Cambridge A Level Thinking Skills 9694 — 2025 Oct/Nov Paper 1 · Variant 2

This document has 16 pages. Any blank pages are indicated. [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/12 Paper 1 Problem Solving October/November 2025 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 9 7 3 6 8 4 4 1 5 * DC (PQ/JG) 344379/1 © UCLES 2025 ,










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2 9694/12/O/N/25 © UCLES 2025 1 Sophie is taking part in a sponsored walk to raise money for her gymnastics club. People can sponsor her for each kilometre walked but can specify a maximum amount they are willing to pay, or they can give a total that they will pay regardless of how many kilometres Sophie walks. Sophie has three sponsors. Name Amount per km Up to a maximum Total donation Arthur $1 $20 Brenda $10 Carol $0.50 – (a) How much would Sophie raise if she walked 19 km? [1] … … … … (b) How far would Sophie have to walk in order to raise $45? [1] … … … … * 0000800000002 * ,










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3 9694/12/O/N/25 © UCLES 2025 [Turn over 2 Ariel, Gemma, Libby, Sage and Virat were the five finalists in a talent competition. After all five had performed, seven judges awarded points. Each judge was instructed to award a total of 15 points. They had to award points to four of the five contestants but could not award the same number of points to two or more of them. (a) What is the greatest number of points that a judge could have given to one contestant? [1] … … … After the first six judges had awarded their points the scores were: Ariel 15 points Gemma 21 points Libby 18 points Sage 19 points Virat 17 points The points awarded by the seventh judge resulted in all five contestants finishing with the same number of points and having to share the first prize. (b) How many points did the seventh judge award each of the contestants? [1] Ariel … Gemma … Libby … Sage … Virat … * 0000800000003 * ,










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4 9694/12/O/N/25 © UCLES 2025 3 My brother has a digital diary, which he keeps on a memory stick that is passcode protected. The passcode is a six-digit number. To access the memory stick he must enter the correct answer to a sum of either two or three of the passcode’s digits, as instructed onscreen. For example, ‘Enter the sum of the 2nd, 4th and 6th digits of your passcode.’ My brother has challenged me to work out his passcode. I have been watching his responses and making a note of them. I have observed: • 2nd digit + 5th digit = 16 • 2nd digit + 6th digit = 12 • 1st digit + 4th digit = 10 • 2nd digit + 4th digit + 5th digit = 18 • 3rd digit + 6th digit = 8 • 1st digit + 3rd digit + 4th digit = 13 I now know his passcode. (a) Explain how it can be deduced that the 4th digit of the passcode is 2. [1] … … … … (b) What is my brother’s passcode? [2] … … … … … … … … … … … … * 0000800000004 * ,










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5 9694/12/O/N/25 © UCLES 2025 [Turn over 4 Duncan has a regular job that pays him $500 a month. He also works occasionally as a teacher to earn extra money. He is paid $180 for each day of teaching that he does. Duncan’s monthly living costs are $1600. (a) How many days of teaching must he work in a month to cover his living costs? [2] … … … … Duncan realises that he has not accounted for tax. He does not pay any tax on the first $1000 he earns each month, but everything over this is taxed at a rate of 20%. He still has both jobs. (b) (i) How many days of teaching must he work each month to pay for his living costs and tax? [2] … … … … (ii) How much tax will he pay if he works exactly this many days? [1] … … … … His teaching job changes so that his teaching work is counted in half-days rather than full days. He is paid $100 for each half-day that he works. (c) How many half-days of teaching must he work in a month to cover his living costs? [1] … … … … * 0000800000005 * ,










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6 9694/12/O/N/25 © UCLES 2025 5 Four teams are taking part in a sports competition. In each event two participants from each team take part. The table shows the number of points that are awarded for each position. Position Points 1st 8 2nd 6 3rd 4 4th 2 5th 1 The participants finishing below 5th place do not score any points for their team. There are 5 events in the competition. (a) What is the highest total score that a team can achieve in the competition? [1] … … After the first event the difference between the team with the highest total score and the team with the lowest total score is the smallest it could possibly be. (b) What are the total scores for the four teams? [1] … … … … After four of the five events have been completed the total scores for the teams are: Red Green Blue Yellow 24 21 21 18 (c) Explain why Red is certain to have the highest total score for the competition if one of their participants finishes 1st in the final event. [1] … … … … * 0000800000006 * ,










