Cambridge A Level Thinking Skills 9694 — 2022 May/June Paper 1 · Variant 1

This document has 16 pages. Any blank pages are indicated. [Turn over Cambridge International AS & A Level * 9 8 7 1 7 4 8 3 2 2 * DC (CE/CT) 303249/2 © UCLES 2022 THINKING SKILLS 9694/11 Paper 1 Problem Solving May/June 2022 1 hour 30 minutes You must answer on the question paper. No additional materials are needed. INSTRUCTIONS ● Answer all questions. ● Use a black or dark blue pen. ● 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. ● You may use a calculator. ● Show your working. Where a final answer is incorrect or missing, you may still be awarded marks for correct steps towards a solution. In most questions, full marks will be awarded for a correct answer without any working. In some questions, however, you will not be awarded full marks if working needed to support an answer is not shown. INFORMATION ● The total mark for this paper is 50. ● The number of marks for each question or part question is shown in brackets [ ].

2 9694/11/M/J/22 © UCLES 2022 1 Luc is organising a meeting for the managers of the local branches of his four stores. He has identified three possible locations in which he could hold the meeting. The prices for hiring each of the rooms and the total distances that each manager would have to travel are shown in the table. Location Price per hour ($) Travelling distance (km) Riverside Hotel 18 8 6 14 9 Grand Hotel 20 9 7 8 10 Central Hotel 19 4 12 5 11 The meeting will last for 2 hours. Luc will pay the managers travelling expenses of $0.50 per kilometre. (a) What would be the total cost for the meeting if Luc chooses the venue so that the furthest distance that any manager travels is as small as possible? [2] … … … … … … … … (b) What would be the total cost for the meeting if Luc chooses the venue so that the total cost for the meeting is as small as possible? [1] … … … … … … … …

3 9694/11/M/J/22 © UCLES 2022 [Turn over 2 During the last two weeks, Julian organised a campaign to get the workers in his office to reduce the amount of waste that they produce each day. Normally they produce a similar amount of waste each day. He recorded the amount of waste, in grams, produced on each day in the table below. Day Mon Tue Wed Thu Fri Sat Week 1 460 236 261 243 249 350 Week 2 410 402 312 301 385 389 In week 1, Julian had run his campaign from Monday to Thursday. While the campaign had no effect on the first day, there was a large reduction in waste produced for the rest of the campaign and the day after the campaign had ended. The amounts of waste then started to increase again. Julian ran the campaign again during week 2 and observed that similar changes in the waste produced occurred. (a) On which day in week 2 did Julian start the campaign? [1] … … … … (b) For how many days in week 2 did Julian run the campaign? [1] … … … …

4 9694/11/M/J/22 © UCLES 2022 3 The Flamingo Club is a club that raises money for charity. It has 203 members, each paying a membership fee of $15 per year. On the 15th day of every month there is a prize draw, with one lucky member winning $30 for 1st prize, one winning $20 for 2nd prize and one winning $10 for 3rd prize. At the end of the year, all the remaining money from membership fees is donated to a local charity. (a) How much money is donated to the local charity each year? [2] … … … … … … The club decides that, from next year, they will have an additional New Year’s Day bonus draw, on the 1st of January, with a doubling of the usual prizes. Members have been asked to pay $2 more each year. (b) How much money will be donated to the local charity next year? [2] … … … … … … … … … …

5 9694/11/M/J/22 © UCLES 2022 [Turn over 4 The standard cost of my gym membership is $50 per week, which I have to pay in advance. However, to encourage more use of the gym, I get a refund (which is a whole number of dollars) for each day that I attend the gym. The refund is the same amount for each day that I attend the gym, and is not so large as to make it possible for the gym to pay me money for my membership. The gym is open 5 days every week. During the last 10 weeks, I attended the gym for the same number of days each week and the overall cost for my gym membership was $360. How much is the refund for each day that I attend the gym? [2] … … … … … … … … … … …

