Cambridge A Level Thinking Skills 9694 — 2023 Oct/Nov Paper 1 · Variant 2

This document has 16 pages. Any blank pages are indicated. [Turn over Cambridge International AS & A Level DC (LK/CGW) 316830/2 © UCLES 2023 THINKING SKILLS 9694/12 Paper 1 Problem Solving October/November 2023 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 most questions, full marks will be awarded for a correct answer without any working. In some questions, however, you will not be awarded full marks if working needed to support an answer is not shown. INFORMATION ● The total mark for this paper is 50. ● The number of marks for each question or part question is shown in brackets [ ]. * 3 8 1 6 5 0 1 0 6 5 *

2 9694/12/O/N/23 © UCLES 2023 1 Voting intentions were collected for an upcoming local election. There are three candidates and three zones in the city. Zone A Zone B Zone C Total Black 44 61 38 143 Carter 43 60 165 Eagle 12 32 76 119 Total 118 136 173 427 One of the figures was omitted from the table. (a) What is the missing figure? [1] … … An error was spotted in the table, although the totals are correct. (b) Which is the incorrect figure? [1] … … … … Six pie charts were drawn: one for each of the candidates and one for each of the zones. One of these pie charts is shown below. (c) Which set of data is represented in this pie chart? [1] … … … …

3 9694/12/O/N/23 © UCLES 2023 [Turn over 2 The organisers of a one-day korfball tournament originally intended each of the participating teams to play one match against each of the other teams. However, fifteen teams have entered the tournament, which would have required 105 matches to fulfil this original intention. As a result of the higher than expected entry, the organisers have decided to divide the teams into one group of eight and one group of seven. Each team will now play one match against each of the other teams in the group, then the top team from each group will play one final match against each other. How many fewer matches will be played than would have been required to fulfil the original intention? [2] … … … … … … … … … … … …

4 9694/12/O/N/23 © UCLES 2023 3 Kay took part in a quiz last night and she was the winner. There were five rounds of 20 questions each. The categories for each round were as follows: Round 1 Science Round 2 History Round 3 Entertainment Round 4 Sport Round 5 Geography Before the quiz began, Kay had to nominate one category in which she would score 3 points per question and one category in which she would score 2 points per question. Otherwise, correct answers scored 1 point each. There were no penalties for incorrect answers. Kay correctly answered 11 questions in the first round, 16 in the second round, 18 in the third round, 15 in the fourth round and 12 in the fifth round. Her winning total was 116 points. Which category did Kay nominate for 3 points per question and which category did she nominate for 2 points per question? [2] … … … … … … … … … … 3 points … 2 points …

5 9694/12/O/N/23 © UCLES 2023 [Turn over 4 Qasim has been invited to a party this Saturday at his friend’s house. The party starts at 18:00 and will finish at 23:30. The distance between Qasim’s house and his friend’s house is 15 km. There is a bus service which stops outside both houses. The price for a bus ticket is $2 plus $0.10 for every kilometre of the journey. If a ticket for the return journey on the same day is bought at the same time then there is a discount of 20% on the price of both tickets. (a) What is the least cost that Qasim could pay to travel to and from the party on the bus? [2] … … … … Qasim would need to leave the party at 22:20 in order to get the last bus home, so he considers using the local taxi service instead. The prices for taxis are as follows: • $0.80 for the first complete kilometre. • $0.50 for each additional complete kilometre for journeys that begin before 23:00. • $0.70 for each additional complete kilometre for journeys that begin after 23:00. Qasim decides that he will stay at the party until it finishes. (b) What is the least cost that Qasim could pay to travel to and from the party? [2] … … … … … Qasim’s friend offers to let him stay overnight at his house, so that he does not have to pay the extra for a taxi. He will get the bus home in the morning instead. Qasim decides that he will give his friend half of the money that he is able to save by staying at his house. (c) How much money will Qasim give to his friend? [1] … … … … …

6 9694/12/O/N/23 © UCLES 2023 5 A concert hall has 33 seats in the front row. The number of seats in each row increases by a constant amount as you move towards the back of the hall. There are 77 seats in the back row. There are more than 5 and fewer than 20 rows of seats. (a) How many seats does the concert hall have? [3] … … … … … … … … … … … For some events, the seats are removed so there is capacity for 1400 people standing. The price of the tickets varies. The first 300 tickets are sold for 30% less than the standard price, the next 900 tickets are sold at the standard price, and the last 200 tickets are sold for more than the standard price. The price for the last 200 tickets is such that, when all 1400 tickets are sold, the average ticket price is equal to the standard price. (b) By what percentage is the price for the last 200 tickets greater than the standard price? [2] … … … … … … … …

7 9694/12/O/N/23 © UCLES 2023 [Turn over 6 A manufacturer operates a process in which each cycle produces one unit of aloop together with one unit of begum. On any day the cost of operating the first cycle is $10, the second $12, the third $14 and subsequent cycles cost $2 more than the previous cycle. The manufacturer receives $10 for each unit of aloop and $15 for each unit of begum she produces. She wants to make as much profit as possible. How many cycles of the process should she operate each day? [2] … … … … … … … … … … … … …

