Cambridge A Level Thinking Skills 9694 — 2024 May/June Paper 1 · Variant 2

This document has 16 pages. [Turn over Cambridge International AS & A Level * 4 7 6 4 6 3 4 3 7 1 * DC (SK) 328360/2 © UCLES 2024 THINKING SKILLS 9694/12 Paper 1 Problem Solving May/June 2024 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 some questions, if you do not show your working, full marks will not be awarded. INFORMATION ● The total mark for this paper is 50. ● The number of marks for each question or part question is shown in brackets [ ].

2 9694/12/M/J/24 © UCLES 2024 1 Kevin makes birdhouses in batches. It takes him 90 minutes to make the first one in the batch. For the next 9 birdhouses, each one takes 2 minutes less than the previous one to make. Once Kevin has made 10 birdhouses, any others take the same time to make as the 10th one. Kevin has an order for 20 birdhouses. How long will it take Kevin to make these 20 birdhouses? [2] … … … … … … … … … … …

3 9694/12/M/J/24 © UCLES 2024 [Turn over 2 Canapés are being served at a formal event. The caterers have made three types of canapé: salmon, caviar and avocado. It has been decided that each tray should contain exactly three individual canapés, either all the same or one of each type. Close to the end of the event, there are 8 salmon canapés, 7 caviar canapés and 5 avocado canapés remaining. (a) The caterers know that they can make six trays of canapés at this point in the evening. List all the possible ways to make six trays. [2] … … … … … … (b) The caterers know that making one extra canapé will enable them to make an extra tray. Which type of canapé should they make? Explain your answer. [1] … … … … … …

4 9694/12/M/J/24 © UCLES 2024 3 In the game of Bongdong, there are two ways to score: a bong scores 7 points and a dong scores 3 points. The Dolphins have won their previous four games with scores of 13, 29, 26 and 19 points. (a) How many bongs did they score in the four games? [2] … … … … … … In their fifth game today, the Dolphins lost in a game in which the combined scores of the two teams was 25. (b) What are the different numbers of points that the Dolphins could have scored in this match? [2] … … … … … … … …

5 9694/12/M/J/24 © UCLES 2024 [Turn over 4 The admission fees for a local museum are shown in the table. Ticket type Mon–Fri Sat Child (Under 16) $2.50 $3.50 Adult $4.00 $6.00 Family (2 adults and 2 children) $12.00 $16.00 Group (Up to 5 people) $17.50 $25.00 A group of 6 adults and 5 children visited the museum on Wednesday. (a) What was the cheapest total cost for the tickets? [2] … … … … … … When buying tickets, it is possible to make a donation on top of the admission fee. The local government gives the museum an additional 20% of the amount donated. A group of 2 adults and 3 children visited the museum on Saturday. They bought the cheapest possible tickets for their admission and made a donation. They paid a total of $25. (b) How much was given to the museum by the local government as a result of this visit? [2] … … … … … … … …

6 9694/12/M/J/24 © UCLES 2024 5 A delivery company provides boxes of types A, B, C and D for its customers. The dimensions of each type of box, the maximum weight each can hold and the costs of delivery are shown in the following table. Type of box Maximum weight Dimensions Cost of delivery Type A 1 kg 40 cm × 30 cm × 20 cm $10 Type B 2 kg 50 cm × 40 cm × 40 cm $15 Type C 3 kg 60 cm × 40 cm × 20 cm $25 Type D 5 kg 80 cm × 80 cm × 80 cm $35 A customer may pack any number of parcels in a box so long as the lid fits on properly. Any space remaining in the box is filled with packing material of negligible weight. Marryk has 72 identical parcels, each of which is a cube with edges of length 20 cm. He packs these parcels tightly into Type C boxes, so that there is no space between them. (a) (i) What is the total cost for delivering these boxes? [2] … … … … … (ii) What can you deduce about the weight of each of these 72 parcels? [1] … … Steve has two parcels, each measuring 40 cm × 30 cm × 20 cm and weighing 1 kg. He will pack both of them into one type of box so that the cost of delivery is as small as possible. (b) What is this least cost? [1] … … … … … … …

