Cambridge A Level Thinking Skills 9694 — 2025 May/June Paper 1 · Variant 2

This document has 16 pages. Any blank pages are indicated. [Turn over Cambridge International AS & A Level DC (CE/CT) 344377/3 © UCLES 2025 * 1 5 7 3 4 9 8 9 2 2 * THINKING SKILLS 9694/12 Paper 1 Problem Solving May/June 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 [ ]. ,










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2 9694/12/M/J/25 © UCLES 2025 1 At Pandora’s Pizza Place all pizzas have the traditional cheese and tomato base and customers may add as many toppings as they wish. The toppings available to choose from are: chicken, garlic, ham, mushrooms, olives, onions, pepperoni, pineapple, prawns, salami, sweetcorn and tuna Regular Large Cheese and tomato base $6.50 $8.50 Toppings $0.80 each $1.20 each Regular pizzas can only have regular size toppings and large pizzas can only have large size toppings. Sally has ordered a large pizza with ham, mushrooms, onions and pepperoni. (a) How much will Sally pay for her pizza? [1] … … … … Gary always orders a regular pizza and has as many toppings as he can afford. Today he has a maximum of $12.00 to spend. (b) How many toppings will Gary have on his pizza today? [1] … … … … * 0000800000002 * ,










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3 9694/12/M/J/25 © UCLES 2025 [Turn over 2 Jo and Sam have separate alarm clocks, both set to wake them up at 07:00. Each clock has a ‘snooze’ button; pressing this button when the alarm sounds causes the alarm to sound again a fixed number of minutes later. On Jo’s clock, this is 9 minutes later; on Sam’s clock, it is 6 minutes later. (a) If each snooze button is pushed whenever the relevant alarm sounds, when will both alarms next sound together? [1] … … … … Sam’s alarm is changed to sound at 07:15. Both snooze buttons are again pushed when their alarms sound. (b) When will the alarms now first sound together? [1] … … … … * 0000800000003 * ,










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4 9694/12/M/J/25 © UCLES 2025 3 Cecily is given a list of six book titles. Information about these books is given in the table. Book Title Number of pages Topic Kings of Spain 358 History The Ancient Greeks 324 Philosophy George Washington 418 Politics Being a Politician 480 Politics The French Revolution 270 History Early Settlements 502 History Before her university course starts, Cecily must read three of these books: at least one book must be History and at least one book must be Politics. Cecily can read up to 40 pages each day. She needs to finish the three books by the end of 30th September. What is the latest date on which Cecily must begin her reading? [3] … … … … … … … … … … … … * 0000800000004 * ,










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5 9694/12/M/J/25 © UCLES 2025 [Turn over 4 In Jemima’s kitchen shop, blue bowls cost $8, green bowls cost $7 and yellow bowls cost $5. Jemima does not sell any other kinds of bowls and does not offer any discounts on multiple purchases. Sam spent $30 buying bowls. (a) State the three possible combinations of bowls which Sam could have bought. [2] … … … … … … Helen spent $35 buying five bowls. (b) State the two possible combinations of bowls which Helen could have bought. [2] … … … … … … Boris spent $42 buying bowls. (c) What is the maximum number of bowls Boris could have bought? [1] … … … … * 0000800000005 * ,










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6 9694/12/M/J/25 © UCLES 2025 5 In an unusual Triathlon competition, six competitors each take part in Swim, Cycle and Run events. All competitors start the Swim event at the same time. All competitors start the Cycle event exactly 2 minutes after the slowest competitor finishes the Swim event. All competitors start the Run event exactly 2 minutes after the slowest competitor finishes the Cycle event. The times, in minutes, for each competitor for the three events are recorded and shown in the table. Competitor Swim time Cycle time Run time Charles 20.4 36.5 14.8 Edward 24.5 32.4 17.1 George 19.7 40.6 15.8 James 22.9 32.5 15.7 Richard 25.6 34.2 16.3 William 18.2 38.8 18.9 (a) How long did William have to wait between completing his Swim event and starting the Cycle event? [1] … … … … (b) How long did Edward have to wait in total between events? [1] … … … … (c) How long was it between the start of the Swim event and the end of the Run event? [1] … … … … * 0000800000006 * ,