8 9694/12/O/N/23 © UCLES 2023 7 Amy, Bet, Cal, Dev, Eve, Fay, Gus and Huw are competing in a tournament consisting of 6 events. At the end of each event, the eight competitors are ranked in order from first to eighth and awarded points as follows: First 10 points Second 8 points Third 6 points Fourth 5 points Fifth 4 points Sixth 3 points Seventh 2 points Eighth 1 point The first four events have been completed and the top five at present are: Eve 35 points Cal 26 points Gus 22 points Amy 21 points Fay 16 points Fay was disappointed to be ranked seventh in Event 1. However, in the next three events she has improved her position each time. (a) (i) In which positions was Fay ranked in Events 2, 3 and 4? [2] … … … … (ii) Can she still win the tournament? Explain your answer. [2] … … … …

9 9694/12/O/N/23 © UCLES 2023 [Turn over Bet, Dev and Huw all have the same number of points as each other after the first four events. (b) How many points do Bet, Dev and Huw each have? [2] … … … … … … … … … Ian and Joy were two of the eight competitors in last year’s tournament. The scoring system was exactly the same as it is this year. They both scored 30 points, but Ian was ranked in a different position in each of the six events, while Joy was ranked in the same position in every event. (c) In which position was neither Ian nor Joy ranked in any of the events last year? [2] … … … … … … … … … …

10 9694/12/O/N/23 © UCLES 2023 8 The system log at the biscuit factory recorded all failed attempts to login using a password. The passwords are required to be between 8 and 10 characters, and must contain (at least) one upper case letter, one lower case letter, one number, and one symbol. Graham sometimes makes a mistake while typing his password: he either misses or mistypes a character. Graham never makes more than one mistake in any attempt to login. The record shows failures ar&724YQ6 and ar7249Q6 What was his password? Explain how it can be deduced from these failures. [3] … … … … … … … … … … 9 17% of the population in a large seaside town ate fish on any given day. After it was decreed that everyone must eat fish on Friday, the proportion eating fish on each other day reduced to 2%. Do these figures suggest that the average daily consumption has increased or decreased, and by what proportion of the population has it changed? [2] … … … … … … … …

11 9694/12/O/N/23 © UCLES 2023 [Turn over 10 Isabella runs four times per week over various distances and terrains. All her routes take the same amount of time to run. Due to the differing terrains, the average speeds she runs on each route are 4.5 km/h, 6 km/h, 7.5 km/h and 9 km/h. Two of the routes are 3 km and 3.6 km in distance. (a) What are the distances of the other two routes? [3] … … … … … … … … … … One day, she runs the four routes one after each other and reduces all her running speeds by a third. (b) What is her average speed to complete all four routes? [2] … … … … … … … … … …

12 9694/12/O/N/23 © UCLES 2023 11 Yesterday I baked 200 cakes and today I am selling them on a market stall. I am selling the cakes for $5 each, with special offers of 6 for $21 or 10 for $33. With two hours left before the market closes, I have taken $440, but I still have 82 cakes left. Three customers have bought 10 cakes for $33, but nobody has bought more than 10. (a) How many cakes have I sold so far today at the full price of $5? [4] … … … … … … … … … … … Any cakes that I don’t sell in the next two hours will have to be thrown away. (b) What would be my minimum further takings for the day if I could sell all the remaining cakes without altering the current price structure? [2] … … … … … … … … …

13 9694/12/O/N/23 © UCLES 2023 [Turn over I have now decided to reduce the price of the remaining cakes. I will sell them all at the same price each, without any discount for buying 6 or 10. I will fix the price of a cake such that if I sell another 30 my profit for the day will be $200. The total cost to make the cakes was $205 and I have paid $80 to hire the stall for the day. (c) (i) At what price will I now sell my cakes? [2] … … … … … … (ii) What is now the maximum profit I could make today? [1] … … … … … …

14 9694/12/O/N/23 © UCLES 2023 12 Ian and Barbara are taking part in a sponsored walk. Ian has been promised $56 for taking part and an additional $41 for each kilometre that he walks. Barbara has been promised $55 for taking part and an additional $26 for each kilometre that she walks. At the end of the sponsored walk Barbara had walked 10 km more than Ian, and raised $19 more. How much was raised in total by Ian and Barbara? [4] … … … … … … … … … … … … … … … … … … … … … …

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16 9694/12/O/N/23 © UCLES 2023 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

This document consists of 9 printed pages. © UCLES 2023 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/12 Paper 1 Problem Solving October/November 2023 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 2023 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 2023 © UCLES 2023 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 descriptors 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 2023 © UCLES 2023 Page 3 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’. 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 2023 © UCLES 2023 Page 4 of 9 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 2023 © UCLES 2023 Page 5 of 9 Question Answer Marks 1(a)(i) 62 1 1(a)(ii) 76 (should be 75) 1 1(a)(iii) Eagle 1 Question Answer Marks 2 55 1 mark for any of the following: • 28 matches played within the group of eight • 21 matches played within the group of seven • 50 matches played in total 2 Question Answer Marks 3 The difference between her winning total (116) and her total number of correct answers (72) is 44 [1] The only combination that works is 16  2 + 12 History: 3 points; Geography: 2 points 2 Question Answer Marks 4(a) Each ticket costs $2 + 15  $0.10 = $3.50 [1] Both tickets would be $7 Applying 20% discount gives $5.60 SC 1 mark for $6.20 as final answer 2 4(b) The journey home will cost $0.80 + 14  $0.70 [1] = $10.60 The journey to the party will still be cheaper on the bus, costing $3.50 $14.10 2 4(c) Total cost with staying at friend’s house will be $7 Saving is $14.10 – $7 = $7.10 Qasim will give $3.55 to his friend 1