6 9694/11/M/J/22 © UCLES 2022 5 Hackers can see mouse movements and clicks on Fred’s computer, but not what is typed. He has been entering his PIN using the mouse as he thought it was more secure. To do this, he clicks the buttons on a PINpad displayed on the screen. 1 4 7 2 5 8 0 3 6 9 From the pattern of mouse activity the hackers can determine that his PIN might be 3296. (a) What are all the other numbers that it might be? [2] … … … … … … (b) Give one example of a PIN with 4 distinct digits whose pattern would give at least one more possible equivalent mouse pattern than 3296 has. [1] … … … … … …

7 9694/11/M/J/22 © UCLES 2022 [Turn over 6 The postage rate in Grendalia is 65¢ for letters up to 50 grams plus 4¢ for every extra 10 grams or part of 10 grams. Pat wishes to send a letter weighing 117 grams. He has plenty of stamps, but their values are all 15¢, 12¢ and 2¢. Assuming that Pat pays exactly the correct postage, what is the minimum number of his stamps that he will use? [3] … … … … … … … … … … … … … … … …

8 9694/11/M/J/22 © UCLES 2022 7 When customers arrive at a drop-in advice centre, they collect a ticket with a three-digit number: beginning each day with 001, 002, 003, etc. Customers are seen in the order of their arrival. When an adviser is free, the next number is displayed and the customer with that number begins their appointment. That number remains on the display until the next adviser is free and the next number is displayed. An appointment lasts at least 5 minutes and no more than 10 minutes. No time is lost between customers and there are always enough customers to fill all the appointments. All advisers start work at 09:00 and have a lunch break from 12:00 to 13:00. Rachel visits the centre on Monday, when only one adviser is working, and she sees that the number 028 is displayed. (a) What is the earliest time that Rachel could have arrived at the centre? [2] … … … … On Tuesday, three advisers are working. When Sam arrives she takes her ticket. It is number 052. (b) What is the latest time that Sam’s appointment could begin? [2] … … … … On Wednesday, one adviser is working. When Tommy arrives he takes his ticket, which has the number 063. The number being displayed is 048. (c) (i) What is the smallest number of minutes that Tommy could have to wait for his appointment to begin? [1] … … (ii) What is the largest number of minutes that Tommy could have to wait for his appointment to begin? [1] … …

9 9694/11/M/J/22 © UCLES 2022 [Turn over 8 In the Pelfas Basketball League each player is given a ‘recent performance rating’ (RPR) once they have played three games during the current season. The RPR is updated after each subsequent game and is the sum of the number of points scored by the player in the game just played and half the total number of points they scored in their previous two games. Ged played his sixth game of this season today. He scored 18 points, which has increased his RPR from 34.5 to 37. He has now scored exactly 100 points so far this season, despite only scoring 8 points in his third game. (a) How many points did Ged score in each of his previous two games? [3] … … … … … … … … (b) What was Ged’s first RPR this season? [2] … … … … … … … …

10 9694/11/M/J/22 © UCLES 2022 9 These are the daily timetables for the ferries that link the islands of Benbow, Livesey and Smollett. Benbow ↔ Livesey journey time 53 mins each way Benbow ↔ Smollett journey time 44 mins each way Livesey ↔ Smollett journey time 72 mins each way Departures from Benbow Departures from Livesey Departures from Benbow Departures from Smollett Departures from Livesey Departures from Smollett 07:45 08:05 08:10 08:30 09:10 09:30 10:15 10:35 10:25 10:45 11:25 11:45 12:25 12:45 12:40 13:00 13:55 14:15 14:40 15:00 14:55 15:15 16:15 16:35 17:10 17:30 17:20 17:40 (a) How many ferries are travelling between islands at 12:50 each day? [1] … … … … … (b) What is the shortest scheduled time interval between any two arrivals at Smollett during the day? [2] … … … … … … … … … … …

