Cambridge A Level Thinking Skills 9694 — 2016 Oct/Nov Paper 3 · Variant 2

This document consists of 7 printed pages, 1 blank page and 1 insert. IB16 11_9694_32/2RP © UCLES 2016 [Turn over  Cambridge International Examinations Cambridge International Advanced Level THINKING SKILLS 9694/32 Paper 3 Problem Analysis and Solution October/November 2016 2 hours Additional Materials: Electronic Calculator READ THESE INSTRUCTIONS FIRST An answer booklet is provided inside this question paper. You should follow the instructions on the front cover of the answer booklet. If you need additional answer paper ask the invigilator for a continuation booklet. Answer all the questions. Show your working. Marks may be awarded for correct steps towards a solution, even if the final answer is not correct. Marks may be lost if working needed to support an answer is not shown. Calculators should be used where appropriate. The number of marks is given in brackets [ ] at the end of each question or part question.

2 © UCLES 2016 9694/32/O/N/16 1 George is planning to take part in a competition next week. The competition is in 5 rounds, each of 5 questions. In each round, contestants are asked questions one at a time and will only be asked the next question if they have correctly answered the current question. George predicts that it will take him 1 minute to answer the first question in each round, and then each other question within any round will take 1 minute longer than the previous one to answer. (a) Based on his prediction, how long would George need to answer every question in the competition? [1] Contestants only have a total of 40 minutes to answer questions; before the start of the competition they must decide how to allocate this time across the 5 rounds. George wants to make sure that he can answer as many questions as possible within the 40 minutes. (b) What is the largest number of questions George would expect to be able to answer and how should he allocate the time among the five rounds to achieve this? [2] The topics for this year’s competition have just been announced. The first round will be Science and George thinks that this is likely to be a good round for him. He thinks that he will be able to answer the first three questions in 1 minute each, with the last two questions taking 2 and 3 minutes respectively. (c) How much time should George now allocate to the different rounds and how many questions does he think he will be able to answer overall? [2] Each correct answer scores 1 point. However, this year the final round will be General Knowledge and the questions in that round will each score 2 points rather than 1. (d) Assuming that all of the questions that he answers are answered correctly, what is the highest score that George can expect to get? [2] The organisers of the competition have decided that they want to encourage more competitors to continue to the fifth questions of the rounds, so they are considering a different scoring system for next year’s competition. Instead of awarding double points for the General Knowledge round, they will award 2 points for each of the first four questions in a round, and then a higher number of points for the final question. Based on the results of previous years they assume that a contestant takes 2 minutes for each of the first 3 questions in a round and 4 minutes for each of the other questions. Based on this assumption they wish to set the points for question 5 so that contestants would need to attempt the fifth question in more than one of the rounds if they were to achieve the best score possible. (e) What is the smallest number of points that they could award for question 5? [3]

3 © UCLES 2016 9694/32/O/N/16 [Turn over 2 The rate of reported crime in Einrossdorf is said to be exceptionally low, but no figures have been published to support this; so Edward, an investigative journalist, tries to get an estimate. He knows that each crime report is given a sequence number, starting from #1 every morning. He assumes, and it is true, that all reports made by townspeople are of real crimes and that the townspeople have all gone to bed by 10 pm. So each day he selects a random time between 11 pm and midnight, makes a false report, and is then given a sequence number. His false reports are #6/Monday, #5/Tuesday and #6/Wednesday. (a) What does Edward think the total number of genuine reports of crime over the three days was? [1] Unknown to him, or to each other, other journalists were doing exactly the same: each putting in one false report between 11 pm and midnight on the same days. Kim obtained reference numbers #3/Monday, #6/Tuesday and #4/Wednesday. Anthony obtained #2/Monday, #7/Tuesday and #8/Wednesday. (b) What is the minimum (total) number of investigative journalists that could be working on this story? [1] There might have been more journalists; unfortunately, we do not know and cannot tell. (c) What are the minimum and maximum of the total number of genuine crime reports over the three days? [2] (d) What are the minimum and maximum of the total number of genuine crime reports over the three days, if there are only the minimum number of journalists? [2] (e) Would knowing the name of the journalist who registered #7/Wednesday help with estimating the number of genuine crimes? Explain your answer briefly. [1] (f) Assuming that the number of journalists is the minimum possible, give the additional false report sequence numbers, and the day(s) on which they occur, which would each be sufficient to deduce the total number of genuine crime reports over the three days. [2] (g) What difference would it make if another journalist, Stella, announced that she had #7/Monday? [1]

