14} (M1)
Note: Award (M1) for listing all elements of sets A and B. May be seen in part (b). Condone the inclusion of 15 in set A when awarding the (M1).
6, 12 (A1)(A1) (C3)
Note: Award (A1) for each correct element. Award (A1)(A0) if one additional value seen. Award (A0)(A0) if two or more additional values are seen.
[3 marks]
3, 9 (A1)(ft)(A1)(ft) (C2)
Note: Follow through from part (a) but only if their A and B are explicitly listed.
Award (A1)(ft) for each correct element. Award (A1)(A0) if one additional value seen. Award (A0)(A0) if two or more additional values are seen.
[2 marks]
2 (A1)(ft) (C1)
Note: Follow through from part (b)(i).
[1 mark]
Examiners report
Syllabus sections
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19M.1.SL.TZ1.T_7b:
In the table indicate which two of the given statements are true by placing a tick (✔) in the right hand column.
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18M.2.SL.TZ2.T_1a.i:
Write down the value of a.
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22M.1.SL.TZ2.5a:
Calculate the expected number of people who will pass this polygraph test.
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22M.1.SL.TZ2.5c:
Determine the probability that fewer than 7 people will pass this polygraph test.
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18N.2.SL.TZ0.T_2a.i:
Find the number of students in the school that are taught in Spanish.
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18M.1.SL.TZ2.S_8a:
Copy and complete the following tree diagram.
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18M.1.SL.TZ1.T_10a:
Complete the Venn diagram using the given information.
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17M.1.SL.TZ2.T_2b:
Complete the Venn diagram using the above information.
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18M.1.SL.TZ2.T_9a.i:
Write down an expression, in set notation, for the shaded region represented by Diagram 1.
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19M.1.SL.TZ1.T_7a:
Place the numbers 2π,−5,3−1 and 232 in the correct position on the Venn diagram.
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18M.1.SL.TZ2.T_9b.i:
Shade, on the Venn diagram, the region represented by the set (H∪I)′.
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17M.1.SL.TZ1.S_1b:
A girl is selected at random. Find the probability that she takes economics but not history.
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18M.2.SL.TZ2.T_1a.ii:
Write down the value of b.
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22M.2.SL.TZ1.5c:
Find, to the nearest integer, the expected increase or decrease in the money made by the airline if they decide to sell 74 tickets rather than 72.
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21N.1.SL.TZ0.11a:
Write down the value of a.
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21N.1.SL.TZ0.11b:
Find an expression, in terms of b, for the probability of a person not having blue eyes and having fair hair.
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21N.2.SL.TZ0.3f.ii:
The wind speed increases. The blades rotate at twice the speed, but still at a constant rate.
At any given instant, find the probability that Tim can see point C from his window. Justify your answer.
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21N.2.SL.TZ0.3e.ii:
Find the time, in seconds, that point C is above a height of 100 m, during each complete rotation.
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22M.1.SL.TZ2.5b:
Calculate the probability that exactly 4 people will fail this polygraph test.
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22M.1.SL.TZ2.2c:
Two different applicants are chosen at random from the original group.
Find the probability that both applicants applied to the Arts programme.
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22M.1.SL.TZ2.2a:
Find the probability that a randomly chosen applicant from this group was accepted by the university.
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22M.1.SL.TZ2.2b:
Find the probability that the applicant applied for the Arts programme.
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21N.1.SL.TZ0.11c.i:
b.
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21N.1.SL.TZ0.11c.ii:
c.
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21N.2.SL.TZ0.1b:
State the null and alternative hypotheses.
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21N.2.SL.TZ0.3c.i:
Write down the amplitude of the function.
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21N.2.SL.TZ0.3e.i:
Find the height of C above the ground when t=2.
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19M.2.AHL.TZ2.H_3a:
Complete the given probability tree diagram for Iqbal’s three attempts, labelling each branch with the correct probability.
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16N.2.SL.TZ0.T_6b:
Express this volume in cm3.
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17M.1.SL.TZ1.T_4b:
Determine whether rock-climbing is offered by the school in the fall/autumn trimester.
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16N.2.SL.TZ0.T_2c:
Write down the value of n(B∩C).
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18N.2.SL.TZ0.T_2a.ii:
Find the number of students in the school that study Mathematics in English.
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17M.2.SL.TZ2.S_10b.i:
Write down the probability of drawing three blue marbles.
