Cambridge A Level Thinking Skills 9694 — 2024 Oct/Nov Paper 1 · Variant 1

This document has 16 pages. [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/11 Paper 1 Problem Solving October/November 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 4 4 9 0 4 8 6 5 6 * DC (SL) 336968/2 © UCLES 2024 ,










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2 9694/11/O/N/24 © UCLES 2024 1 When Angela was 6 years old, the calendar for June was as shown below. June M T W T F S S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 On 1 June, Angela’s mother gave her $1, and she gave Angela another $1 every 3 days (so the next $1 was given on 4 June). (a) How much money did Angela receive from her mother in June? [1] … … … … During the same period of time, her father also gave her money, beginning with $2 on 2 June, and a further $2 every 5 days. However, any money that he paid on a Sunday was given to charity and not to Angela. (b) How much money did Angela receive from her father in June? [1] … … … … (c) On how many of the four full weeks (Monday to Sunday) in June did Angela receive more money from her father than from her mother? [1] … … … … * 0000800000002 * ,










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3 9694/11/O/N/24 © UCLES 2024 [Turn over 2 St John’s College caterers have been given a suggested menu for a three-course meal. There are five categories of food that some of their guests are unable to eat. Dish Meat Eggs Dairy Nuts Wheat Entrée Fisher Pie Y Eagle Eyes Y Y Main Butler’s Surprise Y Y Y Lamb Shrewsbury Y Pudding Beaufort Cheese Y Adam’s Apple Pie Y Guest Meat Eggs Dairy Nuts Wheat Wilberforce N Dirac N N Hoyle N Singh N N (a) Which guests would not be able to have either of the suggested main courses? [1] … … … Butler’s Surprise is replaced by Yale Trotters so everyone has at least one option. (b) Which of the five categories of food could Yale Trotters contain? [1] … … … (c) Give two three-course meals so that everyone can have one or the other. [1] … … … … * 0000800000003 * ,










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4 9694/11/O/N/24 © UCLES 2024 3 Safira makes scented soaps. She makes five different types of soap: Apple, Coconut, Ginger, Lemon and Vanilla. She makes the soap in 10 kg batches. Each type of soap uses a different amount of scent oil. % scent oil in 1 batch Cost per gram of scent oil Apple 2.75 $0.25 Coconut 2.25 $0.30 Ginger 1.75 $0.15 Lemon 2 $0.20 Vanilla 1 $0.50 (a) What is the greatest cost of the scent oil used for a batch of soap? [2] … … … … … … … Safira decides to extend her range by making a batch of soap that combines 6 kg of Vanilla soap with 4 kg of Ginger soap. (b) How many grams of scent oil will be needed for a batch of this new soap? [2] … … … … … … … * 0000800000004 * ,










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5 9694/11/O/N/24 © UCLES 2024 [Turn over 4 We’ve heard all of Australian Uncle Phil’s stories many times. This visit we had some of the ‘when I was a cub…’ series. They included: • We had pounds, shillings and pence for money, none of this decimal stuff. • It was easy for father to drive on the left as it was just like it had been in Sweden. • The Aboriginal farm hands didn’t have a vote in the State elections. • My brother was conscripted and posted to Vietnam. • The Moon landing was timed to be convenient for American TV viewers, not Australians. The encyclopaedia offers the following dates: Event Date Voting was extended to all residents, including Aboriginal residents 17 Dec 1965 Sweden and Iceland switched from driving on the left 3 Sep 1967 Australian troops left Vietnam 2 Dec 1972 Australian decimal currency ($) introduced 14 Feb 1966 Man first walked on Moon 20 Jul 1969 To be a cub in Australia he would have to have been at least 8 years old and below 12, and the stories may not have been true for the entire time. (a) What is the shortest number of (consecutive) calendar months in which he could have been a cub? [2] … … … … … … (b) Just using the information above, what are Uncle Phil’s earliest and latest possible month and year of birth? [2] … … … … … … * 0000800000005 * ,