7 9694/12/M/J/24 © UCLES 2024 [Turn over 6 A company has 8 employees. The names of the employees and the days on which they work each week are shown in the table. Name Monday Tuesday Wednesday Thursday Friday Ann    Ben     Caz    Den  Eva   Flo   Glo      Har    The manager is arranging some training for his employees. The training will take place next week on two non-consecutive days. Each employee must attend the training for one day and there will be four employees on each of the two days. An employee must attend the training on a day when they would normally be at work. (a) (i) Give a reason why one of the days for the training must be Friday. [1] … … (ii) On which other day will the training take place? Explain your answer. [2] … … … … … … Because of the tasks they do at work, Ben and Glo cannot attend training on the same day, and Glo and Har cannot attend training on the same day. (b) Which employees will attend the first training day? [1] … … … …

8 9694/12/M/J/24 © UCLES 2024 7 A tie maker plans to offer a ‘mediaeval heraldic’ range of ties, featuring repeating patterns of coloured stripes of even width. He will use just the five standard original colours (with mediaeval abbreviations): Red(G), Blue(Z), Black(S), Yellow(O) and White(A). Yellow (for gold) and White (for silver) are called metals, and must never be next to each other. Any other combination is permitted. He wants to give names to each colour combination, e.g. ‘Jesus’ (after Jesus College, Cambridge) for Red and Black, or Black and Red. (a) How many names will he need for all such permitted ties with two colours? [2] … … … … … … He thinks that he needs more options, and considers ties with a repeating pattern of three colours. He notes that the repeating ‘Estonian’ pattern …AZSAZSAZS… is the same as repeating ZSA, but not SZA. (b) How many names will he need for all such permitted ties with three colours? [2] … … … … … … … …

9 9694/12/M/J/24 © UCLES 2024 [Turn over 8 The five regions of Pellandia compete in an inter-region football league every season. Each team plays each of the others twice. A team gains 4 points for a win and both teams gain 2 points for a drawn match. In addition, the first team to score in any match gains 1 point, whatever the final result. This is last season’s final table. Played Won Drawn Lost Points East 8 5 2 1 28 South 8 3 2 3 21 West 8 3 1 4 18 Central 8 2 3 3 16 North 8 2 2 4 15 In how many of last season’s inter-region matches were no goals scored? Explain your answer. [2] … … … … … … … … …

10 9694/12/M/J/24 © UCLES 2024 9 Four contestants take part in each edition of the TV quiz show Build Up. In the first part of the show, each of the four contestants is asked 10 questions. For every correct answer the contestant wins $200, but every incorrect answer and every ‘pass’ adds $50 to the cash totals of each of the other three contestants. At the end of this part, the two contestants with the lowest cash totals are eliminated, but they do take home their cash totals. A tie-break may be required to decide who is eliminated, but tie-break questions have no cash value. (a) What would the cash total of each contestant be at the end of the first part if none of the contestants answered any of their ten questions correctly? [1] … … … … The cash totals of the contestants at the end of the first part of yesterday’s show were: Sarah $2400 Jason $2150 Danny $1400 Linda $1150 (b) How many questions were answered correctly in the first part of yesterday’s show? [2] … … … … … … … …

11 9694/12/M/J/24 © UCLES 2024 [Turn over In the second part of the show, the two remaining contestants carry forward their cash totals and continue to increase them by competing against each other. There are 30 questions in this part, each of which is answered by the first to press their buzzer. A correct answer is now worth $500, but an incorrect answer adds $250 to the opponent’s cash total. However, $250 is deducted from both cash totals whenever neither contestant presses their buzzer. At the end of the show the contestant with the lower final cash total wins that total and the ‘champion’ wins double his or her final cash total. If they both finish with the same final cash total, neither has their total doubled. In the second part of yesterday’s show, five of the questions were not attempted. Sarah answered fourteen questions, but four were incorrect, and Jason answered eleven questions, but two were incorrect. (c) How much money was won in total by the four contestants in yesterday’s show? [3] … … … … … … … … … … … … … … … …

12 9694/12/M/J/24 © UCLES 2024 10 Toby is a tree surgeon who prunes trees. The amount he charges for different sizes of trees and the lengths of time he takes to prune these trees are shown in the following table. Size of tree Charge per tree Time taken per tree Small $60 50 minutes Medium $110 90 minutes Large $160 120 minutes Toby works from 09:00 to 17:00 each day, with a lunch break from 13:00 to 13:30. He does not have to finish pruning a tree before he breaks for lunch; but he will only start work on a tree if he can complete it the same day. (a) (i) What is the greatest number of trees that Toby can prune in a single day? [1] … … … (ii) What is the greatest amount of money that Toby can earn in a single day? [1] … … … … A customer requires Toby to prune 10 small trees and 12 medium trees. Toby will start work on these trees at 09:00 next Monday and complete the work as soon as possible. (b) On which day and at what time will he complete the work? [2] … … … … … … … …

