Cambridge A Level Thinking Skills 9694 — 2020 Oct/Nov Paper 1 · Variant 2

Cambridge International AS & A Level This document has 16 pages. Blank pages are indicated. THINKING SKILLS 9694/12 Paper 1 Problem Solving October/November 2020 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 [ ]. * 0 3 2 7 1 6 7 2 5 5 * DC (CJ/SW) 188494/3 © UCLES 2020 [Turn over

2 9694/12/O/N/20 © UCLES 2020 1 A cake decorator charges a fixed fee for icing a message onto a cake, together with a fixed charge per letter of the message. The message “Congratulations” costs a total of $18.25, while “Happy Birthday” costs a total of $16.95. What is the fixed fee? [2] … … … … … … … … … 2 The admission price to a theme park is determined by the size of the group entering. The admission prices for all group sizes are given in the table below. Number in group 1 2 3 4 5 6 7 to 9 10 to 15 16 to 20 21+ Admission price $10 $19 $28 $36 $43 $49 $60 $80 $100 $164 27 students arrive together and decide to arrange themselves in groups so that in total they pay the least possible admission price. What is the total admission price the students pay? [2] … … … … … … … … …

3 9694/12/O/N/20 © UCLES 2020 [Turn over 3 Daphne and Eric buy ice creams from the local stall. They both always choose one scoop of each of two different flavours. The flavours they choose from are chocolate, coffee, lemon, mango, pistachio, strawberry, and vanilla. Daphne does not eat pistachio and Eric does not eat chocolate or coffee ice cream. How many more ice cream combinations can Daphne choose from compared to Eric? [3] … … … … … … … … … … … … … … … … … … … … … … … … …

4 9694/12/O/N/20 © UCLES 2020 4 Details of the films showing at the five studios of the Elsinore Cinema Complex this week are as follows: Studio Film Running time Screenings daily at: 1 The Question 118 mins 11:30 13:50 16:10 18:30 20:50 – 2 Slings And Arrows 102 mins 11:15 13:15 15:15 17:15 19:15 21:15 3 Outrageous Fortune 131 mins 11:00 13:30 16:00 18:30 21:00 – 4 Take Arms 93 mins 11:40 13:30 15:20 17:10 19:00 20:50 5 Sea Of Trouble 124 mins 11:20 13:45 16:10 18:35 21:00 – All the times of the screenings in the table are the times at which the films start. Adverts and trailers are shown between screenings. All tickets are for one specific screening only, in a specified seat. They cost $5 for all screenings that begin before 18:00 and $8 for all screenings from 18:00 onwards. Studios 1 and 2 both have 250 seats, Studios 3 and 4 both have 200 seats and Studio 5 has 150 seats. (a) Horatio and Ophelia have arranged to meet today to see the 15:15 screening of Slings And Arrows. They also intend to see the next film that begins after Slings And Arrows has finished. At what time will their second film finish? [2] … … … … … … … … …

5 9694/12/O/N/20 © UCLES 2020 [Turn over Slings And Arrows has been very popular. Yesterday’s ticket sales for Studio 2 totalled $6760. (b) (i) What is the total number of tickets available for Studio 2 each day this week? [1] … … … … … … (ii) What is the minimum number of tickets that could have been sold for Studio 2 yesterday? [3] … … … … … … … … … … … …

6 9694/12/O/N/20 © UCLES 2020 5 Thursday is Quiz Night at Wenwatt Social Club. Contestants compete for a sum of money known as the ‘Horde’. Each week there are 50 questions and the contestant with the most correct answers wins all or part of the Horde, depending upon the winning score, as follows: Winning Score Prize money 47–50 the whole Horde 43–46 $90 39–42 $75 35–38 $60 less than 35 $40 If two or more contestants have the same winning score, they share the prize money, but the prize money is reduced (if necessary) to the largest amount that will give each person a multiple of $5. For instance, if three contestants have a winning score of 44 correct answers they win $30 each, but if four contestants have a winning score of 44 the prize money is reduced to $80 and the contestants win $20 each. On any particular Thursday the Horde consists of the amount left over from the previous week (if any) plus $125. Three weeks ago one contestant had a winning score of 48 and won a record $765. Two weeks ago there were three winners, with a score of 36. Last week there were two winners, with a score of 41. How much will the Horde be this week? [3] … … … … … … … … … … … … … …