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7 9694/12/M/J/25 © UCLES 2025 [Turn over Points are awarded to the competitors for each of the three events: 10 points for 1st, 8 points for 2nd, 5 points for 3rd, 3 points for 4th, 2 points for 5th and 1 point for 6th. (d) Which competitor had the most points in total, and how many points did he have? [2] … … … … … … … … … … 6 I need to choose a 4-digit PIN for my new bank card. My daughter’s date of birth is 09/12/14, so, to help me remember my PIN, I want the first and second digits to add up to 9, the second and third digits to add up to 12 and the third and fourth digits to add up to 14. List all the 4-digit PINs that would satisfy my requirements. [3] … … … … … … … … * 0000800000007 * ,










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8 9694/12/M/J/25 © UCLES 2025 7 In Lateralia, all roads join towns in straight lines. Parker is travelling between Anglina and Bramly. He doesn’t have a map and doesn’t know how far the distance is between the towns. Parker comes across a signpost, but one digit cannot be read. Later on, he comes across a second signpost, but this also has one digit that cannot be read. First signpost Anglina 42 km Bramly 12 km Second signpost Anglina 63 km Bramly 1 6 km What is the distance between Anglina and Bramly? [2] … … … … … … … … * 0000800000008 * ,










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9 9694/12/M/J/25 © UCLES 2025 [Turn over 8 Toni and Kevin are inviting 1200 people to their wedding. They decide to write out invitation cards by hand and put them into envelopes. Toni takes 25 seconds to write an invitation and 15 seconds to put an invitation into an envelope. Kevin takes 40 seconds to write an invitation and 20 seconds to put an invitation into an envelope. They both write invitations and put them into envelopes for 3 hours. (a) How many invitations in envelopes are complete after this time? [2] … … … … … … Kevin now says that his hand hurts from so much writing. So, for the next 3 hours, Toni only writes invitations and Kevin only puts them into envelopes. (b) (i) How many additional invitations in envelopes are complete after this time? [2] … … … … … … (ii) In total, how much time does Kevin spend waiting during these 3 hours? [1] … … … … … … * 0000800000009 * ,










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10 9694/12/M/J/25 © UCLES 2025 9 In the TV quiz show Dodeka each contestant is asked 10 questions. Questions 1 and 2 are worth 1 point each, questions 3 and 4 are worth 2 points each, questions 5 and 6 are worth 3 points each, questions 7 and 8 are worth 4 points each and questions 9 and 10 are worth 5 points each. Each time a question is answered correctly, the contestant selects a square on a 4 × 4 grid to place the points value of the question into before receiving the next question. The squares on the grid are lettered, as shown below, for identification purposes. A B C D E F G H I J K L M N O P A contestant’s score is the sum of all the numbers in the grid plus a bonus of 12 points for each full row or column that adds up to 12. Below is a summary of Judy’s progress. Question Answer Square Selected 1 correct K 2 correct H 3 correct G 4 incorrect – 5 correct L 6 correct J 7 incorrect – 8 correct O 9 correct I 10 incorrect – (a) Complete Judy’s grid below and state her score, [2] A B C D E F G H I J K L M N O P Score … * 0000800000010 * ,










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11 9694/12/M/J/25 © UCLES 2025 [Turn over (b) What is the maximum total that any contestant can score? [2] … … … … Ian has answered his first five questions correctly and he is aiming to score the maximum possible total. This is his grid at present: A 3 C D E 2 G H 1 J K 2 M N O 1 (c) On the grid below, show how Ian could score the maximum if he answers all of his questions correctly. [2] A 3 C D E 2 G H 1 J K 2 M N O 1 (d) What is the greatest total score still available for a contestant who has answered all of the first four questions incorrectly? Explain your answer. [2] … … … … … … * 0000800000011 * ,