4 © UCLES 2016 9694/32/O/N/16 3 Carla manages a local store and wants to work out how long the queues are likely to be at different times of the day. There is only one queue for the checkouts and customers go to the next available checkout once they have reached the front of the queue. Carla assumes that it takes two and a half minutes to serve each customer. The store opens at 09:00. Carla assumes that one customer joins the queue every 2 minutes, starting at 09:02:00. Therefore, customer 1 arrives at the checkouts at 09:02:00 and is served immediately; customer 2 arrives at 09:04:00 and starts a queue. The number of customers in the queue for each 30-second period of the first 5 minutes are shown in the diagram below: 09:00:00 09:01:00 09:02:00 09:03:00 09:04:00 09:05:00 Queue 0 0 0 0 0 0 0 0 1 0 No customers at checkouts Customer 1 being served The first time that there is one customer in the queue waiting to be served is at 09:04:00. (a) How long will customers 2 and 3 each have to wait to be served? [1] (b) At what time will customer 5 have finished being served? [2] (c) At what time will there first be two customers in the queue? [2] A second member of staff begins work at the second checkout at 10:32:00. (d) How many customers will be in the queue at 10:31:00? [2] (e) At what time will there first be no customers in the queue, after the second checkout has opened? [3] Carla would like to change the time that the second member of staff starts work. The start time must be either on an hour or at half past an hour and Carla wishes this time to be as late as possible, whilst ensuring that there will be no queue at 14:00:00. (f) (i) What time should the second member of staff start work at the second checkout? Justify your answer. [2] (ii) What is the longest time that a customer would have to wait to be served if the second member of staff starts work at this time? [3]

5 © UCLES 2016 9694/32/O/N/16 [Turn over [Question 4 begins on the next page]

6 © UCLES 2016 9694/32/O/N/16 4 Teams representing the twelve Provinces of Ercaland compete against each other every four years in the Ercalympic Games. The Games were first held in 1958, and most recently in 2014. Year Games designation Host city Province 1958 I Lipanj Unje 1962 II Enero Yarjuan 1966 III Okosita Stugua 1970 IV Duben Prali 1974 V Kasim Merbenvo 1978 VI Vasaris Bauerfry 1982 VII Sausis Yarjuan 1986 VIII Rujan Presbetem 1990 IX Aralik Drembeec 1994 X Gusht Stugua 1998 XI Enero Yarjuan 2002 XII Frar Bauerfry 2006 XIII Kasim Merbenvo 2010 XIV Tetor Rebotoc 2014 XV Kolovoz Stugua Stugua are the current holders of the Gregor Trophy. This trophy was introduced in 1990 and is presented to the highest-ranked team in the medals table. This is the 2014 medals table. Rank Province Gold Silver Bronze 1 Stugua 32 21 26 2 Rebotoc 27 23 17 3 Merbenvo 20 26 18 4 Bauerfry 17 22 15 5 Yarjuan 13 11 17 6 Presbetem 12 18 15 7 Rhamc 12 10 14 8 Aym 12 10 10 9 Drembeec 10 7 12 10 Unje 6 11 5 11 Lyju 6 6 9 12 Prali 3 5 12 The teams are ranked by the number of gold medals won. If two or more teams have the same number of gold medals, the number of silver medals is taken into consideration, then, if necessary, the number of bronze medals.

