Cambridge A Level Thinking Skills 9694 — 2024 Oct/Nov Paper 1 · Variant 2

This document has 20 pages. Any blank pages are indicated. [Turn over * 3 0 8 5 9 2 8 2 1 2 * Cambridge International AS & A Level THINKING SKILLS 9694/12 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 [ ]. DC (DE/CT) 336156/1 © UCLES 2024 ,










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2 9694/12/O/N/24 © UCLES 2024 1 Callum lives in Gallows End and often goes for a drive in the surrounding rural area. Each pair of local villages is connected by one road between them. The lengths of these roads, in kilometres, are shown in the table below. Blackstock Effington Edge Gallows End High Ketteridge Blackstock 4 3 2 Effington Edge 4 1 6 Gallows End 3 1 5 High Ketteridge 2 6 5 (a) How many roads connect these 4 villages? [1] … … … … … … Callum starts at Gallows End and travels to each of the other villages once before returning home. He will drive only on the roads between the villages and wants to take the longest route. (b) How far will he drive? [1] … … … … … … … … … … * 0000800000002 * ,










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3 9694/12/O/N/24 © UCLES 2024 [Turn over 2 The local sports club has a squash court which members can hire. Each slot for which the court can be hired lasts for 15 minutes, but it is possible to hire the court for several slots in a row. The price to hire the court is different for different periods of the day. Between 08:00 and 14:00, the price is $5 per 15 minutes. Between 14:00 and 18:00, the price is $7 per 15 minutes. Between 18:00 and 22:00, the price is $6 per 15 minutes. (a) What is the cost to hire the court from 13:30 until 14:15? [1] … … … … … … Tanya booked the squash court for 1 hour. The cost was $26. (b) What are the two possible start times for the booking? [2] … … … … … … … … … … * 0000800000003 * ,










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4 9694/12/O/N/24 © UCLES 2024 3 Jenny has a recipe for fruit salad which contains six ingredients. The ingredients, the quantities needed and the prices at which they can be bought are given in the table. They can only be bought in the amounts stated. Ingredient Quantity required Price Pineapple 2 $3 each Orange 1 $2.50 for 4 Grapes 200 grams $5 for 400 grams Strawberries 300 grams $2.25 for 200 grams Blueberries 125 grams $1.50 for 100 grams Sugar 100 grams $1.75 for 500 grams This recipe makes one dish of fruit salad and serves 8 people. Jenny is hosting a party and she will make fruit salad for 32 people. She needs to buy all the ingredients. (a) How much will Jenny have to pay, in total, for these ingredients? [2] … … … … … … Two friends are each making one dish of fruit salad. They already have most of the ingredients, but still need to buy strawberries and blueberries. They realise that they can save money by buying them all together as one purchase. (b) How much money can they save by doing this? [2] … … … … … … … * 0000800000004 * ,










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5 9694/12/O/N/24 © UCLES 2024 [Turn over Karin is making one dish of fruit salad and she needs to buy all the ingredients. She decides to save on costs by adapting the recipe: she will use any combination of strawberries and blueberries, as long as their combined weight is the same as in the recipe. (c) How much money can Karin save by doing this? [1] … … … … … … * 0000800000005 * ,










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6 9694/12/O/N/24 © UCLES 2024 4 Carol checks data entry sheets on a computer and is paid for each item that she checks. It takes Carol 40 seconds to complete each item and she is paid 25¢ per item. Carol discovers that, by using a large monitor rather than her usual screen, she can reduce the time taken to check each item by a quarter. The large screen would cost her $420, but she knows that, after a certain number of hours worked, the extra money that she has been able to earn will have offset the cost of the monitor. What is this number of hours? [2] … … … … … … … … … … … … * 0000800000006 * ,