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18M.2.SL.TZ2.T_1c.i:
Find the value of x.
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18M.2.SL.TZ2.T_1c.ii:
Find the value of y.
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17M.1.SL.TZ2.T_2d:
Write down the value of n(F).
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17M.1.SL.TZ1.S_1a.i:
Find the value of p;
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19M.1.SL.TZ2.T_11a:
Write down the elements that belong to A∩B.
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18M.2.SL.TZ2.T_1d:
Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.
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19N.2.SL.TZ0.T_1d.ii:
the p-value.
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19M.2.SL.TZ1.S_10c.i:
Write down the value of x.
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19M.2.SL.TZ1.S_10c.ii:
Hence, find the value of y.
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18M.1.SL.TZ2.T_9b.ii:
Shade, on the Venn diagram, the region represented by the set J∩K.
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18M.1.SL.TZ2.S_8d:
Given that Pablo is late for work, find the probability that he left home before 07:00.
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19M.1.SL.TZ1.S_1b:
Find the value of q.
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19M.1.SL.TZ1.S_1c:
Find P(A′∪B).
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17M.1.SL.TZ1.T_4a:
Write down the number of sporting activities offered by the school during its school year.
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18M.2.SL.TZ2.T_1e:
Find n((C∪B)∩P′).
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18M.1.SL.TZ2.S_8b:
Find the probability that Pablo leaves home before 07:00 and is late for work.
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18N.1.SL.TZ0.S_9c:
Hayley plays the game when n = 5. She pays $20 to play and can earn money back depending on the number of draws it takes to obtain a blue marble. She earns no money back if she obtains a blue marble on her first draw. Let M be the amount of money that she earns back playing the game. This information is shown in the following table.
Find the value of k so that this is a fair game.
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18N.2.SL.TZ0.T_2c.i:
Find the probability that this student studies Mathematics.
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17N.1.SL.TZ0.S_1b:
Find the probability that exactly one of the selected balls is green.
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16N.1.SL.TZ0.T_3a:
In the table indicate whether the given statements are True or False.
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19N.2.SL.TZ0.T_1d.i:
the χ2 statistic.
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19N.2.SL.TZ0.T_1b:
Write down the number of degrees of freedom.
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19N.2.SL.TZ0.T_1a:
State H0, the null hypothesis for this test.
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19M.2.SL.TZ1.S_10a.ii:
Find the probability of rolling two or more red faces.
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19M.2.SL.TZ1.S_10a.i:
Find the probability of rolling exactly one red face.
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18N.2.SL.TZ0.T_2a.iii:
Find the number of students in the school that study both Biology and Mathematics.
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18M.1.SL.TZ2.S_8c:
Find the probability that Pablo is late for work.
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17N.1.SL.TZ0.S_1a:
Complete the following tree diagram.
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17M.1.SL.TZ1.T_4c.i:
Write down the elements of the set F∩W′;
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19N.2.SL.TZ0.T_1f.ii:
Calculate the probability that the customer is an adult or that the customer chose shrimp.
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18M.1.SL.TZ1.T_10c:
Write down the value of n((F∪H)∩S′).
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19N.2.SL.TZ0.T_1f.iii:
Given that the customer is a child, calculate the probability that they chose pasta or fish.
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18M.2.SL.TZ1.S_5a:
Find P(A ∩ B′ ).
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18M.1.SL.TZ2.T_9a.ii:
Write down an expression, in set notation, for the shaded region represented by Diagram 2.
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18N.2.SL.TZ0.T_2b.ii:
Write down n(B∩M∩S′).
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17M.1.SL.TZ1.T_4c.ii:
Write down n(W∩S).
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16N.1.SL.TZ0.T_3b:
On the Venn diagram, shade the region A∩(B∪C)′.
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17M.2.AHL.TZ2.H_5a:
Draw a tree diagram to represent this information for the first three days of July.
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18N.1.SL.TZ0.S_9a.i:
Find the probability, in terms of n, that the game will end on her first draw.
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19N.2.SL.TZ0.T_1e:
State the conclusion for this test. Give a reason for your answer.
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19N.2.SL.TZ0.T_1c:
Show that the expected number of children who chose shrimp is 31, correct to two significant figures.
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17M.2.AHL.TZ2.H_5c:
Find the probability that the 1st July was calm given that the 3rd July is windy.
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17M.1.SL.TZ2.T_2c:
Find the number of children who play only football.