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12 9694/12/M/J/25 © UCLES 2025 10 Fiona’s three children all have a bowl of cereal for breakfast every morning. Julia only eats the chocolate-covered cereal and Karl only eats the sugar-covered cereal. Peter likes both types of cereal and chooses one each morning. Each child has 30 g of cereal for their breakfast each day. Yesterday all of the cereal was used up so Fiona bought a 750 g box of the chocolate-covered cereal and a 1000 g box of the sugar-covered cereal. (a) What is the smallest possible number of days on which there could be enough cereal available for all three children to have their breakfast? [1] … … … … Fiona tells Peter to choose his cereal for breakfast so that there is enough cereal available for as many days as possible before she needs to buy any more. (b) What is the maximum number of times that Peter could have the sugar-covered cereal? [2] … … … … … … … … … * 0000800000012 * ,









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13 9694/12/M/J/25 © UCLES 2025 [Turn over 11 All the books on sale in the second-hand bookshop Rainbow Books are colour-coded red, yellow, green or blue, priced as follows: • Red books are $15 each. • Yellow books are $12 each. • Green books are $10 each. • Blue books are $8 each. Last week the shop had two special offers: 20% off any two books with the same colour code, bought together. 50% off any three books with the same colour code, bought together. I bought 2 red books, 5 yellow books, 3 green books and 2 blue books and made the best possible use of the special offers. (a) How much did I pay for my twelve books last week? [2] … … … … … … This week the special offers are: 20% off any two books with different colour codes, bought together. 50% off any three books with different colour codes, bought together. (b) What is the lowest amount I could have paid for my twelve books if I had bought them this week instead of last week? [3] … … … … … … … … … * 0000800000013 * ,









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14 9694/12/M/J/25 © UCLES 2025 12 Douglas is in charge of naming the icebergs which come from the ‘D’ quadrant of Antarctica. He is proposing a new system for assigning names. Names will only be given to ‘large’ icebergs – those with an area of at least 10 km2. Icebergs will be given sequential numbers within the quadrant, e.g. D27. If an iceberg splits into two large pieces, the larger piece retains its previous ‘name’ and the new piece gets the next available letter. (If both pieces are the same size, which of them gets which name is chosen at random.) So D27 would split into D27 and D27a, and then if either of those split into large enough pieces, the new one would be D27b. (a) If D34f is 14 km2, what is the smallest that D34 could have been? [2] … … … … (b) If D42 is 246 km2, what is the largest that D42c could be? [2] … … … … * 0000800000014 * ,









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15 9694/12/M/J/25 © UCLES 2025 13 Patricia is organising a conference. Each person attending the conference will attend four talks, one in each of the four available sessions. The table shows the maximum number of people who could attend each of the talks. Session Maximum numbers for each talk A 50 40 40 30 B 50 50 30 C 60 60 30 30 D 40 40 40 30 (a) What is the maximum number of people that could attend the conference? [1] … … … … Patricia decides to change the sessions that some of the talks will take place in, so that she can increase the total number of people who could attend the conference and attend four talks. There are plenty of rooms available, so she can have any number of talks taking place in each session. (b) What is the maximum number of people that could attend the conference once the talks have been moved? [2] … … … … … … … … … … * 0000800000015 * ,









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16 9694/12/M/J/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 9 printed pages. © Cambridge University Press & Assessment 2025 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/12 Paper 1 Problem Solving May/June 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 May/June 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 May/June 2025 © Cambridge University Press & Assessment 2025 Page 2 of 9 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 2025 © Cambridge University Press & Assessment 2025 Page 3 of 9 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.