7 9694/12/O/N/20 © UCLES 2020 [Turn over 6 Last autumn I bought and planted 30 daffodil bulbs, 30 tulip bulbs and 30 hyacinth bulbs, but only 54 of the bulbs grew. The resulting display of flowers in my garden had 5 more tulips than hyacinths and 2 more daffodils than tulips. How many of the daffodil bulbs grew? [3] … … … … … … … … … … … … … … … … … … … … … … … … …

8 9694/12/O/N/20 © UCLES 2020 7 Between 01:00 and 02:00, Bill’s clock works normally, with the minute hand moving forwards 1 minute every minute. Between 02:00 and 03:00 – in real time – the minute hand on Bill’s clock moves at half of the correct speed, showing 1 minute’s progress every 2 minutes. Between 03:00 and 04:00 (real time), the minute hand on Bill’s clock moves even slower, showing 1 minute’s progress every 3 minutes of real time. This pattern continues for subsequent hours. (a) Bill sets his clock to 01:00 when the real time is also 01:00. What time will Bill’s clock show when the real time is 07:00? [2] … … … … … … … … … … (b) When the real time is 03:30, Bill decides to set his clock to 02:30. What time will Bill’s clock show when the real time is 06:30? [2] … … … … … … … … … … …

9 9694/12/O/N/20 © UCLES 2020 [Turn over 8 The normal cost of entry to Phelthorpe Swimming Pool is $4 per session. A year ago a Splash! card was introduced, aimed at regular swimmers. Valid for twelve months, and costing $25, it entitles the holder to use the pool for $2 per session for the first 6 sessions, then unlimited use for $1 per session. Rebecca decided not to buy a Splash! card, but now she wishes she had bought one, having used the pool 23 times during the last twelve months. (a) How much would Rebecca have saved over the last twelve months if she had bought a Splash! card? [2] … … … … … … … … … It has been proposed to change the Splash! card so that customers pay a fixed amount monthly for the card and then only pay $1 for each visit to the pool. The monthly price will be a whole number of dollars, and set so that swimmers must use the pool at least 5 times in the month in order to save money by owning the card. (b) What is the cheapest monthly price that could be set for the new Splash! card? [2] … … … … … … … … …

10 9694/12/O/N/20 © UCLES 2020 9 A referendum has been held in the district of Mirth, to determine whether it should declare independence from Bolandia. All adult members of the district could vote; all of them either voted in favour of independence or voted against it, or did not vote at all. According to the local newspapers: ‘80% of those who voted voted in favour of independence’ and ‘80% of the adult members of the district did not vote for independence’ (a) What percentage of the adult members of the district voted against independence? [2] … … … … … … … … … (b) What percentage of the adult members of the district did not vote? [1] … … … … … (c) What percentage of those who did not vote would have had to have voted against independence, in order to ensure that as many voted in favour as voted against? [1] … … … … … …

11 9694/12/O/N/20 © UCLES 2020 [Turn over 10 The clear waters between Scylla and Charybdis have not been charted, but the depth has been measured 10 m from each bank. In both cases it was 6 m. The river is 60 m across. Little sea monsters live in the river. Penelope knows that any two sea monsters could see each other, wherever they are in the water. (a) (i) What is the maximum possible depth 5 m from one of the banks? … [1] (ii) What is the maximum possible depth 20 m from the same bank? … [1] (iii) Why can it not be both of these at the same time? … … [1] The depth 20 m from the Charybdis bank is measured as 8 m. Diomedes has to identify a channel for boats which is at least 7 m deep. (b) (i) What is the minimum width that he can be sure is available, and where is it? [2] … … … … (ii) What is the maximum possible depth? [1] … …