11 9694/11/M/J/22 © UCLES 2022 [Turn over I need to get from Smollett to Livesey as early as possible tomorrow, but I have just heard that the first ferry of the day tomorrow on this route has been cancelled. The other routes will both be operating their full schedule. (c) How much sooner can I get to Livesey tomorrow travelling via Benbow than if I wait for the 11:45 ferry from Smollett? [2] … … … … … … … … (d) Assuming that they both travel at constant speed, at what time do the first two Benbow ↔ Smollett ferries of the day pass each other? [2] … … … … … … … …

12 9694/11/M/J/22 © UCLES 2022 10 The computer game Gem Rush involves collecting gemstones. A timer on the screen counts down from 120 seconds at the beginning of a game and the game ends when it reaches zero. There are four types of gemstone to be collected: • Diamonds, which score 10 points each • Emeralds, which score 7 points each • Sapphires, which score 3 points each • Rubies, which do not score points, but each one adds 10 seconds to the timer I played a game of Gem Rush yesterday and scored a total of 1490 points. At the end of the game the statistics displayed showed that the game had lasted for 1070 seconds and I had collected a total of 327 gemstones. I noticed that I had collected exactly the same number of emeralds as sapphires. How many gemstones of each type did I collect in yesterday’s game of Gem Rush? [4] … … … … … … … … … … … … … … … … … … …

13 9694/11/M/J/22 © UCLES 2022 [Turn over 11 The first version of accountancy software provided figures with unwanted leading zeros. A correction was attempted, but unfortunately it removed all zeros. For example: $000004708.08 was displayed as $478.8 The following table shows what was displayed for some items. All the items actually cost something between $999 and $9999. Weland $176.2 Xiland $194.9 Yiland $214. Zeland $4283.78 (a) What is the largest possible difference between the displayed amount for Yiland and the actual cost of that item? [1] … … … … (b) What is the smallest possible difference (but greater than zero) between the displayed amount for one of these items and the actual cost of that item? [2] … … … … … (c) Vyland’s actual cost is also between $999 and $9999. The difference between this and the amount displayed is the largest possible. What is this difference? [1] … … … … …

14 9694/11/M/J/22 © UCLES 2022 12 One length of the swimming pool at Uppetodray Leisure Centre is 30 metres. Today Adam and Ben are swimming in neighbouring lanes in the pool. They are both swimming at constant speed, with Adam swimming each full length in 75 seconds and Ben swimming each full length in 50 seconds. They both started from the same end of the pool, but Adam had already swum 80 metres when Ben began. (a) How long after Ben began did they first pass each other, swimming in opposite directions? [3] … … … … … … … … … … … … (b) What distance had they both swum when they had swum the same distance as each other? [2] … … … … … … … … … …

15 9694/11/M/J/22 © UCLES 2022 13 A cable car has an average speed of 4.8 km / h on a trip up to the top of a hill and back down. The average speed for the section up the hill is 4 km / h. What is the average speed for the section down the hill? [2] … … … … … … … … … … … … … … … … … … … … … … … … …

16 9694/11/M/J/22 © UCLES 2022 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. Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. BLANK PAGE

This document consists of 8 printed pages. © UCLES 2022 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/11 Paper 1 Problem Solving May/June 2022 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 International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the May/June 2022 series for most Cambridge IGCSE, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 2 of 8 Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with:  the specific content of the mark scheme or the generic level descriptors for the question  the specific skills defined in the mark scheme or in the generic level descriptors for the question  the standard of response required by a candidate as exemplified by the standardisation scripts. GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively:  marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate  marks are awarded when candidates clearly demonstrate what they know and can do  marks are not deducted for errors  marks are not deducted for omissions  answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous. GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently, e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind.