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7 9694/12/O/N/24 © UCLES 2024 [Turn over 5 Josh owns a company which hires out boats on a lake near his home. Boats may be hired for any whole number of hours up to a maximum of 10 hours. The charge for hiring a boat is divided into a basic charge for hiring the boat, plus an amount for each hour that the boat is hired. The bar chart shows the charges for hiring the boat. 0 1 2 3 4 5 Hours 6 7 8 9 10 5 10 15 20 25 30 35 40 Charge ($) (a) (i) What is the cost per hour to hire a boat? [1] … … (ii) What is the basic charge for hiring a boat? [1] … … In order to do the necessary safety checks, there must always be a gap of 20 minutes between the return of a boat from one hire and the next time it is taken out. Boats are always returned on time and are never returned earlier than has been paid for. Josh’s company opens at 08:00 each day and closes at 18:00. (b) What is the maximum that can be earned in a day from hiring out one boat? [2] … … … … … … … … * 0000800000007 * ,










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8 9694/12/O/N/24 © UCLES 2024 6 Paul Starmer and Roy Clegg both made their first appearance for Kikett United football club in the same match, five years ago. Paul has scored exactly 40% of all the team’s goals since then and Roy has scored exactly 40% of the rest of the goals. Paul and Roy have scored a combined total of 208 goals for Kikett United. How many goals have Paul and Roy scored individually? [3] … … … … … … … … … … … … … … … … Paul … Roy … * 0000800000008 * ,










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9 9694/12/O/N/24 © UCLES 2024 [Turn over 7 Adele lives in Ocken. Her friend Ed lives in Tupa. The journey between their two homes comprises: • A 10-minute walk between Adele’s home and Ocken bus station • A number 6 bus between Ocken station and Roville station • A number 8 bus between Roville station and Tupa station • A 15-minute walk between Tupa station and Ed’s home Number 6 buses between Ocken and Roville, in both directions, leave at 20 and 50 minutes past each hour. The journey takes 35 minutes. Number 8 buses between Roville and Tupa, in both directions, leave at 15 and 45 minutes past each hour. The journey takes 40 minutes. (a) What is the shortest time that it can take Adele to travel from her home to Ed’s home? [2] … … … … … … Adele wants to arrive at Ed’s home by 15:20 at the latest. (b) What is the latest time that Adele can leave home? [2] … … … … … … Adele and Ed agree to meet at Roville station. They both leave home at 10:10. (c) Who will arrive first and by how many minutes? [1] … … … … * 0000800000009 * ,










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10 9694/12/O/N/24 © UCLES 2024 8 The University bookshop sells the three Economics books that are needed by first year students. The individual prices of the three books are $35, $25 and $15. In the first week, students spent a total of $1785 on buying 81 of these books. (a) (i) The amount spent on one of the books was $560. How many copies of this book were sold? [1] … … … … (ii) How many copies of each of the other two books were sold? [3] … … … … … … In the second week, the bookshop introduced a special offer: all three books could be bought together at a discount of 20% on the cost of buying them all separately. Overall, twice as many copies of the three books were bought using the special offer than were bought individually in the first week. (b) How much money in total was spent on buying all three books using the special offer? [2] … … … … … … … * 0000800000010 * ,










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11 9694/12/O/N/24 © UCLES 2024 [Turn over 9 Alan wants to take a 12-day holiday some time during June, July, August or September next year. He has the following days booked in his diary for business meetings, and none of these can be changed. Meeting Date 1 6 June 2 7 June 3 13 June 4 21 June 5 28 June 6 2 July 7 4 July 8 14 July 9 24 July 10 31 July 11 14 August 12 16 August 13 21 August 14 25 August 15 30 August 16 10 September 17 20 September 18 22 September He does not want any meeting days to fall within his holiday. (There are 30 days in June and September, and 31 days in July and August.) (a) State the two possible start dates for his holiday. [2] … … … Alan decides that he wants a longer holiday. He is willing to have one meeting day fall within his holiday, but no more than that. (b) What is the longest holiday that he can take, and on what days could it begin? [3] … … … … … * 0000800000011 * ,









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12 9694/12/O/N/24 © UCLES 2024 10 In a college of 100 students, only three games are available: chess, basketball and football. 65 students play more than one game, and 5 play none. No one plays chess as their only game, but 12 students play basketball as their only game. (a) Based on this information, what is the largest possible number of students who might play football? [1] … … … … … … (b) Based on the given information, what is the smallest possible number of students who might play football? [1] … … … … … … … * 0000800000012 * ,









