Cambridge A Level Thinking Skills 9694 — 2022 May/June Paper 1 · Variant 3

This document has 16 pages. [Turn over Cambridge International AS & A Level DC (EF) 312070 © UCLES 2022 THINKING SKILLS 9694/13 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 [ ]. * 9 5 8 5 8 5 0 8 8 2 *

2 9694/13/M/J/22 © UCLES 2022 1 The direct distances in kilometres between six different towns are given in the table below. A dash indicates that there is no direct route available and the journey must be made via other towns. Anglemouth Bournsea Covenham Doncatry Eppington Bournsea 4 Covenham 10 7 Doncatry – 9 5 Eppington 8 10 11 14 Farmley 16 – 7 8 10 (a) What is the total distance for the shortest possible route from Anglemouth to Doncatry? [1] … … … … … … … … (b) What is the total distance for the shortest possible route from Bournsea to Farmley? [1] … … … … … … … …

3 9694/13/M/J/22 © UCLES 2022 [Turn over 2 In the TV Game Show Guesswork the aim is to score as few points as possible. In one round of yesterday’s show, the seven contestants had to guess the number of pebbles in a box. Each contestant scored the difference between their guess and the correct number. The guesses, in the order they were given, were: 272, 236, 352, 298, 247, 283 and 334. The two closest guesses both scored 18 points. How many pebbles were there in the box? [2] … … … … … … … … … … … … … …

4 9694/13/M/J/22 © UCLES 2022 3 Information about the courses offered by a language college is given in the following table. Course Days available Duration (minutes) Number of sessions in course Cost per session French Monday, Tuesday, Wednesday 60 12 $40 German Every day except Wednesday 90 10 $60 Mandarin Tuesday, Friday, Saturday 45 18 $45 Russian Every day 75 15 $50 Spanish Monday, Wednesday, Friday 40 20 $25 The college is open from Monday to Saturday each week. All sessions begin at 10:00. Students attend one session each week for the duration of their course. Freddie wants to do a course in each of two different languages. He has $1200 to spend. (a) List all the pairs of courses that he can afford to attend. [2] … … … … George and Hetty want to attend the same course. George cannot attend courses on Tuesdays or Thursdays. He does not want to spend more than $750 and he wants the course to be no more than 15 hours total duration. Hetty does not want to study Spanish. She cannot attend courses on Wednesdays or Saturdays and she wants each session to be less than 75 minutes in duration. (b) Which course(s) can George and Hetty take, and on what day(s)? [2] … … … … … …

5 9694/13/M/J/22 © UCLES 2022 [Turn over The college is offering a reduction of 25% for two people booking for the same course on the same day. (c) Would this offer change your answer to part (b)? Justify your answer. [1] … … … … 4 A company packs 1000 kg of sardines per day into tins. Each tin contains between 125 g and 160 g of sardines, depending on the size of the fish. The tin is then topped up with vegetable oil to make the total weight, including the tin, to be 180 g. (a) What is the maximum number of tins that can be packed in a day? [2] … … … … … … … … (b) The weight of one tin is 15 g. What is the minimum weight of vegetable oil that could be used in a day? [2] … … … … … … … …

6 9694/13/M/J/22 © UCLES 2022 5 Gregory is looking at an old calendar of a year that is not a leap year. In particular he is examining what day of the week each month begins on. He remembers the following rhyme: ‘Thirty days have September, April, June and November. All the rest have thirty-one, Except February, it’s a different one, it has 28 days clear, and 29 each leap year.’ (a) He notices that there is one other month that starts on the same day of the week as April. Which month is that? [1] … … … … … … … … (b) Three months all begin on the same day of the week. Which are they? [2] … … … … … … … …

7 9694/13/M/J/22 © UCLES 2022 [Turn over 6 At a small medical centre, with only one doctor, each appointment lasts at least 5 minutes and at most 10 minutes. Each day the doctor works from 09:00 to 18:00 with a one-hour lunch break from 13:00 to 14:00. He also takes two 15-minute tea breaks, one at any time between 09:00 and 13:00 and one at any time between 14:00 and 18:00. (a) What is the greatest number of appointments that the doctor could have in one day? [1] … … … New regulations are introduced and the doctor is now allowed to have no more than 60 appointments in a day. (b) Assuming that all appointments are taken, what is the earliest time that the doctor could finish his final appointment of the day? [2] … … … … … … Yesterday, the doctor’s final appointment (his 60th) ended at exactly 16:30. All his appointments lasted either exactly 5 minutes or exactly 10 minutes. (c) What are the two possible combinations of 5- and 10-minute appointments that the doctor could have had? [3] … … … … … … … … …