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 3 of 8 NOTES FOR MARKERS Working Where a final answer is underlined in the mark scheme, full marks are awarded for a correct answer, regardless of whether there is any supporting working, unless an exception is noted in the mark scheme. For partial credit, the evidence needed to award the mark will usually be shown on its own line in the mark scheme, or else will be defined in italic text. For explanations and verbal justifications, apply the principle of ‘words to that effect’. No response If there is any attempt at a solution award 0 marks not NR. “-” or “?” constitute no attempt at a solution. Abbreviations The following abbreviations may be used in a mark scheme: AG answer given (on question paper) awrt answer which rounds to ft follow through (from earlier error) oe or equivalent SC special case soi seen or implied

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 4 of 8 Annotations Where the answer is underlined in the mark scheme, and a candidate’s correct final answer is both clear and clearly identified (encircled, underlined etc.), it is not necessary to annotate that item; nor is it necessary to annotate when there is No Response. Where there is a response that scores 0, either SEEN should be used, or some other annotation(s) to indicate why no marks can be awarded (Caret, TE, NGE, Cross). Partial credit should be indicated with a 1 (or, occasionally, a 2) at the point at which that mark has been earned. The highlighter should be used anywhere it is helpful to clarify the marking. Correct item Incorrect item Individual mark of partial credit Double mark of partial credit Essential element of answer/working missing Judged to be not good enough to earn the relevant credit Benefit of doubt Correct follow through Transcription error Special case Working seen but no credit awarded; blank page checked Highlight Use anywhere it is helpful to clarify the marking

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 5 of 8 Question Answer Marks 1(a) The smallest maximum distance for any manager is 10 for the Grand Hotel [1] 2  20 + 0.5  (9 + 7 + 8 + 10) = $57.00 2 1(b) Central: 2 x 19 + 0.5 x (4 + 12 + 5 + 11) = $54.00 1 Question Answer Marks 2(a) Tuesday 1 2(b) 2 1 Question Answer Marks 3(a) Total draw money, (203  $15 =) $3045 Prize money, (12  $60 =) $720 1 mark for either Amount donated to local charity in one year = $3045 – $720 = $2325 2 3(b) Total prize money, $840 Total membership fees, (203  $17 =) $3451 1 mark for either Amount donated to local charity in next year = $3451 – $840 = $2611 OR ($2325 + $406 =) $2731 ($2325 – $120 =) $2205 ($406 – $120 =) $286 1 mark for any one of these Amount donated to local charity in next year = $2325 + $286 = $2611 2 Question Answer Marks 4 (I paid $36 per week, which is a reduction of) $14 [1]. This must have been 2 days of a reduction per day of $7. 2 Question Answer Marks 5(a) 2185 [1] 5408 [1] If 3 or more answers are given, award 1 mark for 2 correct with 1 incorrect No marks if more than 1 incorrect 2

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 6 of 8 Question Answer Marks 5(b) Only a small square gives the maximum, so, (with digits in any order): 1245 OR 2356 OR 4578 OR 5689 1 Question Answer Marks 6 117 grams rounds up to 120 grams, which is 50 grams + 7  10 grams, so the postage cost is 65¢ + 7 4¢ = 93¢ [1] 1 mark for any correct construction of 93¢ from the stamps available, e.g. 5  15¢ + 1  12¢ + 3  2¢ or 1  15¢ + 6  12¢ + 3  2¢ 3  15¢ + 4  12¢ uses the minimum number of stamps, which is 7. 3 Question Answer Marks 7(a) 27 customers have completed their 5-minute appointments [1] Time that has elapsed after 09:00 is 27 x 5 = 135 minutes so 11:15 If 0 scored, award 1 mark for final answer of 11:20 2 7(b) 17 appointments per advisor at 10 minutes each [1] So Sam’s appointment would begin at 11:50 2 7(c)(i) Appointment 048 is just ending, then 14  5 minutes, so 70 minutes 1 7(c)(ii) Appointment 048 is just beginning, then another 14  10 minutes, so 150 minutes 1 Question Answer Marks 8(a) (37 – 18 = 19, so) he scored a total of 38 points in the two games [1] 5th game’s score plus half of 8 and half of 4th game’s scores is 34.5 [1] 15 and 23 in either order OR x + y = 38 [1] y + ½ (8 + x) = 34.5 [1] 15 and 23 3 8(b) In his first two games he scored a total of 100 – 18 – ‘38’ – 8 [1] ft (= 36 points) His first RPR was therefore 8 + (36 ÷ 2) = 26 2