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6 9694/11/O/N/24 © UCLES 2024 5 Bags of Jolly sweets contain different flavours of sweet in different quantities: Flavour Number in one bag (inclusive) Apple 7 to 10 Coffee 8 to 12 Orange 5 to 8 Strawberry 6 or 7 Different bags of Jolly sweets may contain different total numbers of sweets. Ray’s bag of Jolly sweets contains 30 sweets altogether and there are twice as many coffee sweets as strawberry sweets. (a) How many apple sweets are in Ray’s bag? [1] … … … … … … Jemma’s bag of Jolly sweets contains an even number of each flavour of sweet, and every flavour has a different number of sweets. (b) How many sweets of each flavour are in Jemma’s bag? [1] … … … … … … * 0000800000006 * ,










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7 9694/11/O/N/24 © UCLES 2024 [Turn over 6 On each of the last 10 days, there was a higher number of power cuts than had ever been previously recorded. The greatest number of power cuts on any day before this period was 3. On each of the last 5 days, the number of power cuts was greater than the sum of the number of power cuts on the two previous days. What is the smallest possible number of power cuts that could have occurred on the final day of this period? [2] … … … … … … … … … … * 0000800000007 * ,










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8 9694/11/O/N/24 © UCLES 2024 7 The current production at the Letzy Theatre is a children’s show. The theatre has 408 seats. The price of a ticket for this show is $4 for adults and $10 for children. At yesterday’s performance the theatre was full, and the number of children in the audience was exactly twice as many as the number of adults. (a) What was the income from ticket sales for yesterday’s performance? [2] … … … … … … … A total of 355 tickets have been sold for today’s performance. The income from the sale of these tickets is $2860. (b) How many children will there be in the audience today? [2] … … … … … … … … … … … * 0000800000008 * ,










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9 9694/11/O/N/24 © UCLES 2024 [Turn over All children must be accompanied by at least one adult, but an adult may accompany up to four children. (c) What would be the maximum possible income from ticket sales for any performance of this show? [2] … … … … … … … … … … * 0000800000009 * ,










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10 9694/11/O/N/24 © UCLES 2024 8 A hotel maid must clean each hotel room after the guest leaves it vacant at the end of their stay. She spends 8 minutes cleaning each room and stops to rest only when there are no vacant rooms to clean. The maid ends her rests and resumes cleaning as soon as another room becomes vacant. She begins work at 08:00, when there are already 3 vacant rooms. Further guests leave their rooms vacant at the following times during her shift, which ends at 10:00. 08:04 08:39 08:52 09:03 09:16 09:17 09:41 09:52 09:55 (a) When does the maid begin her first rest and how long does she rest for? [2] … … … … … … (b) From this first rest until her shift ends, how many more rooms does she clean, and how many more minutes of rest does she have? [2] … … … … … … … … … … … … * 0000800000010 * ,










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11 9694/11/O/N/24 © UCLES 2024 [Turn over 9 A convenience store buys its bread from a local bakery. It pays a lower price per loaf when it buys more loaves. Number of loaves 1–9 10–29 30–49 50–69 70+ Bread cost/loaf $1.10 $1.05 $1.00 $0.90 $0.80 The store sells each loaf of bread for $1.40. In the first week, the store bought 45 loaves and they were all sold before the end of the week. In the second week, the store bought more loaves and sold 54 of them. The store’s profit from selling bread was the same in both weeks. What are the two possible numbers of loaves that the store might have bought in the second week? [3] … … … … … … … … … … … … … … * 0000800000011 * ,









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12 9694/11/O/N/24 © UCLES 2024 10 Alice needs to select a team for a sporting event next week. She has 6 people to choose from and needs a team of 3. To help her to test their skills, Alice has devised a game for them to play against each other in pairs. In each match the players attempt to score goals and the player with the most goals wins. In the table below, the number in each cell is the number of goals that Player 1 scored in the match against Player 2. Player 2 Fred Gemma Harold Ian Jasmine Kelly Player 1 Fred 8 4 7 Gemma 4 2 3 Harold 4 5 5 Ian 4 5 2 Jasmine 2 4 6 Kelly 3 1 3 For example, when Ian played Gemma, he won the match by 5 goals to 2. (a) Which two players were involved in the match where there was the biggest difference in the number of goals scored? [1] … … … … Alice has arranged the schedule so that 3 matches take place at the same time. In the next set of 3 matches Fred will play against Harold. (b) What are the pairings for the two matches that will be played at the same time as Fred plays Harold? [2] … … … … … … … … * 0000800000012 * ,