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17M.2.AHL.TZ2.H_1a:
One of the players is chosen at random. Find the probability that this player’s score was 5 or more.
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18M.2.SL.TZ2.T_1b.ii:
Use the tree diagram to find the probability that an employee was late for work.
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18N.1.SL.TZ0.S_9b.ii:
fourth draw.
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19M.2.AHL.TZ2.H_3c:
Find the probability that Iqbal passes his third paper, given that he passed only one previous paper.
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18M.1.SL.TZ2.S_8e:
Two days next week Pablo will drive to work. Find the probability that he will be late at least once.
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17N.1.SL.TZ0.T_7b:
One of the students who joined the sports club is chosen at random. Find the probability that this student joined both clubs.
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16N.2.SL.TZ0.T_2b:
Show that x=3.
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18M.2.SL.TZ2.T_1b.i:
Use the tree diagram to find the probability that an employee encountered traffic and was late for work.
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16N.2.SL.TZ0.T_6f:
Using your answer to part (e), find the value of r which minimizes A.
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SPM.1.SL.TZ0.13a:
Find the probability that on any given day Mr Burke chooses a female student to answer a question.
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18N.2.SL.TZ0.T_2b.i:
Write down n(S∩(M∪B)).
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19N.2.SL.TZ0.T_1f.i:
Calculate the probability that the customer is an adult.
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20N.1.SL.TZ0.S_8a:
Find the value of a.
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20N.2.SL.TZ0.S_9d:
Find the probability that Fiona will arrive on time.
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20N.1.SL.TZ0.T_6a.ii:
Find the probability that the first ball chosen is labelled A or labelled N.
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17M.2.SL.TZ2.S_10d:
Grant plays the game until he wins two prizes. Find the probability that he wins his second prize on his eighth attempt.
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20N.1.SL.TZ0.S_8b:
Write down the value of the median distance in kilometres (km).
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20N.1.SL.TZ0.S_8d:
Find m.
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20N.2.SL.TZ0.S_9c:
Find the probability that the bus journey takes less than 45 minutes.
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20N.2.SL.TZ0.S_9e:
This year, Fiona will go to school on 183 days.
Calculate the number of days Fiona is expected to arrive on time.
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16N.2.SL.TZ0.T_6e:
Find dAdr.
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19N.1.SL.TZ0.T_9b:
Find the probability that Sungwon scores greater than 4 on both of her first two turns.
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17N.1.SL.TZ0.T_7c:
Determine whether the events S and M are independent.
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17M.2.AHL.TZ2.H_5b:
Find the probability that the 3rd July is calm.
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16N.1.SL.TZ0.S_5a:
Find P(B).
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19M.2.SL.TZ1.S_10b:
Show that, after a turn, the probability that Ted adds exactly $10 to his winnings is 13.
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17M.1.SL.TZ2.T_2a:
Write down an expression, in terms of x, for the number of children who play only basketball.
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18M.1.SL.TZ2.T_9a.iii:
Write down an expression, in set notation, for the shaded region represented by Diagram 3.
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SPM.1.SL.TZ0.13b:
Find the probability he will choose a female student 8 times.
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18M.1.SL.TZ1.T_10b:
Find the value of x.
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17M.2.SL.TZ2.S_10a.i:
Find q.
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18M.2.SL.TZ1.S_5b:
Given that P((A ∪ B)′ ) = 0.19, find P(A | B′ ).
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SPM.1.SL.TZ0.13c:
Find the probability he will choose a male student at most 9 times.
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17N.1.SL.TZ0.T_7a:
Complete the Venn diagram for these students.
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17M.1.SL.TZ1.S_1a.ii:
Find the value of q.
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19N.1.SL.TZ0.T_9a:
Find the probability that Sungwon’s score on her first turn is greater than 4.
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20N.2.SL.TZ0.S_9b:
Find σ.
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20N.1.SL.TZ0.S_8c:
Find the value of b.
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19M.2.AHL.TZ2.H_3b:
Calculate the probability that Iqbal passes at least two of the papers he attempts.
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20N.1.SL.TZ0.T_6c:
Find the probability that both balls chosen are labelled N.
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20N.1.SL.TZ0.T_6a.i:
Find the probability that the first ball chosen is labelled A.
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20N.1.SL.TZ0.S_8e:
The first 150 athletes that completed the race won a prize.
Given that an athlete took between 22 and m minutes to complete the 5 km race, calculate the probability that they won a prize.