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7 9694/12/O/N/25 © UCLES 2025 [Turn over In fact, the Yellow team had the highest total score, followed by Green, then Blue. Red finished in last place. All four teams finished on different scores. (d) Which team did each of the participants finishing in the top five positions belong to? [2] … … … … … … … … … … … … … * 0000800000007 * ,










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8 9694/12/O/N/25 © UCLES 2025 6 At Dave’s sandwich shop, customers can choose from any of the items in the table below. Category Choices Bread Rye Sour dough White Wholemeal Spread Butter Margarine Hummus Tahini Filling Aubergine Chicken Pulled pork Salmon Vegetable Cucumber Lettuce Onion Tomatoes Topping Barbecue Cheese Chilli Mayonnaise A ‘standard’ sandwich is made up from one item in each category. (a) How many different standard sandwiches can be made? [1] … … … … Dave decides to have a simple way to price the sandwiches by allocating a number of units to each item in the sandwich: bread 2 units, spread 1 unit, filling 3 units, vegetable 1 unit, topping 1 unit. He wants a standard sandwich to cost less than $5, but as close to $4.99 as possible. (b) (i) What should the price of 1 unit be? [2] … … … … (ii) Jim buys a sandwich containing rye bread, aubergine, salmon, butter, tahini, chilli, tomatoes and lettuce. What is the price of Jim’s sandwich? [2] … … … … * 0000800000008 * ,










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9 9694/12/O/N/25 © UCLES 2025 [Turn over 7 Gwen sells second-hand books on a market stall. The books are all priced at $6, but 3 can be bought for $15. Yesterday Gwen had 84 customers and took a total of $981. Every customer bought either 1 book only or 3 books. How many books did Gwen sell yesterday? [3] … … … … … … … … … … … … … … … … * 0000800000009 * ,










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10 9694/12/O/N/25 © UCLES 2025 8 Eddie lives in Danes and his grandmother lives in Glames. To visit his grandmother, Eddie catches a bus from Danes to Everson, then a train from Everson to Falton and finally a ferry from Falton to Glames. • Buses leave Danes for Everson, and Everson for Danes, at 15 and 45 minutes past each hour. The journey in either direction takes 20 minutes. • Trains leave Everson for Falton, and Falton for Everson, at 10, 30 and 50 minutes past each hour. The journey in either direction takes 70 minutes. • Ferries leave Falton for Glames, and Glames for Falton, at 5 and 35 minutes past each hour. The journey in either direction takes 75 minutes. Eddie needs to allow at least 10 minutes for each of the changes at Everson and Falton. Eddie leaves Danes on the 10:45 bus. (a) What is the earliest time that he could arrive in Glames? [2] … … … … … … … … … … … … … … … … * 0000800000010 * ,










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11 9694/12/O/N/25 © UCLES 2025 [Turn over Eddie will stay with his grandmother for two days. On his return journey he will stop off in Falton to have coffee with a friend. He will allow at least 50 minutes between his ferry and train journeys. He wishes to be able to catch the 16:15 bus from Everson to Danes. (b) What is the least amount of time that Eddie could take between leaving Glames and arriving in Danes? [3] … … … … … … … … … … … … … 9 A song book has songs numbered from 1 to 123. The three (different) songs selected for singing are put up on a board using a separate card for each digit. How many cards of each digit are needed to ensure that all possible sets of three song numbers can be displayed? [3] 0 1 2 3 Each of 4–9 Answer: … … … … … * 0000800000011 * ,









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12 9694/12/O/N/25 © UCLES 2025 10 Michael’s fuel tank is a hexagonal prism that can contain 1200 litres of fuel. The top and bottom halves of the tank are symmetrical (so the tank has a horizontal line of symmetry). He can measure the depth, not the volume, of the fuel. He uses the fuel at a constant daily rate. He can specify and pay for an amount to add, but the delivery date is not specified and could be any time within 11 days of the order. He must not waste any fuel by ordering too much, and must not let the tank get empty. It was full when it was installed on day 0. An automatic gauge records the day when the depth is a multiple of 10% of the height. Depth Day 100% 0 90% 11 80% 24 70% 39 60% 56 50% 75 (a) On which day will the depth of the fuel be 30%? [1] … … … … (b) Which is the last day on which he can order more fuel? [1] … … … … (c) What is the maximum order? [2] … … … … … * 0000800000012 * ,