8 9694/13/M/J/22 © UCLES 2022 7 In my wallet I have some $5 notes, along with 6 times as many $1 notes, as well as some $10 notes. Altogether, I have $200. How many $10 notes do I have? [2] … … … … … … … … … … … … … … …

9 9694/13/M/J/22 © UCLES 2022 [Turn over 8 A spelling test has been taken by all children in the English counties, and the published average scores rounded down. Some of the differences between the scores of counties are not considered to be significant. Agatha has worked out that the method used to decide if a difference was significant or not was to allow a range either side of the published figures: ±2 for large counties, ±3 for medium, and ±4 for small. If the two ranges overlap then the difference was deemed not significant. For example, 503 ±4 and 509 ±2 could both be samples with average score of 507, and so not significantly different, but 504 ±2 and 509 ±2 are significantly different as there is no overlap. (a) (i) What is the smallest difference between two scores that could be considered significant? [1] … … … … (ii) What is the largest that might not be? [1] … … … … Policy makers were surprised to be informed that there was no significant difference between D and A, nor between D and B, nor between D and C; yet C was significantly better than B and B was significantly better than A. B is a medium-sized county. (b) What is the smallest possible difference between the published figures for A and C if they are not counties of the same size? [1] … … … … … …

10 9694/13/M/J/22 © UCLES 2022 9 The charges per night at the Windmill Hotel are shown in the following table. Night of the week Charge per night Monday, Tuesday, Wednesday, Thursday or Friday $100 Saturday or Sunday $120 Discounts 10% per night for any block of 3 consecutive nights* 15% per night for any block of 5 consecutive nights* *Each night can be discounted only once Pedro stays at the Windmill Hotel for 4 nights from Tuesday to Friday inclusive. (a) What is the total charge for Pedro’s stay? [1] … … … … … … Juan stays at the Windmill Hotel for 7 nights from Saturday to Friday inclusive. (b) What is the least possible total charge for Juan’s stay? [2] … … … … … … … …

11 9694/13/M/J/22 © UCLES 2022 [Turn over The hotel manager now decides that he will not allow any discount on the charges for a Saturday night stay. The discounts for 3 and 5 consecutive nights still apply, so long as the consecutive nights do not include a Saturday night. Sasha arrives at the Windmill Hotel on a Tuesday and stays for 15 consecutive nights. (c) What is the least possible total charge for Sasha’s stay? [3] … … … … … … … … … …

12 9694/13/M/J/22 © UCLES 2022 10 There are six rowing crews at Cambridge Creeks University. There is a definite order from best crew to worst crew. To adjust for varying performance, every day two people swap between crews, and those crews must be next to each other in the order. The order of the crews is unchanged by any swap. Last week the swaps (with pairs given in alphabetical order) were between these crews: Monday Tuesday Wednesday Thursday Friday Saturday Sunday Leo Aquarius Capricorn Capricorn Leo Capricorn Leo Taurus Pisces Taurus Pisces Sagittarius Pisces Taurus Alex was in Tuesday’s swap, and he can tell from the quality of the rowing that he had been moved up into a better crew. He has also deduced from the other swaps that he is not yet in the best one. Show how the best crew can be deduced from what is known, and identify which one it is. [3] … … … … … … … … … … … … … … … … … …

13 9694/13/M/J/22 © UCLES 2022 [Turn over 11 A shop sells envelopes for $1 each. By mistake, the shop makes two different offers available on this product: Offer 1: Six envelopes for the price of 5 Offer 2: Ten envelopes for the price of 8 The manager decides that a customer may use either offer, but not both. (a) Show that, if 15 envelopes are purchased, the cheapest price is the same using either offer. [2] … … … … Colin buys a number of envelopes, choosing to use Offer 1 as it gives him the cheapest price. (b) State all the possible numbers of envelopes that Colin might have bought. [2] … … … … … … … …