7 © UCLES 2016 9694/32/O/N/16 The following table records all the gold medals won in the Games up to 2010. Number of gold medals won at: I II III IV V VI VII VIII IX X XI XII XIII XIV Aym 8 3 5 4 6 5 2 7 9 10 11 8 9 10 Bauerfry 26 20 14 18 19 23 16 19 23 21 24 30 22 16 Drembeec 6 9 11 11 7 11 8 6 15 7 6 12 9 7 Lyju 5 4 7 5 6 2 5 8 5 6 5 3 3 4 Merbenvo 12 17 11 28 23 20 16 15 22 25 23 19 28 31 Prali 9 7 15 17 10 6 5 4 1 5 4 7 4 5 Presbetem 3 7 5 6 7 11 12 17 10 12 7 9 5 8 Rebotoc 8 12 6 10 11 15 17 15 14 22 31 25 24 30 Rhamc 2 5 4 5 4 7 3 7 5 7 8 10 12 11 Stugua 21 17 33 20 16 18 22 27 25 18 17 18 20 23 Unje 19 11 9 7 10 12 12 10 8 6 8 7 10 11 Yarjuan 17 24 16 13 25 18 30 21 19 17 19 15 17 14 A Province wishing to host the Games must submit a formal application at the opening ceremony of the previous Games. The current host Province and the last two hosts may not apply. At the closing ceremony, the applicant Province with the most gold medals won in total at the three most recent Games is announced as the host of the next Games. This procedure was introduced at the XI Games in 1998. Previously, the host Province had been selected by a committee. At the opening ceremony in 1998, Yarjuan, Stugua and Drembeec were not eligible to apply. Bauerfry and Rebotoc were the only Provinces who applied to host the XII Games in 2002. At the closing ceremony it was announced that Bauerfry had been successful, with a total of 68 gold medals in the three most recent games, just one ahead of Rebotoc’s 67. (a) List the Provinces in which the Games have not yet taken place. [2] (b) In 2013 the Presbetem Games Committee launched an appeal to raise money to improve training facilities. One donor promised $500 for every gold medal, $200 for every silver medal and $80 for every bronze medal won by Presbetem in 2014. How much was received from this donor? [2] (c) In which years was the Gregor Trophy presented to the host Province? [3] At the opening ceremony of the XV Games in 2014, Aym, Drembeec and Unje applied to host the next Games. (d) (i) In which Province will the XVI Games be held in 2018? Justify your answer. [2] (ii) If all the eligible Provinces had applied to host the XVI Games, which one would have been successful? [3] Julian Perido is the only person to have competed in seven Games. His first Games, during which he celebrated his 17th birthday, and his last Games, during which he celebrated his 41st birthday, were both held in his home Province. (e) In which year was Julian born? [3]

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® IGCSE is the registered trademark of Cambridge International Examinations. This document consists of 9 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International Advanced Level THINKING SKILLS 9694/32 Paper 3 Problem Analysis and Solution October/November 2016 MARK SCHEME Maximum Mark: 50 Published This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 32 © UCLES 2016 1 (a) Based on his prediction, how long would George need to answer every question in the competition? [1] 75 minutes (1 hour 15 minutes) In each round he would require 1 + 2 + 3 + 4 + 5 = 15 minutes, so a total of 5 × 15 = 75 minutes would be needed for the whole competition. (b) What is the largest number of questions George would expect to be able to answer and how should he allocate the time among the five rounds to achieve this? [2] 17 6,6,6,10,10 with up to two minutes added anywhere or 6,6,6,6,15 with or without one minute added or 3,6,6,10,15 or 3,6,10,10,10 with or without one minute added. To achieve the maximum number of questions, George should make sure that he answers as many of the quicker questions as possible. He can answer 5 questions at 1 minute each, 5 at 2 minutes each and 5 at 3 minutes each, leaving 10 minutes which he could use either to answer two questions at 4 minutes or 1 question at 4 minutes and 1 question at 5 minutes. Award 1 mark for the answer of 17. Award 1 mark for a possible allocation of time to the rounds. Ignore subsequent working. FT if deducting time from a wrong answer to (a) (must be greater than 40). (c) How much time should George now allocate to the different rounds and how many questions does he think he will he be able to answer overall? [2] 8 minutes for round 1, 6 minutes for each of two other rounds and 10 minutes in each of the remaining two rounds [1], allowing him to answer 19 questions [1]. There are now 7 questions that will take 1 minute each, 5 that will take 2 minutes and 5 that will take 3 minutes. George will then have a further 8 minutes for a 4 minute question in each of two rounds. Award 1 mark for recognition that George can answer all the 3-minute questions.

Page 3 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 32 © UCLES 2016 (d) Assuming that all of the questions that he answers are answered correctly, what is the best score that George can expect to get? [2] 23 points EITHER 5 + (3 + 3 + 4) + 8 = 23 points 5 + (3 + 3 + 4) + 4 questions 8 + (6 + 6 + 10) + 10 = 40 minutes OR 5 + (3 + 3 + 2) + 10 = 23 points 5 + (3 + 3 + 2) + 5 questions 8 + (6 + 6 + 3) + 15 = 38 minutes [with 1 or 2 minutes available to any individual question] Award 1 mark for 23 without working. Award 1 mark for evidence of splitting the questions between rounds appropriately for 23 or sub-optimal 22 points. (e) What is the smallest number of points that they could award for question 5? [3] 5 (only credit with working) The contestant would need a total of 14 minutes to answer all of the questions in a round, so if all of the questions were answered in two rounds there would be 12 minutes left, which could be used for 6 questions in the other rounds. The total score would be 28, plus twice the score for a final question in a round. If the contestant maximised the number of 2-minute questions then all 15 of those would be answered and there would be time for two more questions, one of which could be the final question of a round. The total score would be 32, plus the score for a final question in a round. 4 points for the final question in a round would mean that either strategy would lead to a score of 36, so 5 points would need to be allocated to ensure that all questions need to be attempted in two of the rounds (allowing a score of 38, beating 37). 28 + 2p > 32 + p where p is the score in the 5th question M1: expressions equivalent to either side of the inequality expressed above M1: expressions equivalent to the other side of the inequality expressed above SC2: p = 4 with working showing that this was derived from 34 < 28 + 2p (i.e. not appreciating that one Question 5 would be one of the 4 minute questions even if the contestant only tried one). Award SC1 if not treated as an inequality. SC2: more than 4 marks because you should get (more than) twice the points if you are spending twice the time. Award SC1 if not treated as an inequality. Working which shows that it is preferable to choose 2 question 5s when p = 5: 12345/123/123/123/123 = (5 × 3 × 2 + 4 × 2) 38 minutes & (16 × 2 + 5) 37 points 12345/12345/123/123 = (4 × 3 × 2 + 2 × 2 × 4) 40 minutes & (14 × 2 + 10) 38 points [2 marks] + comparison with 4 (not possible) [1 mark]