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 7 of 8 Question Answer Marks 9(a) 4 1 9(b) arrivals (from Benbow) at 08:54, 11:09, 13:24; 15:39 and 18:04 arrivals (from Livesey) at 10:22, 12:37, 15:07 and 17:27 1 mark for either complete correct list 15:07 to 15:39 OR 32 minutes 2 9(c) the 10:15 ferry from Benbow to Livesey arrives at 11:08 [1] 1 hour 49 minutes / 109 minutes earlier than the 11:45 ferry 2 9(d) (At 8:30 the Benbow to Smollett ferry will have) 24 minutes remaining [1] The two ferries will meet halfway, at 08:42 2 Question Answer Marks 10 Scheme for 95 rubies (maximum 4 marks): Rubies added 950 seconds to the timer So 95 rubies [1] D + E = 149 (may be in words) oe [1] 83 emeralds and 83 sapphires [1] 66 diamonds [1] 4 marks for correct numbers of all four gems OR Scheme for incorrect number of rubies (maximum 2 marks): D + E = 149 (may be in words) oe [1] Correct number of emeralds, sapphires, diamonds for their number of rubies [1] ft 4 Question Answer Marks 11(a) 2140 down to 214 = $1926. 1 11(b) Xiland gives the smallest amount, from $1094.09 – 194.9 = $899.19 1 mark for final answer of $899.82 or $900 OR 1 mark for clearly using 1094.(..) or 1076.(..) and contributing to final answer 2 11(c) $9900.xx – $99.xx = $9801 1

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 8 of 8 Question Answer Marks 12(a) When Ben starts, Adam is 10 metres from the far end and heading away from Ben OR Adam turns 25 seconds after Ben begins, when Ben is 15 metres from the start OR The distance between them then reduces by 1 metre per second 1 mark for any one of these They pass each other 24 metres (from the start) OR They have a total of 40 metres to travel before they meet 1 mark for either so when they pass each other Ben has been swimming for 40 seconds OR algebraic method Suppose that they pass after Ben has swum x metres, then Adam will have swum 10 +(30 – x) metres x/0.6 = (40 – x)/0.4 [1] so x = 24 [1] Ben will swim 24 metres taking 40 seconds 3 12(b) The difference between the distances they have swum reduces by 0.2 metres per second, so when they have both swum the same distance Ben will have been swimming for 80 ÷ 0.2 = 400 seconds [1] In this time Ben has swum 400  0.6 = 240 metres OR both have swum 480 metres in total OR Adam swims 80 metres in 80 ÷ 0.4 = 200 seconds Ben swims for 200 seconds less than Adam Let T be time for Adam’s swim, then 0.4T = 0.6(T – 200) [1] T= 600, so distance swum by each is 240 metres OR 480 metres in total 2 Question Answer Marks 13 For example, suppose for convenience that the distance up hill is 9.6 km. This means that the journey up and down takes 4 hours. Since the speed up the hill is 4 km/h, going up must take 9.6/4 = 2.4 hours [1], leaving 1.6 hours to descend 9.6 km, meaning that the average speed going down is 9.6/1.6 = 6 km/h. OR Suppose that distance each way is d km and speed down is v km/h Time going up is d/4, time for up and down is 2d/4.8, so 2d/4.8 = d/4 + d/v [1] leading to v = 6 km/h 2 3