14 9694/13/M/J/22 © UCLES 2022 12 A bus driver switches off the engine and reads her book whenever her bus arrives at a bus stop before the time when it is timetabled to leave that stop. At the timetabled leaving times, she puts away her book and drives on. If she arrives at a bus stop after the timetabled time, she omits the stop (does not stop there). Here is part of the bus timetable: Bus stop Leave Bus station 10:35 Wallaby Road 10:42 Kangaroo Street 10:51 Wombat Avenue 11:03 Camel Lane 11:09 Railway station 11:20 On Monday, the bus left the bus station on time and took exactly 7 minutes to get from each stop to the next one. (a) How many minutes did the driver spend reading between leaving the bus station and leaving the railway station, and which bus stop did the bus omit? [2] … … … … … … … … … …

15 9694/13/M/J/22 © UCLES 2022 [Turn over On Tuesday, the bus took exactly 6 minutes to get from each stop to the next one, but left the bus station 5 minutes late. (b) How many minutes did the driver spend reading between leaving the bus station and leaving the railway station, and which bus stops did the bus omit? [3] … … … … … … … … … … On Wednesday, the bus took exactly 5 minutes to get from each stop to the next one, and the driver spent a total of 13 minutes reading between leaving the bus station and leaving the railway station. (c) At what time between 10:35 and 11:00 did the bus leave the bus station? [2] … … … … … … … … … … [Turn over for Question 13]

16 9694/13/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. 13 The path around the lake in West Park is popular with joggers, including Ali, Kim and Viv. A complete circuit is 600 metres. Ali is running at a constant speed of 4 metres per second. Kim is running at a constant speed of 2.5 metres per second in the same direction as Ali. Viv is running at a constant speed of 3.5 metres per second in the opposite direction to Ali. Momentarily they are side by side, passing each other. How long will it be before all three of them are next side by side? [3] … … … … … … … … … … … … … … … … … … …

This document consists of 8 printed pages. © UCLES 2022 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/13 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.

9694/13 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.

9694/13 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

9694/13 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

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 5 of 8 Question Answer Marks 1(a) 13 km (via B) 1 1(b) 14 km (via C) 1 Question Answer Marks 2 The two guesses that scored 18 have a difference of 36 [1] The only pair of consecutive (in order of size) guesses that fit is 298 and 334, so 316 2 Question Answer Marks 3(a) Cost of courses: $480, $600, $810, $750, $500 Possible combinations are $480 + $600, $480 + $500, $600 + $500, So French and German, French and Spanish, German and Spanish 1 mark for 2 correct combinations in a list of no more than 4 combinations 2 3(b) French: Monday 1 mark for final answer French (without specifying day or with wrong day) OR 1 mark for evidence of excluding TWO of Russian (is too long (18¾ hours) for G) Mandarin (costs too much for G) German (session too long for H) 2 3(c) Yes, could do Mandarin on Fridays 1 Question Answer Marks 4(a) To produce the maximum number of tins, the lower 125 g of sardines per can must be used. [1] 1000/0.125 = 8000 tins SC: 1 mark for 8  10n 2 4(b) For the minimum amount of oil, the upper 160 g of sardines must be used Oil in each tin: (180 – 160 – 15 =) 5 g Number of tins: (1000/0.160 =) 6250 1 mark for either Minimum weight of vegetable oil is 6250  5 = 31.25 kg 2

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 6 of 8 Question Answer Marks 5(a) July 1 5(b) February, March and November 1 mark for any two correct months in a list of no more than 3 months OR 1 mark for January and October OR 1 mark for September and December 2 Question Answer Marks 6(a) 90 1 6(b) Before lunch, 225 minutes or 45  5-minute appointments [1] 75 minutes or 15 appointments after lunch, so ends at 15:15 OR 30 fewer appointments at 5 minutes each will take 2.5 hours less to complete [1] If he doesn’t take a break then he could finish at 15:15 SC: 1 mark for final answer of 15:30 (tea break taken) 2 6(c) Total time worked is either 375 or 360 minutes [1] Number of appointments = 15 long and 45 short [1] OR 12 long and 48 short [1] 3 Question Answer Marks 7 1  $5 + 6  $1 = $11 [1] Since the total is a multiple of 10 less than $200, there must be 10 sets like this. So there must be 9 $10 notes. OR Search using 11x + 10y = 200 oe [1] x = 10, y = 9, so 9 $10 notes 2 Question Answer Marks 8(a)(i) Lower plus 2 and upper minus 2 must be different by at least 1, so 5 1 8(a)(ii) Within 4 of any point could be, so 8 1 8(b) For example: 2 + 1 + 2  3 + 1 + 3 13 1