Page 4 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 32 © UCLES 2016 2 (a) What does Edward think the total number of genuine reports of crime over the three days was? [1] (6 – 1) + (5 – 1) + (6 – 1) = 5 + 4 + 5 = 14 (Condone daily totals calculated) (b) What is the minimum (total) number of investigative journalists that could be working on this story? [1] All numbers from the first journalist's onwards must be fake, so there must be at least 5 to get from 2 to 6 on Monday and 4 to 8 on Wednesday. (c) What are the minimum and maximum of the total number of genuine crime reports over the three days? [2] It is possible that there was no crime and it’s all journalists, minimum is 0. [1 mark] Maximum is (2 – 1) + (5 – 1) + (4 – 1) = 1 + 4 + 3 = 8. [1 mark] (d) What are the minimum and maximum of the total number of genuine crime reports over the three days, if there are only the minimum number of journalists? [2] Minimum is (6 – 5) + (7 – 5) + (8 – 5) = 1 + 2 + 3 (= 6). FT minimum 3, if 6 given in (b) Maximum is still 8. (e) Would knowing the name of the journalist who registered #7/Wednesday help with estimating the number of genuine crimes? Explain your answer briefly. [1] No. We already knew that there was a false report at #7 – we know that #4 was a false report, so all those afterwards are journalists. (f) Assuming that the number of journalists is the minimum possible, give the additional false report sequence numbers, and the day(s) on which they occur, which would each be sufficient to deduce the total number of genuine crime reports over the three days. [2] #3/Tuesday (FT #4/Tues if 4 given in (b)) #9/Tuesday (FT #8/Tues if 4 given in (b)) SC1: #4&#8/Tuesday SC1: #3&#4/Tuesday OR #8&#9/Tuesday (g) What difference would it make if another journalist, Stella, announced that she had #7/Monday? [1] The minimum possible number of journalists would be six. (FT their (b)+1) OR The minimum number of genuine crimes would be four.

Page 5 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 32 © UCLES 2016 3 (a) How long will customers 2 and 3 each have to wait to be served? [1] Customer 2: 30 seconds Customer 3: 60 seconds (b) At what time will customer 5 have finished being served? [2] It will take 12 minutes 30 seconds to serve 5 customers 09:02:00 + 12 minutes 30 seconds = 09:14:30 2 marks for the correct time; 1 mark for the correct duration soi. (c) At what time will there first be two customers in the queue? [2] Customer 2 waits for 30 seconds from 09:04:00 before being served. Customer 3 waits for 60 seconds from 09:06:00 before being served. Therefore customer 6 waits for 150 seconds from 09:12:00 and customer 7 joins the queue at 09:14:00 as the second customer in the queue. Award 1 mark for a correct extraction of the information from their table OR a correctly derived set of arrival times and service-starting times for the first 7 customers. SC1: 09:12:00 for one arriving as other leaves, with FT for initial starting time. (d) How many customers will be in the queue at 10:31:00? [2] By 10:31:00, 45 customers will have joined the queue By 10:31:00, 36 customers will have gone to be served at a checkout (35 will have been served). There will be 45 – 36 = 9 customers in the queue. 1 mark for 45/44.5 joined OR 36 (started serving) OR 35 (finished serving) OR The length of the queue increases by 1 customer every 10 minutes. [1 mark] At 09:11 there was one customer in the queue, so there will be 9 customers at 10:31:00. OR The number of customers who have joined the queue is (the number of minutes after 09:00:00) / 2 The number of customers who have been served is (the number of minutes after 09:02:00) / 2.5 1 mark for either valid algebraic representation, or correct answer from FT of wrong start.