12 9694/12/O/N/20 © UCLES 2020 11 In a quiz show, four contestants are asked 24 questions each. Every correct answer scores 5 points but 1 point is deducted for every wrong answer. There is no penalty for choosing not to answer a question by passing. The contestant with the highest score is the winner of the show, and gets an opportunity to win the money in the prize pot. At the beginning of each show, the prize pot contains any money left in it after the previous show. Once the contestants have answered all their questions, their scores are added up and $10 is added to the prize pot for each point in the total. (a) What is the maximum amount that the prize pot can increase by in one show? [1] … … … … Today’s contestants and their scores were: Clare 81 Simon 77 Angela 65 Paul 63 In today’s show, there were a total of 16 passes. (b) How many of today’s questions were answered correctly? [4] … … … … … … … … … … … … …

13 9694/12/O/N/20 © UCLES 2020 [Turn over The winner of the show is given four puzzles to solve within a time limit. The amount they win depends on how many they solve correctly: 4 correct – the whole prize pot 3 correct – 50% of the prize pot 2 correct – 25% of the prize pot 1 correct – 10% of the prize pot 0 correct – nothing Clare solved three of the four puzzles correctly. She won $2050. (c) What was the value of the prize pot at the beginning of today’s show? [2] … … … … … … … … … … [Turn over for Question 12]

14 9694/12/O/N/20 © UCLES 2020 12 At a conference the 100 delegates were asked to rank three possible menus (A, B and C) in order of preference for dinner. All the delegates completed this ranking. 55 ranked A above B; 65 ranked B above C; 35 ranked C above A. B was ranked first by 40 delegates. (a) Megan correctly deduces that the number of delegates who ranked the menus in the order CBA is 5. Explain how she can know this. [1] … … … … 30 delegates ranked A third. (b) Deduce the number of delegates who chose each of the other five possible orders of preference. [5] … … … … … … … … … … … ABC = … ACB = … BAC = … BCA = … CAB = …

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16 9694/12/O/N/20 © UCLES 2020 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 the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge. BLANK PAGE

This document consists of 8 printed pages. © UCLES 2020 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/12 Paper 1 Problem Solving October/November 2020 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 2020 series for most Cambridge IGCSE™, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 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 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 2020 © UCLES 2020 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’. 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 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 2020 © UCLES 2020 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 that this helps to identify the precise piece of the working to which another stamp pertains (or an inexplicit correct answer). Correct item Incorrect item Individual mark of partial credit Double mark of partial credit Essential element of answer/working missing Correct follow through Transcription error Judged to be not good enough to earn the relevant credit Benefit of doubt Working seen but no credit awarded; blank page checked Highlight Identifies the part of the working to which another stamp pertains

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 5 of 8 Question Answer Marks 1 ‘Congratulations’ has 2 more letters than ‘Happy Birthday’ and costs $1.30 more, so each letter must cost $0.65. [1] This means that the fixed fee must be $8.50 2 Question Answer Marks 2 Dividing into groups of 20, 6 and 1 yields $159 which is the lowest possible. 1 mark for $160 (e.g. groups of 20 and 7) 2 Question Answer Marks 3 The options available are: Daphne: (ch,co), (ch,l), (ch,m), (ch,s), (ch,v), (co,l), (co,m), (co,s), (co,v), (l,m), (l,s), (l,v), (m,s), (m,v), (s,v). Eric: (l,m), (l,p), (l,s), (l,v), (p,m), (p,s), (p,v), (m,s), (m,v), (s,v). 1 mark for obtaining at least 6 options from 1 list. OR Totals are Daphne: 15, Eric: 10 2 marks for either correct value identified with the person. 15 – 10 = 5. 3 Question Answer Marks 4(a) (Slings And Arrows will finish at 16:57, so) their second film will be the (Take Arms) 17:10 [1] which will finish at 18:43. 2 4(b)(i) (6 screenings × 250 seats =) 1500 1 4(b)(ii) 500 tickets were available at $8 [1] So at least ($6760 – $4000 =) $2760 [1] came from a minimum of 552 tickets sold at $5 each, the minimum number of tickets that could have been sold yesterday for Studio 2 is 1052. 3