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 7 of 8 Question Answer Marks 9(a) $370 1 9(b) Split the 7 nights as 5 plus 2 which gives a charge of $(120 + 120 + 300)  0.85 + $200 = $659 1 mark for final answer of $662 (1 + 5 + 1 nights) OR $665 (2 + 5 nights) OR $676 (3 + 3 + 1 nights) OR $678 (1 + 3 + 3 nights) OR $659 seen but not as final answer 2 9(c) Splits as 4 + 6 + 3 apart from the 2 Saturdays. 6 nights Sunday to Friday $520  0.85 + $100 (= $542) [1] 3 nights Sunday to Tuesday $320  0.9 (= $288) [1] Least total charge = $370 + $542 + $288 + $240 = $1440 3 Question Answer Marks 10 Adjacency means order is A-P-C-T-L-S (or S-L-T-C-P-A) [1] We are not told if he went P→A or A→ P, but he knows. If he went up from P to A he would be at the top [1] so up from A to P means it’s the second possibility, so best crew is Sagittarius. [1] OR (P, C, T and L all have (three) swaps with two different crews, so cannot be best.) S and A have only one swap, so one is best and the other is worst. [1] A cannot be best because Alex is in the swap of A and P and neither is best. [1] So best crew is Sagittarius. [1] 3 Question Answer Marks 11(a) Offer 1: (12 for) $10 + $3 = $13 [1] Offer 2: (10 for) $8 + $5 = $13 [1] OR Offer 1 has been used twice and Offer 2 once; in both cases, 2 free envelopes have been obtained [1] at a cost of $13 [1]. 2 11(b) 6, 7, 8, 9 (offer 1 applies once, while offer 2 does not apply) 18, 19 (offer 1 applies three times, while offer 2 applies only once) Award 1 mark for either of these two lists of values. 2

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2022 © UCLES 2022 Page 8 of 8 Question Answer Marks 12(a) 10 minutes [1] Camel lane [1] 2 12(b) 2 marks for 10 minutes 1 mark for omits Wallaby Road and Kangaroo Street If 0 scored, allow 1 mark for sight of arrival times for all stops: 10:40, 10:46, 10:52, 10:58, 11:09, 11:15 3 12(c) The whole journey would take 25 minutes driving. The schedule allows 45 minutes, so 20 minutes difference OR To have 13 minutes reading time, a total of 38 minutes is needed OR One complete correct trial for starting time between 10:35 and 11:00 1 mark for any one of these The bus must have left the bus station at 10:42 2 Question Answer Marks 13 Ali passes Kim every 600/(4 – 2.5) = 400 seconds Ali and Viv pass each other every 600/(4 + 3.5) = 80 seconds Kim and Viv pass each other every 600/(2.5 + 3.5) = 100 seconds 1 mark each for any two of the above They will all be side-by-side again after 400 seconds. Must see some evidence that third runner has been considered in order to award 3 marks. OR Ali passes Kim every 600/(4 – 2.5) = 400 seconds In 400 seconds Ali travels 1600 metres and Viv travels 1400 m In 400 seconds Kim travels 1000 metres and Viv travels 1400 m 1 mark each for any two of the above At this point they are all at the same point on the track, so 400 seconds is the answer. Must see some evidence that third runner has been considered in order to award 3 marks. OR Fix Viv, then relative speeds of Ali and Kim are 7.5 m/s and 6 m/s [1] HCF of these is 1.5 [1] 600 m at 1.5 m/s takes 400 seconds SC: 1 mark for final answer 1200 seconds 3