Page 6 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 32 © UCLES 2016 (e) At what time will there first be no customers in the queue, after the second checkout has opened? [3] The customers get served at the following times: Customer 36 at 10:29:30 Customer 37 at 10:32:00 Customer 38 at 10:32:00 Customer 39 at 10:34:30 Customer 40 at 10:34:30 Continuing … Customer 45 at 10:42:00 Customer 46 at 10:42:00 Customer 53 at 10:52:00 Customer 54 at 10:52:00 Customer 55 at 10:54:30 Customer 56 at 10:54:30 Customer 57 at 10:57:00 Customer 58 at 10:57:00 Customer 58 joins the queue at 10:56:00 and is served at 10:57:00 so at 10:57:00 there will be no customers in the queue. Award 1 mark for customer numbers arriving, and being served at appropriate starting times OR precise statement of how many are in the queue and how many at the tills at a particular time. Award 1 mark for a clear attempt to establish a pattern (including continuation of the pattern for 10 minutes, or making a 10-minute jump down the list) Award 1 mark a correct conclusion from a table which is appropriately structured (differences of 2 and 2.5).

Page 7 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 32 © UCLES 2016 (f) (i) What time should the second member of staff start work at the second checkout? Justify your answer. [2] The customer coming to the checkouts at 14:00:00 would be customer 150. With just one checkout open throughout, 120 customers could be served. The extra checkout will allow for an additional 12 customers to be served every 30 minutes. [1 mark] Three sets of half an hour will be needed, so the second member of staff should start working at 12:30:00 1 mark for correct answer not rounded up to half hour OR for any method which shows explicit awareness of how the queue grows when there is one queue (e.g. 6 per hour) AND how it decreases when there are two queues (e.g. 9 per half hour). (ii) What is the longest time that a customer would have to wait to be served if the second member of staff starts work at this time? [3] The customer who has to wait the longest will be one of those served at around the time that the second checkout opens. Customer 84 would be served at 12:29:30 having joined the queue at 11:48:00 – a wait of 41 minutes 30 seconds. Customer 85 would be served at 12:30:00 having joined the queue at 11:50:00 – a wait of 40 minutes. The longest wait is therefore 41 minutes 30 seconds. 1 mark for working which shows the appreciation that the longest wait must be around the time that the second checkout opens. 1 mark for appropriate working to find out how long that customer has been in the queue (e.g. conversion of 83/84/85th customer into time of arrival, allowing for one precision error). SC1: attempting to find the waiting time of the person at the back of the queue when the second cashier arrives. SC2: if this calculation is performed correctly.

Page 8 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 32 © UCLES 2016 4 (a) List the Provinces in which the Games have not yet taken place. [2] Aym, Lyju and Rhamc If 2 marks cannot be awarded, award 1 mark for all three plus no more than one other Province OR for one or two of the above without any others. (b) How much was received from this donor? [2] $10 800 If 2 marks cannot be awarded, award 1 mark for sight of 12, 18 and 15 soi. (c) In which years was the Gregor Trophy presented to the host Province? [3] 2002, 2006 and 2014 (Accept XII, XIII and XV) If 3 marks cannot be awarded, award 1 mark for each correct year, provided no other years are given. If other years are given, consider any of 1962, 1966, 1978 and 1982 as a single year and award one mark for each correct year that exceeds the total of incorrect ones. (d) (i) In which Province will the XVI Games be held in 2018? Justify your answer. [2] Aym (with reason based on data, not just rules) For 2 marks to be awarded it must be stated that (in the three most recent Games) Aym has won 31 gold medals. If 2 marks cannot be awarded, award 1 mark for correct calculation of the gold medals won by at least one of the three teams. (ii) If all the eligible Provinces had applied to host the XVI Games, which one would have been successful? [3] Bauerfry If 3 marks cannot be awarded, award 1 mark for each of the following: • Acknowledgement that Merbenvo, Rebotoc and Stugua were not eligible. • Correct calculation of the gold medals won (in the three most recent Games) by Bauerfry (55) or Yarjuan (44) or Rhamc (35).

Page 9 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 32 © UCLES 2016 (e) In which year was Julian born? [3] 1961 If 3 marks cannot be awarded: Award 1 mark for appreciation that his last Games was 24 years after his first Games, Award 2 marks for appreciation that he must have represented Bauerfry. SC1: An answer of 1949, visibly deriving from a reckoning that 7 games would be 28 years apart and so Julian represented Stugua. Condone 1962 (or 1950 from SC1) if evidence that arrived at correctly but with oriental birthday measurement.