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13 9694/11/O/N/24 © UCLES 2024 [Turn over Alice awards each player 2 points for each match that they win and 1 point for each match that is a draw. Each player also earns 1 point for each goal that they scored. The table shows the number of points that each player earned in each of their matches and their total number of points. Match 1 Match 2 Match 3 Match 4 Match 5 Total Fred 5 10 9 8 7 39 Gemma 4 4 2 4 11 25 Harold 7 6 7 6 3 29 Ian 5 2 7 8 3 25 Jasmine 4 8 2 0 1 15 Kelly 4 3 1 2 3 13 (c) Who did Harold play in his first match? [2] … … … … … … The three players with the highest total numbers of points are chosen for the team. Since Gemma and Ian have the same total number of points, it has been decided that the player who has the highest total number of points if the matches against Fred are ignored will earn the place on the team. (d) Which one of Gemma and Ian earns the final place on the team? Explain your answer. [2] … … … … … … … … * 0000800000013 * ,









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14 9694/11/O/N/24 © UCLES 2024 11 Graham is packing chocolates into boxes to sell in his shop. There are 3 sizes of box available. The prices and the numbers of each type of chocolate in each box are shown in the table. Size Price ($) Dark chocolates Milk chocolates White chocolates Small 12 4 2 4 Medium 19 6 8 6 Large 29 12 12 12 Graham has 200 of each type of chocolate. Initially he plans to make equal numbers of each type of box. (a) What will be the total price of the boxes that Graham packs? [2] … … … … … … … … Graham decides instead that he will pack boxes with the maximum total price even if there are different numbers of each type of box. (b) What is the maximum total price of the boxes that Graham could pack? [2] … … … … … … … … * 0000800000014 * ,









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15 9694/11/O/N/24 © UCLES 2024 [Turn over 12 In winter it can take each of my ducks from 1 to 2 days to produce an egg. A chicken will take anything from 2 to 4 days to produce an egg. I sell my eggs in boxes of 12 (a ‘dozen’). In any week, I receive orders for at least 5 dozen eggs and at most 7 dozen eggs. As not everyone likes duck eggs, I can only use them to make up at most a third of the order. (a) What is the minimum total number of birds I would need to have to make sure I can fulfil the orders for any week? [3] … … … … … … … … … In fact, I have 12 ducks and 72 chickens. Any surplus eggs that I do not need to fulfil the orders in any week get taken to a local shop, where I receive a lower price. (b) What is the maximum number of eggs that could be taken to the shop? [3] … … … … … … … … … [Turn over for Question 13] * 0000800000015 * ,









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16 9694/11/O/N/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 Margaret, David and Andrew enjoy dinner at a local fish restaurant. Afterwards, Andrew pays the bill, which is $78. The three colleagues wish to share the cost of dinner equally among them and at the same time also settle some unpaid debts: • David owes Andrew $4 • Andrew owes Margaret $9 • Margaret owes David $6. Margaret has only a $20 note, so she gives this to Andrew. David has only a $50 note, so he gives this to Andrew. Following this, Andrew and Margaret correctly conclude that, if each of them gives some money to David, the cost of dinner and all of the debts will be settled. How much should Andrew give to David and how much should Margaret give to David? [2] … … … … … … … … … … … … … … … … * 0000800000016 * ,









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This document consists of 8 printed pages. © Cambridge University Press & Assessment 2024 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/11 Paper 1 Problem Solving October/November 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 October/November 2024 series for most Cambridge IGCSE, Cambridge International A and AS Level components, and some Cambridge O Level components.

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 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.