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13 9694/12/O/N/25 © UCLES 2025 [Turn over 11 The Farnham Animal Park is open every day from 10:00 to 17:30. There are three special events each day which visitors may choose to attend during their visit. The timings for these events are shown in the table. Special event Starting times Duration Penguin Feeding 11:30, 13:30, 15:30 45 minutes Sea Creatures Talk 11:15, 13:20, 15:15, 16:20 25 minutes Train Ride Round the Park 11:00 and every hour until 16:00 70 minutes Visitors must buy tickets for the special events in advance. They must allow at least 20 minutes between any two special events. Mr and Mrs Lyons and their children Lenny and Leonora plan to arrive at the park at 10:30 and stay until it closes. They will attend each of the special events once. (a) What is the earliest time by which they could have attended all three special events? [2] … … … … … … … (b) What is the latest time that the Lyons family could arrive at the first of the three special events that they have chosen to attend? State the times at which they attend each event. [3] … … … … … … … … … * 0000800000013 * ,









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14 9694/12/O/N/25 © UCLES 2025 12 The planet of Qunes is in a mythical solar system. • There are 6 months in a year. • The last month of the year is Helum, which has 22 days. • The month of Jura has 26 days. • The shortest day is on the 4th of Mules and the longest day is on the 4th of Polij. • The number of days from the shortest day to the longest day is the same as the number of days from the longest day to the shortest day. • The longest day of the year is in the 4th month, which has 24 days. • Zelum is the month after the month with the shortest day and has 26 days. • Sirop is the month before the month with the longest day and has 25 days. (a) What is the order of the six months? [2] … … … … … … … … (b) How many days are in the month of Mules? [2] … … … … … … … … * 0000800000014 * ,









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15 9694/12/O/N/25 © UCLES 2025 13 Handwritten digits can sometimes be changed to others by using more ink. In Gareth’s handwriting the following are possible: From To 0 6 or 9 1 7 2 3 3 8 4 9 5 6 6 8 7 9 9 8 Two or more changes are also possible, e.g. 2 changed to 3 and then to 8. (a) What is the largest two-digit number that can be increased by changing a digit? [1] … … … … (b) Give an example of a sequence of two-digit numbers where each has changed from the last (up or down) and where the list is as long as possible. [2] … … … … … … … … … * 0000800000015 * ,









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16 9694/12/O/N/25 © UCLES 2025 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 * 0000800000016 * ,









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This document consists of 8 printed pages. © Cambridge University Press & Assessment 2025 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/12 Paper 1 Problem Solving October/November 2025 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 2025 series for most Cambridge IGCSE, Cambridge International A and AS Level components, and some Cambridge O Level components.

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2025 © Cambridge University Press & Assessment 2025 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 October/November 2025 © Cambridge University Press & Assessment 2025 Page 3 of 8 Annotations guidance for centres Examiners use a system of annotations as a shorthand for communicating their marking decisions to one another. Examiners are trained during the standardisation process on how and when to use annotations. The purpose of annotations is to inform the standardisation and monitoring processes and guide the supervising examiners when they are checking the work of examiners within their team. The meaning of annotations and how they are used is specific to each component and is understood by all examiners who mark the component. We publish annotations in our mark schemes to help centres understand the annotations they may see on copies of scripts. Note that there may not be a direct correlation between the number of annotations on a script and the mark awarded. Similarly, the use of an annotation may not be an indication of the quality of the response. The annotations listed below were available to examiners marking this component in this series. Annotations Annotation Meaning 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 Highlighter Use anywhere it is helpful to clarify the marking