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17M.2.SL.TZ2.S_B10c:
Jill plays the game nine times. Find the probability that she wins exactly two prizes.
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18N.1.SL.TZ0.S_9b.i:
third draw.
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17M.2.SL.TZ2.S_10b.ii:
Explain why the probability of drawing three white marbles is 16.
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16N.2.SL.TZ0.T_2a:
Draw a Venn diagram to represent the given information, using sets labelled B, C and H.
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16N.2.SL.TZ0.T_6c:
Write down, in terms of r and h, an equation for the volume of this water container.
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16N.2.SL.TZ0.T_6a:
Write down a formula for A, the surface area to be coated.
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16N.2.SL.TZ0.T_6h:
Find the least number of cans of water-resistant material that will coat the area in part (g).
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17M.2.SL.TZ2.S_10a.ii:
Find p.
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17M.1.SL.TZ1.T_4d:
Write down, in terms of F, W and S, an expression for the set which contains only archery, baseball, kayaking and surfing.
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19M.1.SL.TZ1.S_1a:
Find the value of p.
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16N.2.SL.TZ0.T_6d:
Show that A=πr2+1000000r.
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19N.1.SL.TZ0.T_9c:
Sungwon will play the game for 11 turns.
Find the expected number of times the score on a turn is greater than 4.
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17M.2.AHL.TZ2.H_1b:
Calculate the mean score.
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18N.2.SL.TZ0.T_2c.ii:
Find the probability that this student studies neither Biology nor Mathematics.
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20N.1.SL.TZ0.T_6b:
Find the probability that the second ball chosen is labelled A, given that the first ball chosen was labelled N.
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17M.2.SL.TZ2.S_10b.iii:
The bag contains a total of ten marbles of which w are white. Find w.
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19M.1.SL.TZ2.T_11b.i:
Write down the elements that belong to A∩B′.
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16N.2.SL.TZ0.T_6g:
Find the value of this minimum area.
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16N.1.SL.TZ0.S_5b:
Find P(A∪B).
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18N.1.SL.TZ0.S_9a.ii:
Find the probability, in terms of n, that the game will end on her second draw.
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18M.2.SL.TZ2.T_1b.iii:
Use the tree diagram to find the probability that an employee encountered traffic given that they were late for work.
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19M.2.SL.TZ1.S_10d:
Ted will always have another turn if he expects an increase to his winnings.
Find the least value of w for which Ted should end the game instead of having another turn.
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18N.2.SL.TZ0.T_2c.iii:
Find the probability that this student is taught in Spanish, given that the student studies Biology.
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20N.2.SL.TZ0.S_9a:
Find the probability that it will take Fiona between 15 minutes and 30 minutes to walk to the bus stop.
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16N.2.SL.TZ0.T_2d:
Find the probability that this person
(i) went on at most one trip;
(ii) went on the coach trip, given that this person also went on both the helicopter trip and the boat trip.
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21N.2.SL.TZ0.1a.i:
prefers a tablet.
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21N.2.SL.TZ0.1a.ii:
is 11–13 years old and prefers a mobile phone.
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21N.2.SL.TZ0.1a.iii:
prefers a laptop given that they are 17–18 years old.
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21N.2.SL.TZ0.1a.iv:
prefers a tablet or is 14–16 years old.
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21N.2.SL.TZ0.1c:
Write down the number of degrees of freedom.
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21N.2.SL.TZ0.1d.i:
Write down the χ2 test statistic.
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21N.2.SL.TZ0.1d.ii:
Write down the p-value.
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21N.2.SL.TZ0.1d.iii:
State the conclusion for the test in context. Give a reason for your answer.
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21N.2.SL.TZ0.3a.i:
maximum value of h.
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21N.2.SL.TZ0.3a.ii:
minimum value of h.
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21N.2.SL.TZ0.3b.i:
Find the time, in seconds, it takes for the blade [BC] to make one complete rotation under these conditions.
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21N.2.SL.TZ0.3b.ii:
Calculate the angle, in degrees, that the blade [BC] turns through in one second.
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21N.2.SL.TZ0.3c.ii:
Find the period of the function.
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21N.2.SL.TZ0.3d:
Sketch the function h(t) for 0≤t≤5, clearly labelling the coordinates of the maximum and minimum points.
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21N.2.SL.TZ0.3f.i:
At any given instant, find the probability that point C is visible from Tim’s window.