13 9694/12/M/J/24 © UCLES 2024 [Turn over Toby upgrades his equipment and finds that he can reduce the time taken to prune each tree by 10 minutes. He does not change his charges. (c) What is now the greatest amount of money that Toby can earn in a single day? [1] … … … … … In a park there are 27 small trees and 8 large trees. Toby will prune these trees using his upgraded equipment. He will start work at 09:00 on a Monday. He knows that he can finish the work on Friday of the same week. (d) What is the earliest possible time on Friday at which Toby could complete this work? [4] … … … … … … … … … … … … … … … …

14 9694/12/M/J/24 © UCLES 2024 11 I was born on 27 March 1981. When written in the form DD/MM/YY (where DD is the day of the month, MM is the numerical form of the month and YY the last two digits of the year) this is date 27/03/81. All six digits are different and DD × MM = YY. I have four cousins. They were all born on different dates during the 1970s and the date of birth of each one of them is also a date for which the digits of DD/MM/YY are all different and DD × MM = YY. What are the dates of birth of my four cousins? [3] … … … … … … … … … … … … …

15 9694/12/M/J/24 © UCLES 2024 [Turn over 12 The Bolandia Music Society has 600 members. Last week, every member voted either for or against each of two proposals. The results were that 422 members voted for Proposal 1 and 163 members voted against proposal 2. (a) What is the smallest possible number of members who could have voted for both proposals? [1] … … … … … … … … In fact, 351 people voted for both proposals. (b) How many members voted against both proposals? [2] … … … … … … … … … … … … [Turn over for Question 13]

16 9694/12/M/J/24 © UCLES 2024 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 In our garden recently, my son decided to count the number of birds he could see and my daughter decided to count the number of bees she could see. When my son announced his total, my daughter, who knows that a bee has six legs and four wings, said ‘together we have seen a total of 142 legs and 110 wings’. How many birds and how many bees had the children counted? [2] … … … … … … … … … … … Birds … Bees …

This document consists of 8 printed pages. © Cambridge University Press & Assessment 2024 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/12 Paper 1 Problem Solving May/June 2024 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 2024 series for most Cambridge IGCSE, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 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 descriptions 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.

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 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’. Units Unless required by the question or mark scheme, units such as $ do not need to be seen to award the marks. 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 dep mark depends on earlier, asterisked (*), mark ft follow through (from earlier error) oe or equivalent SC special case soi seen or implied

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 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