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 6 of 8 Question Answer Marks 5 Two weeks ago the ‘Horde’ was $125 and the prize money was $60 ($20 × 3), so last week’s ‘Horde’ was $125 – $60 + $125 = $190. [1] Last week’s prize money was $35 × 2 = $70. [1] So this week’s ‘Horde’ will be $190 – $70 + $125 = $245. 3 Question Answer Marks 6 The number of daffodils (d) = t + 2 The number of hyacinths (h) = t – 5 1 mark for both correct relations Therefore 3t – 3 = 54 oe [1] The number of tulips is 19, so 21 daffodils grew. Search method: The criteria for the search are (t = h + 5 AND d = t + 2) and total = 54. 1 mark for an initial search that meets either one of the criteria 1 mark for an adjustment that gets closer to the solution 3 Question Answer Marks 7(a) The successive times on Bill’s clock will be: real time 2:00: 2:00 real time 3:00: 2:30 real time 4:00: 2:50 1 mark for this time or better real time 5:00: 3:05 real time 6:00: 3:17 real time 7:00: 3:27 SC: 1 mark for seeing all of 30, 20, 15, 12 and 10 2 7(b) The successive times on Bill’s clock will be: real time 3:30: 2:30 real time 4:00: 2:40 real time 5:00: 2:55 1 mark for this time or better real time 6:00: 3:07 real time 6:30: 3:12 SC: 1 mark for seeing all of 10, 15, 12 and 5 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 7 of 8 Question Answer Marks 8(a) 23 visits to the pool cost Rebecca 23 × $4 = $92. With a Splash! card she would have paid $25 + (6 × $2) + (17 × 1) = $54. 1 mark for either $92 or $54. $92 – $54 = $38 2 8(b) The cheapest price will be such that 4 visits would cost the same either with or without the card. [1] 4 visits without the card would cost $16, so the monthly price of the card would be $12. SC: 1 mark for final answer of $14 (makes 5 visits cheaper but not cheapest possible). 2 Question Answer Marks 9(a) 20% of the district must have voted for independence [1] and that constituted 80% of those who voted, so % who voted is 25% % who voted against is 25 – 20 = 5% 2 9(b) 20% and 5% voted: % who did not vote is 75% 1 9(c) 15/75 = 20% 1 Question Answer Marks 10(a)(i) 6 m 1 10(a)(ii) 12 m 1 10(a)(iii) Second case has bed of river straight from bank, other has flat bottom; it cannot be both. 1 10(b)(i) 20 m [1] between 25 m and 45 m from the Scylla bank / between 15 m and 35 m from the Charybdis bank [1] 2 10(b)(ii) 12 m 1

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2020 © UCLES 2020 Page 8 of 8 Question Answer Marks 11(a) $4800 (96 × 5 × $10) 1 11(b) 286 points (81 + 77 + 65 + 63) were scored from 80 questions (96 – 16). A search reveals that (61 × 5) – (19 × 1) = 286, therefore the total number of correct answers was 61. The criteria for the search are {total score = 286} and {total questions = 96 OR correct + incorrect = 80} 1 mark for using total of individual scores (286) 1 mark for an initial search that meets either one of the criteria for the totals 1 mark for an adjustment that gets closer to the solution If no marks scored, 1 mark for any individual’s score achieved with 24 or fewer questions 4 11(c) Clare won 50% of the prize pot, so it was $4100. 286 points were scored in the show, adding $2860 to the pot. 1 mark for either value. At the start of the show the pot contained $1240 2 Question Answer Marks 12(a) 55 preferring A to B means that 45 preferred B to A, and this includes 40 with B first choice. Hence the number with order CBA is 5. 1 12(b) ABC is 25 [1] ACB is 25 [1] BAC is 15 [1] BCA is 25 [1] CAB is 5 [1] 5