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 4 of 9 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 May/June 2025 © Cambridge University Press & Assessment 2025 Page 5 of 9 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 2025 © Cambridge University Press & Assessment 2025 Page 6 of 9 Question Answer Marks 1(a) $13.30 1 1(b) 6 1 Question Answer Marks 2(a) 07:18 1 2(b) 07:27 1 Question Answer Marks 3 For least number of days of reading, books have 270, 324, 418 pages [1] Number of days of reading is 1012/40 = 25.3 [1] or 26 5th (September) 3 Question Answer Marks 4(a) 6 yellow 2 blue and 2 green 1 blue, 1 green and 3 yellow 1 mark for any two correct in a list of no more than three 2 4(b) 5 green 2 blue, 2 green and 1 yellow 1 mark for one correct in a list of no more than two 2 4(c) 8 1 Question Answer Marks 5(a) 25.6 – 18.2 + 2 = 9.4 1 5(b) (25.6 – 24.5) + (40.6 – 32.4) + 4 = 13.3 1 5(c) 25.6 + 2 + 40.6 + 2 + 18.9 = 89.1 SC: 1 mark for 85.1 if their (a) is 7.4 1 5(d) Winner is James [1] with 19 points [1] SC: 1 mark for ‘James has 19 points’ when this is not given as final answer 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 7 of 9 Question Answer Marks 6 2759; 3668; 4577; 5486; 6395 Award marks as follows: Number of answers given Number correct 1 2 3 4 5 6 7 8 9 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 3 2 1 0 0 0 0 0 4 2 2 1 0 0 0 5 3 2 2 1 0 3 Question Answer Marks 7 169 km 1 mark for 127 and 106 OR 63 – 42 = 21 2 Question Answer Marks 8(a) Toni: 10800 seconds ÷ 40 = 270 Kevin: 10800 seconds ÷ 60 = 180 1 mark for either 450 2 8(b)(i) Toni writes 3  60  60/25 = 432 invitations [1] Kevin does not have time to put the last one into an envelope 431 2 8(b)(ii) Kevin puts 431 invitations in envelopes in 143 mins 40 secs – so he is waiting for 180 mins – 143 mins 40 secs = 36 mins 20 secs or 2180 secs Alternative solution: He has to wait 25 seconds for the first invitation And 5 seconds for each subsequent invitation And 5 seconds to wait at the end 25 + 430  5 + 5 = 2180 seconds 1

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 8 of 9 Question Answer Marks 9(a) [1] Score: (19 + 12 =) 31 [1] A B C D E F 2 1 5 3 1 3 M N 4 P 2 9(b) Up to 3 bonus lines can be made [1], worth 36 points. The total of the points for correct answers is 30. 66 SC: 1 mark for answer of 54 (which has bonus of 24 instead of 36) 2 9(c) There are two possibilities: A 3 C 5 E 2 G 4 1 4 5 2 M 3 O 1 2 marks for either grid 1 mark for the five numbers 3, 4, 4, 5 and 5 placed in squares D, H, J, K and N in any order A 3 C 4 E 2 G 5 1 4 5 2 M 3 O 1 2 9(d) (Total score =) 24 [1] It is not possible to make a sum of 12 from 4 figures without 1s or 2s [1] 2 Question Answer Marks 10(a) 12 1 10(b) There is 1750 g of cereal in total, so the maximum number of days is 1750 / 90 = 19 [1] Karl will eat 19  30 = 570 g of the sugar-covered cereal, so Peter will have this cereal at most (1000 – 570) / 30 = 14 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2025 © Cambridge University Press & Assessment 2025 Page 9 of 9 Question Answer Marks 11(a) Red: $24.00 Yellow: $37.20 Green: $15.00 Blue: $12.80 1 mark for the correct cost for any two of the colours OR for savings total $47 $89(.00) 2 11(b) $80 from YRG, YRG, YGB, YB, Y 2 marks for $80.60 from YRG, YGB, YBR, YG, Y or for $82.10 from YRG, YGB, YGB, YR, Y OR 1 mark for $86.60 from YRG, YRG, YG, YB, YB OR 1 mark for YRG, YRG, YGB, YB, Y identified as optimal solution with no or incorrect total amount 3 Question Answer Marks 12(a) a–e could have been the minimum of 10 each [1] for f to be not the larger the original must still be at least 14, so 14 + 10 + 10 + 10 + 10 + 10 + 14 = 78 2 12(b) a and b could be 10 soi [1] so 226/2 = 113 2 Question Answer Marks 13(a) 130 1 13(b) Total of all talk capacities = 620 620 / 4 = 155 [1] Since all capacities are multiples of 10, the maximum is 150, which can be achieved as e.g. 60 + 60 + 30 50 + 50 + 50 40 + 40 + 40 + 30 40 + 40 + 30 + 30 + 30 SC: 1 mark for no final answer but schedule for 150 seen 2