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2025 © Cambridge University Press & Assessment 2025 Page 4 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 October/November 2025 © Cambridge University Press & Assessment 2025 Page 5 of 8 Question Answer Marks 1(a) 10 + 19 + 9.50 = $38.50 1 1(b) 45 – 20 – 10 = 15 15 ÷ 0.5 = 30 km 1 Question Answer Marks 2(a) 9 1 2(b) Ariel: 6 Gemma: 0 Libby: 3 Sage: 2 Virat: 4 1 Question Answer Marks 3(a) 2nd + 5th = 16 and 2nd + 4th + 5th = 18, so 4th must be (18 – 16 =) 2 1 3(b) 4th is 2 and 1st + 4th = 10, so 1st is 8 1st + 4th = 10 and 1st + 3rd + 4th = 13, so 3rd is 3 3rd is 3 and 3rd + 6th = 8, so 6th = 5 6th is 5 and 2nd + 6th = 12, so 2nd is 7 2nd is 7 and 2nd + 5th = 16, so 5th is 9 The complete passcode is 873295 1 mark for any three digits (except 2) correct 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2025 © Cambridge University Press & Assessment 2025 Page 6 of 8 Question Answer Marks 4(a) Teaching must cover the shortfall of $1600 – $500 = $1100 [1] So the minimum number of days is 7 SC:1 mark for final answer of 9 2 4(b)(i) In order to have $1600, tax must have been paid on a sum which results in $600, so the amount earned must be at least $1000 + $600/0.8 = $1750 [1] The shortfall is now $1250, so the minimum number of days is 1250/180 = 7 OR 7 (days earned him $1760, on which he will pay 20%  760 =) $152 [1] leaving him with $1608, which is sufficient 2 4(b)(ii) $152 ft from (b)(i) provided it is 8, 9 or 10 1 4(c) 13 1 Question Answer Marks 5(a) 70 1 5(b) 8, 6, 4, 3 1 5(c) 8 points for 1st place gives a total score of 32 AND The most that Green could score is 6 + 4 = 10 points, which would only give them a total of 31 1 5(d) Yellow, Green, Blue, Yellow, Blue 1 mark for any correctly processed sets of points where Red is not in the first five positions and Yellow scored at least 8 2 Question Answer Marks 6(a) 4  4  4  4  4 = 1024 1 6(b)(i) 8 units for a sandwich [1] $4.99/8 = $0.62375 Unit price $0.62 2 6(b)(ii) 13 units [1] 13  0.62= $8.06 ft their answer to (b)(i), provided it is in money format 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2025 © Cambridge University Press & Assessment 2025 Page 7 of 8 Question Answer Marks 7 190 books 2 marks for 31  $6 AND 53  $15 1 mark for sight of any correct calculation of: multiples of $6 and $15 that add up to $981, e.g. (61  $6) +(41  $15) = $981 OR multiples of $6 and $15 with a total of 84 customers, e.g. (50  $6) + (34  $15) = $810 OR for correct subtraction from 981 of a multiple of 6 or 15 and verifying whether the remainder is a multiple of the other OR If all bought 1 book 84  $6 = $504. [1] Each one that bought 3 instead increases this by $9, so ($981 – $504) ÷ 9 = 53 [1] bought 3 books. Number of books sold = 53  3 + 31 = 190. OR a + b = 84 6a + 15b = 981 1 mark for both a = 31, b = 53 1 mark for both 190 3 Question Answer Marks 8(a) (Arrives in E at 11:05, leaves on) 11:30 train [1] Arrives in F at 12:40, leaves on 13:05 ferry, arriving in G at 14:20 SC: 1 mark for answer 13:50 2 8(b) (Eddie needs to be in E by 16:05, so must catch the train from F at) 14:50 [1] Needs 50 minutes in F, so must arrive in F by 14:00 (He needs to catch the ferry at) 12:35 [1] giving a total journey time of 4 hours 3 Question Answer Marks 9 4, 7, 5, 4, 4 1 mark for any two correct OR 2 marks for any four correct 3

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2025 © Cambridge University Press & Assessment 2025 Page 8 of 8 Question Answer Marks 10(a) 70% to 50% took 75-39 days, so 75 + 36 = day 111 1 10(b) Empty on day 150 so last date is 11 days before that day 139 1 10(c) Consumption is 600/75 = 8 litres per day. [1] Only safe to order what is missing on order date. 1200 – (8  11) litres = 1112 litres 2 Question Answer Marks 11(a) Sea Creatures talk: (11:15 –) 11:40 [1] Train Ride: 12:00 – 13:10 Penguin Feeding: 13:30 – 14:15 2 11(b) Train Ride: 16:00 (– 17:10) [1] Sea Creatures talk: 15:15 (– 15:40) [1] Penguin Feeding: 13:30 (– 14:15) [1] SC:1 mark for a set of three times with final event Sea Creatures talk at 16:20 3 Question Answer Marks 12(a) 3 months in correct place [1] 1 Mules 2 Zelum 3 Sirop 4 Polij 5 Jura 6 Helum 2 12(b) 4th Polij to 4th Mules 72 days [1] 21 days 2 Question Answer Marks 13(a) 97 1 13(b) Longest possible sequence for a single digit is 1 7 9 8 soi [1] Any seven numbered sequence starting 11, ending 88 and stepping one or other each time, e.g. 11 17 19 79 99 98 88. SC: 1 mark for any valid sequence of 5 numbers or more 2