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13 9694/12/O/N/24 © UCLES 2024 [Turn over 11 Laid Fresh Farms use Swiftpost to deliver their eggs to retailers. Swiftpost is paid 3 cents for every egg delivered intact and fined 6 cents for every broken egg. Last week, Swiftpost were given 300 eggs to deliver to Parkside convenience store. The payment for this delivery, after fines had been deducted, was $7.65. How many eggs were delivered intact? [3] … … … … … … … … … … … … … … … * 0000800000013 * ,









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14 9694/12/O/N/24 © UCLES 2024 12 How fast you can go on a bicycle depends on several things. Two of the most important things are the bicycle gear you are using (which affects how many times the wheels turn compared with the pedals) and your cadence (how many times you rotate the pedals through a full turn each minute). A bicycle gear is made up of two cogs, one at the front and one at the back. An example of a ‘gear ratio’ is 36 by 20, which means the front cog has 36 teeth and the back cog has 20 teeth. A bicycle will have several choices of front and back cogs to change between as you ride. The change of cogs and cadence affects the speed proportionally, for example: • Doubling the front cog size doubles the speed • Doubling the back cog size halves the speed • Doubling your cadence doubles the speed Craig’s bicycle has front cogs sized 24, 36 and 48, and back cogs of every size from 8 to 24 (8, 9, 10…24). Craig is currently using the gear ratio 36 by 12. (a) Without changing his cadence, which other gear ratios could Craig use to cycle at the same speed? [2] … … … … … … … (b) If instead he doubles his cadence, which gear ratios could he use to cycle at the same speed? [2] … … … … … … … * 0000800000014 * ,









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15 9694/12/O/N/24 © UCLES 2024 [Turn over Craig’s friend Aston’s bicycle has different front cogs. He has a choice of 30, 42 and 54, but has the same choice of back cogs as Craig. (c) If Aston cycles at double the cadence of Craig, which gear ratio could he select to ride at the same speed as Craig? [2] … … … … … … … … [Turn over for Question 13] * 0000800000015 * ,









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16 9694/12/O/N/24 © UCLES 2024 13 In the inclusive 100 m race at a school sports day, everyone is given a fair chance to win regardless of their ability to run. Participants are given a head start based on their previously set times in the event. The fastest runner is placed at the start line and slower runners placed further up the track to give them enough track to complete the race in the same time as the fastest runner. Previous set times for the event were 16 seconds for the fastest runner and 20 seconds for the slowest. (a) What is the distance between the fastest and slowest runners at the start of the race? [2] … … … … … … … … The race was run and won in 15 seconds by the runner who started on the start line. The second- placed runner started with a 10 m head start and completed the race in 18 seconds. Each participant ran at a constant speed. (b) How far behind was the second-placed runner when the winner crossed the finish line? [2] … … … … … … … … * 0000800000016 * ,









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20 9694/12/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. BLANK PAGE * 0000800000020 * ,










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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 9694/12 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.

9694/12 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.