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 6 of 9 Question Answer Marks 5(a) There must be 4 extra seats in each row [1] So there are 12 rows [1] 77 + 73 + 69 + 65 + 61 + 57 + 53 + 49 + 45 + 41 + 37 + 33 = 660 seats SC: 1 mark for answer 275 from 5 rows increasing by 11 each time 3 5(b) Assuming a standard price of $10: 300 tickets sold at 30% discount means $900 have been discounted [1] $900/200 = $4.5 per ticket So the last 200 tickets must be sold at 45% greater than the standard price OR There are 2/3 as many higher-priced tickets, so the percentage differential from the standard must be 3/2  30% = 45% Algebraic: S = standard price N = non-standard price 300(0.7S) +900S + 200N = 1400S [1] N = 1.45S 45% 2 Question Answer Marks 6 The first cycle makes a profit of $15 and the second cycles makes a profit of $13 [1] Each subsequent cycle makes $2 less in profit, so the process is no longer profitable after 8 cycles OR 15/2 = 7.5 [1] 8 cycles 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 7 of 9 Question Answer Marks 7(a)(i) 6th; 4th; 3rd 1 mark for 3rd; 4th; 6th in any order. OR 1 mark for sight of (2 +) 3 + 5 + 6 points (= 16) 2 7(a)(ii) No Eve must score at least 2 more points/37 points [1] Fay can score at most 36 [1] Max 1 mark if Yes is stated 2 7(b) Total number of points awarded in Events 1 – 4 = 156 Total number of points scored by top five = 120 1 mark for either statement Bet, Dev and Huw each have 12 points 2 7(c) Joy scored 5 points each time OR Ian scored 10, 8, 6, 3, 2 and 1 [1] Only 4 points was not scored by either of them, which is fifth position 2 Question Answer Marks 8 ar&7249Q6 [1] The second version (is shorter so) is missing a character so otherwise must be correct [1] The first version has a Y instead of 9, so & must be correct [1] OR ar&7249Q6 [1] The second version doesn’t have a symbol, (so that must be its error and) so the & in the first version must be correct [1] So the Y in the first version must be its error, and should be a 9 [1] 3 Question Answer Marks 9 In 700 meals, was 7*17, now 6*2 + 100 soi [1] 119 then [112 = 16%] so 1% decrease. 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 8 of 9 Question Answer Marks 10(a) 1 mark for finding the time for both of the distances at one of the speeds OR for finding the time for one of the distances at all of the speeds The 3 km route is run at 7.5 km/h and the 3.6 km route is run at 9 km/h [1] The 4.5 km/h route is 1.8 km long The 6 km/h route is 2.4 km long 3 10(b) Reduced speed by a third: 3 km/h, 4 km/h, 5 km/h and 6 km/h [1] Average speed is 4.5 km/h 2 Question Answer Marks 11(a) The 3 sets of 10 cakes sold for $99 So the other 88 cakes sold for $341 [1] 88 cakes @ $5 each would be $440, but each set of 6 reduces this by $9 [1] $99 / 9 is 11 sets of 6 sold [1] So 22 individual cakes OR 88 cakes sold for $341 [1] x + 6y = 88 [1] 5x + 21y = 341 [1] OR 1 mark for 88 cakes sold for $341 [1] 1 mark for a search attempt in which either the total number of cakes is 88 or the total cost is ($)341 1 mark for a second attempt closer to 88 or 341 4 11(b) 7 tens and 2 sixes [1] $273 SC: 1 mark for $274 seen 2 11(c)(i) Profit already is ($440 – $285 =) $155 [1] $45 ÷ 30 = $1.50 2 11(c)(ii) $278 1

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2023 © UCLES 2023 Page 9 of 9 Question Answer Marks 12 If Ian only had the money for participation and Barbara walked 10 km then Ian would raise $56 and Barbara $315, so Barbara would have raised $259 more [1] For each extra kilometre that they both walked the difference would reduce by $15 [1] To reduce the difference by $240 would require 16 km extra to be walked [1] Total raised is $56 + $315 + 16 × ($41 + $26) = $1443 Trial and error method: For any given distance greater than zero calculate amount Ian raised [1] Calculate amount Barbara would raise for 10 km greater distance [1] Choose new value which will move difference closer to $19 and correct calculation of both values [1] Correct answer of $1443 Algebraic: If Ian walks d km: 19 + 56 + 41d = 55 + 26(d + 10) [2] 1 mark for either side correct d = 16 [1] Ian raises $712 and Barbara raises $731, so total is $1443 4