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 5 of 8 Question Answer Marks 1 1 mark for either 90 + 88 + 86 + 84 + 82 + 80 + 78 + 76 + 74 + 72 OR 10  72 1530 minutes or 25 hours 30 minutes 2 Question Answer Marks 2(a) 5 mixed and 1 salmon 4 mixed, 1 salmon and 1 caviar 2 mixed, 2 salmon, 1 caviar and 1 avocado 1 mixed, 2 salmon, 2 caviar and 1 avocado 1 mark for any two 2 marks for all four with no extras 2 2(b) Caviar; because (two of the ways to make six trays mean) two caviar canapes are left over (so making another will allow a seventh tray of three caviar) OR Caviar, because (the other two ways to make six trays mean) one salmon and one avocado canapes are left over (so making another will allow a seventh mixed tray) 1 Question Answer Marks 3(a) 13 = 7 + 3 + 3 29 = 7 + 7 + 3 + 3 + 3 + 3 + 3 26 = 7 + 7 + 3 + 3 + 3 + 3 19 = 7 + 3 + 3 + 3 + 3 1 mark for any two number of bongs correct They scored 6 bongs 2 3(b) 0, 3, 6, 7, 9, 10, 12 1 mark for 4 correct and none incorrect, OR 5 correct and no more than 1 incorrect, OR 6 correct and no more than 2 incorrect, OR 7 correct and no more than 3 incorrect 2 Question Answer Marks 4(a) Cheapest is 1 Group ticket (for 5 adults), 5 Child tickets and 1 Adult ticket [1] This costs $17.50 + $4 + 5  $2.50 = $34 1 mark for $34.50 2 4(b) $19.50 is the best price for 2 adults and 3 children. [1] Therefore the donation was $5.50, so the government gave the museum $1.10 If 0 marks scored, allow 1 mark for final answer $2.10 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 6 of 8 Question Answer Marks 5(a)(i) One box can hold 3  2  1 = 6 parcels [1] Number of boxes = 72/6 = 12, so cost is 12  $25 = $300 2 5(a)(ii) Maximum weight per parcel = 500 g 1 5(b) $15 1 Question Answer Marks 6(a)(i) Den only works on Fridays 1 6(a)(ii) Ann and Eva are not at work on Fridays [1] They only both work on Tuesdays [1] OR Only 3 employees work on Monday AND Thursday is consecutive, so must be Tuesday or Wednesday [1] Ann does not work on Wednesday, so must be Tuesday [1] 2 6(b) Ann, Ben, Eva, Har 1 Question Answer Marks 7(a) Red with 4, Blue with 3 others, and Black with 2 1 mark for any complete set of combinations for a starting colour 9 2 7(b) A comes with 6 options GZ ZG GS SG ZS SZ Similarly O Only two others: GZS GSZ 14 1 mark for 20 (omitting metal constraint) or 7 (omitting direction) 2 Question Answer Marks 8 1 mark for (All 20 matches have 5 points available but) the total number of points scored is 98 OR The additional points scored for the first goals were 4 + 5 + 4 + 2 + 3 = 18 (and there were 20 matches) (so) the 1 point for scoring the first goal was not awarded in 2 matches [1] Note: unsupported answer does not score full marks 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 7 of 8 Question Answer Marks 9(a) $1500 1 9(b) Minimum sum of the cash totals is $6000 AND yesterday’s sum was $7100 [1] The difference (of $1100) is $50  22 OR Maximum sum of the cash totals is $8000 AND yesterday’s sum was $7100 [1] The difference (of $900) is $50  18, so number answered correctly is 22 2 9(c) Both Sarah and Jason won $4250 in the second part of the show [1] Sarah’s cash total = $13 300 [1] Total money won = ($13 300 + $6400 + $1400 + $1150 =) $22 250 SC: 2 marks for final answer $15 600 3 Question Answer Marks 10(a)(i) 9 1 10(a)(ii) 3 large trees and 1 medium tree give $590 1 10(b) Two of Mon, Tues and Wed done optimally with 9S or 5M pruned in a day [1] Then one more optimal day leaving 1S + 2M, pruned in (50 + 90 + 90 =) 230 minutes, so finishes on Thursday at 12:50 2 10(c) $660 1 10(d) Toby can prune 3L + 3S in one day (taking 330 + 120 = 450 minutes) [1] Two days of this leaves 2L + 21S Next most efficient use of a day is pruning 11S (taking 440 minutes) [1] This leaves 2L + 10S 4th day: 1L + 8S (taking 430 minutes) [1] leaving 1L + 2S on 5th day, taking 190 minutes Earliest finish time on Friday is 12:10 SC: 3 marks for (sub-optimal) final answer of 12:20 4

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2024 © Cambridge University Press & Assessment 2024 Page 8 of 8 Question Answer Marks 11 18 April 1972 or 18/04/72 19 April 1976 or 19/04/76 26 March 1978 or 26/03/78 13 June 1978 or 13/06/78 2 marks for 2 right and 0 wrong, or 3 right and 1 wrong or 4 right and 1 wrong; 1 mark for 1 right and 0 wrong or 2 right and 1 wrong or 3 right and 2 wrong; 0 marks if more than 5 answers 3 Question Answer Marks 12(a) 259 1 12(b) 422 – 351 = 71 [1] voted for Proposal 1 and against Proposal 2 163 – 71 = 92 voted against both proposals OR (600 – 163) – 351 = 86 [1] voted for Proposal 2 and against Proposal 1 (600 – 422) – 86 = 92 voted against both proposals 2 Question Answer Marks 13 23 birds and 16 bees 1 mark for (142 – 110) ÷ 2 seen OR for 16 (bees) OR 23 birds OR for a trial with at least 10 birds and at least 10 bees OR 2x + 6y = 142 and 2x + 4y = 110 2