9694/12 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

9694/12 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

9694/12 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) 6 1 1(b) 18 1 Question Answer Marks 2(a) $17 1 2(b) 13:45 [1] 17:30 [1] 2 Question Answer Marks 3(a) $59.25 P: 8  $3 = $24 O: 1  $2.50 = $2.50 G: 1  $10 = $10 St: 6  $2.25 = $13.50 B: 5  $1.50 = $7.50 Su: 1  $1.75 = $1.75 1 mark for any 4 ingredient costs correct OR for all quantities correct SC: 1 mark for final answer of $58.90 2 3(b) Separately they will pay $3 + $4.50 each, so in total $15 Together they will pay $4.50 + $6.75 = $11.25 1 mark for either OR for saving $1.50 + $2.25 Total saving = $15 – $11.25 = $3.75 2 3(c) $1.50 1 Question Answer Marks 4 Old rate: 3600 ÷ 40 = 90 items per hour, 90  25¢ = $22.50 per hour New rate: 3600 ÷ 30 = 120 items per hour, 120  25¢ = $30.00 per hour 1 mark for either old or new pay rate correct $7.50 extra per hour 420 ÷ $7.50 = 56 hours OR $420 ÷ $0.25 = 1680 items to check 1680  30seconds = 14 [1] hours 14 ÷ ¼ = 14  4 = 56 hours 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 6 of 8 Question Answer Marks 5(a)(i) $3 1 5(a)(ii) $5 1 5(b) 1-hour hires could start at 08:00, 09:20, 10:40, 12:00, 13:20, 14:40, 16:00, [1] but there would not be time for a boat to be hired at 17:20. One of the hires can be extended to 2 hours. 6  $8 + 1  $11 = $59. 2 Question Answer Marks 6 Roy has scored 40% of 60% = 24% of all the goals scored.[1] Then either: 208 divides in the ratio 5 : 3 [1] to give Paul – 130 goals and Roy – 78 goals or: 208 is 64% of all the goals scored, so 1% is 3.25 [1] and therefore the total number of goals scored is 325 of which 40% and 24% give Paul – 130 goals and Roy – 78 goals. OR A search attempt, correctly calculated, involving 40% of an amount and 40% of the remaining 60% [1] A second attempt with the totals closer to 208 [1] Paul – 130 goals and Roy – 78 goals 0.4x + 0.6(0.4x) = 208 [1] X = 325 [1] Paul – 130 goals and Roy – 78 goals 3 Question Answer Marks 7(a) For example, Adele leaves at 10:10, catches 10:20 to Roville arriving 10:55, then 11:15 to Tupa [1] arriving 11:55, then 15-minute walk, so arrives at 12:10 This is shortest since minimises first walk and all buses are at 30-minute intervals. Shortest journey time is 2 hours OR The second bus can be caught no earlier than 65 minutes after leaving her house [1] A further 55 minutes gives a total of 2 hours 2 7(b) Adele must arrive at Tupa by 15:05, so catches 14:05 bus from Roville [1] Catches 13:20 from Ocken, so must leave home by 13:10 2 7(c) Adele arrives at Roville at 10:55 and Ed arrives at 11:25, so Adele arrives first by 30 minutes. 1

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 7 of 8 Question Answer Marks 8(a)(i) Only $35 divides into $560 16 books 1 8(a)(ii) ($1785 – 560 =) $1225 for (81 – 16 =) 65 books for the two books [1] 1 mark for any search with $1225 or 65 books AND more $15 books than $25 books 40 of the $15 and 25 of the $25 OR Algebraic approach: ($1785 – 560 =) $1225 for (81 – 16 =) 65 books for the two books [1] x + y = 65 AND 15x + 25y = 1225 oe [1] 40 of the $15 and 25 of the $25 3 8(b) 162 books bought with special offer 54 sets bought [1] 0.8  $75  54 = $3240 2 Question Answer Marks 9(a) 1 August [1] and 2 August [1] 2 9(b) 20 days [1], beginning on either 25 July [1] or 31 August [1] 3 Question Answer Marks 10(a) 83 1 10(b) 18 1

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2024 © Cambridge University Press & Assessment 2024 Page 8 of 8 Question Answer Marks 11 If all 300 were delivered intact, Swiftpost would have been paid $9, which is $1.35 [1] more than they were paid. Each broken egg reduces their payment by 9c [1] $1.35/9 = 15 eggs were broken, so 285 delivered intact. OR A search attempt, correctly calculated, with a total of 300 eggs and a minimum of 201 unbroken eggs [1] A second attempt with number of unbroken eggs closer to 285 [1] 285 OR x + y = 300 and 3x – 6y = 765 oe [2] 285 3 Question Answer Marks 12(a) 24  8 [1] 48  16 [1] 2 12(b) 24  16 [1] 36  24 [1] 2 12(c) 30  20 Award 1 mark for 42  28 OR 54  36 2 Question Answer Marks 13(a) The slowest runner will complete 16/20 [1] of the 100 m in the time the fastest runner runs 100 m. 4/20  100 = 20 m (100/16 – 100/20 =) 1.25 [1] 1.25  16 = 20 2 13(b) When the winner crosses the finish line, the second-placed runner is 15/18 [1] of the 90 m they have to run. 15/18  90 = 7 5m, so 15 m behind the winner. OR The second-placed runner runs 90 m in 18 s, so at 5 m/s [1]. In 15 seconds this runner runs 75 m, so is 15 m from the finish line. 2