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 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

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 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

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 5 of 8 Question Answer Marks 1(a) $10 1 1(b) $10 1 1(c) 1 1 Question Answer Marks 2(a) Dirac and Singh 1 2(b) Nuts and Wheat 1 2(c) Fisher Pie, Lamb Shrewsbury and Beaufort Cheese Eagle Eyes, Yale Trotters and Adam’s Apple Pie 1 Question Answer Marks 3(a) (Apple is the most expensive) 2.75  0.25 = 0.6875 [1] 275  0.25 = $68.75 If 0 scored, award 1 mark for any soap calculated correctly 2 3(b) 6 kg of Vanilla soap requires 60 g of scent oil 4 kg of Ginger soap requires 70 g of scent oil 1 mark for either 130 g 2 Question Answer Marks 4(a) (From before 17) Dec 1965 to (at least 20) July 1969 [1] 44 2 4(b) July (’69 – 12 = ) ’57 earliest [1] Dec (’65 – 8 =) ’57 is latest [1] 2 Question Answer Marks 5(a) 7 1 5(b) A:10, C:12, O:8, S:6, 1

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 6 of 8 Question Answer Marks 6 111 1 mark for any of: Day 6 16 Day 7 25 Day 8 42 Day 9 68 SC: 1 mark for final answer 64 OR for final answer 99 2 Question Answer Marks 7(a) Sight of 272 (children) and 136 (adults) [1] (272  $10) + (136  $4) = $3264 2 7(b) A search attempt, correctly calculated, involving 355 people, including at least 200 children, e.g. ((200  $10) + (155  $4) = $2620 [1] 240 children OR Algebraic approach: c + a = 355 AND 10c + 4a = 2860 oe [1] 240 children 2 7(c) Maximum income results from as close as possible to 4 children for every adult 408 ÷ 5 [1] = 81 remainder 3, so there would be 82 adults and 81  4 + 2 = 326 children (326  $10) + (82  $4) = $3588 2 Question Answer Marks 8(a) 08:32 [1] for 7 min [1] 2 8(b) 7 rooms [1] and 25 min [1] 2 Question Answer Marks 9 Week 1 profit = 45  ($1.40 – $1) = $18 [1] In week 2, 54 loaves sold at $1.40 = $75.60, so cost = &75.60 – $18 = $57.60 Number sold = $57.60/$0.90 or $57.60/$0.80 = 64 or 72 3 marks for both 64 and 72 and no others 2 marks for only one of them with no more than 1 incorrect 3

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 7 of 8 Question Answer Marks 10(a) Jasmine and Fred 1 10(b) Gemma v Jasmine [1] Ian v Kelly [1] Award 1 mark for both correct and 1 extra 2 10(c) HI 4-2, HJ 5-4, HK 5-1 [1] As all lost to Harold their score should be the same as their number of goals, so Harold must have played Jasmine 2 10(d) (When points from games against Fred are discarded:) Gemma would lose 4 points/will have 21 points Ian would lose 5 points/will have 20 points 1 mark for either 2 marks for both statements and ‘Gemma’ 2 Question Answer Marks 11(a) 1 of each box requires 22 of each type of chocolate. [1] So 9 boxes can be made. Total cost is 9  $(12 + 19 + 29) = $540. 2 11(b) (10 of each type can be packed as a small and medium box for a total of $31, which is better than the price of a large box for fewer chocolates,) so large boxes should not be packed. [1] 20 sets of 10 of each type would cost $620 2 Question Answer Marks 12(a) Maximum eggs from order = 84, up to 28 [1] can be duck Minimum duck eggs per bird per week = 3 AND minimum chicken eggs per bird per week = 1 [1] 10 ducks and 56 chickens OR 9 ducks and 57 chickens 66 3

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 8 of 8 Question Answer Marks 12(b) Minimum eggs used for orders = 60 Maximum duck eggs per bird per week = 7 Maximum chicken eggs per bird per week = 4 1 mark for any two of the above Maximum eggs = 372 [1] 312 SC: 2 marks for final answer of 240 SC: 1 mark for 84D and 216C (= 300) seen 3 Question Answer Marks 13 Andrew $23 [1], Margaret $3 [1] 1 mark for A owes D $20, A owes M $3, M owes D $6 2