Cambridge A Level Thinking Skills 9694 — 2021 Oct/Nov Paper 1 · Variant 1

This document has 16 pages. Cambridge International AS & A Level THINKING SKILLS 9694/11 Paper 1 Problem Solving October/November 2021 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 [ ]. * 5 8 1 2 4 3 4 7 7 0 * DC (MB) 205582/1 © UCLES 2021 [Turn over

2 9694/11/O/N/21 © UCLES 2021 1 Jane has booked a flight for her holiday tomorrow which departs at 17:30. Passengers are able to enter the airport from 4 hours before the scheduled departure time of the flight and must arrive at least 2 hours before the scheduled departure time. Jane will be taking the train to the airport. Trains leave the station near Jane’s home at 05:20 and every 30 minutes after that. It takes 45 minutes for the train to reach the airport. At what time does the latest train that Jane could take leave the station near her home? [2] … … … … … … … … … … 2 Suzy makes and sells two types of cakes. The prices for which she sells her cakes are shown in the table. Single Pack of 4 Pack of 6 Cupcake $0.80 – $4.50 Muffin $1.00 $3.60 – Jen buys 10 cupcakes and 10 muffins. (a) What is the least possible amount that Jen could pay? [1] … … … … … … …

3 9694/11/O/N/21 © UCLES 2021 [Turn over Keira wants to buy 18 cakes for her employees. At least 9 of the cakes must be cupcakes and at least 7 of the cakes must be muffins. (b) What is the least possible amount that Keira could pay? [2] … … … … … … … … … … … … … It costs Suzy $0.60 to make one muffin. (c) Last Saturday Suzy sold 120 muffins. (i) What was the greatest profit that Suzy could have made on the sale of these muffins? [1] … … … … (ii) What was the least profit that Suzy could have made on the sale of these muffins? [1] … … … …

4 9694/11/O/N/21 © UCLES 2021 3 An electronic notice board, measuring 3 m × 2 m, is mounted on a square wall with sides 6 m × 6 m. Pablo must paint all of the wall not covered by the notice board. A litre of paint covers 2.80 m2 of wall. Paint can be bought in 1 litre cans costing $10 each or 2.5 litre cans costing $20 each. What is the least that Pablo can spend on paint that allows him to complete his painting job? [3] … … … … … … … … … … … … … … … … … … … … … … …

5 9694/11/O/N/21 © UCLES 2021 [Turn over 4 Harriet and Kevin are playing a game. There are a total of 11 rounds in the game and at the end of each round only one of the players will score some points. In each round the number of points scored is equal to the number of the round, so 1 point is scored in round 1, 2 points in round 2 and so on. Harriet and Kevin have played a total of 8 rounds. Harriet has scored a total of 19 points. (a) How many points has Kevin scored? [1] … … … … (b) What is the minimum number of rounds that Harriet can have won so far? [1] … … … … (c) What is the smallest difference that there could be between Harriet’s and Kevin’s scores when they have finished all 11 rounds of the game they are currently playing? [2] … … … … … … … … … … … … …

6 9694/11/O/N/21 © UCLES 2021 5 FlyYou airlines discount their tickets to Timbuktu by up to 80% of the full price of $100. Tickets are sold starting at $20 for the first twenty; then the thirty $50 tickets start to sell, and so on. The number of tickets in each band is shown in the table below. Price $20 $50 $70 $80 $90 $100 Number of tickets 20 30 50 80 100 100 The airline will make a profit if the total value of tickets sold is more than $20 000. How many tickets will have to be sold for the airline to make a profit? [3] … … … … … … … … … … … … … … … … … … … … … …

7 9694/11/O/N/21 © UCLES 2021 [Turn over 6 Each of the three singers (A, B and C) in a trio has a different range of notes they can sing. They want to sing one of four songs (Summer, Bright, Light, and Merry). The diagram shows the ranges of the singers and the highest and lowest notes that each singer is required to sing in each of the four songs. Singers’ Ranges Summer Bright Light Merry A B C A B C A B C A B C A B C High ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ⁞ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ ♪ Low ♪ ♪ Each song has at least one note that is too high or low for someone. However, the songs can be transposed up or down one or two notes, i.e. all the notes for all the singers are moved the same amount in the same direction. Which song can they sing and by how many notes must it be moved? [2] … … … … … … … …

8 9694/11/O/N/21 © UCLES 2021 7 There are four hotels in Kateland. The charges per person and the available facilities at each hotel are given in the table below. These charges apply for any 24-hour period from midday. Hotel Bed and breakfast Dinner Wi-Fi Gym Pool Car parking Argyle $100 $20 $2.50 $3 $2 $10 Banton $90 $25 $4.00 $2 Free $12 City $105 $25 $1.50 No gym No pool Free Devon $120 $22 Free $5 Free $8 Mo and Harry are staying in Kateland for five nights from Monday to Friday inclusive. They will require dinner, bed and breakfast, and Wi-Fi. They will use the pool each morning, but will not use the gym or the car park. They wish to stay in either the Argyle or the Banton. (a) Which hotel would be cheaper, and by how much? [2] … … … … … To attract customers, the Devon hotel introduces three special offers: the total charge for stays of 2, 3, or 4 consecutive nights will be discounted by 10%, 15%, and 25% respectively. These offers can be combined, so for example a 5-night stay can be charged as a 3-night stay and a 2-night stay. Flo will stay at the Devon for six nights next week, from Wednesday to Monday inclusive. She will have dinner, bed and breakfast, but she will not use the gym. She will park her car in the hotel car park. (b) What is the least possible charge for her stay? [2] … … … … … … … … …

9 9694/11/O/N/21 © UCLES 2021 [Turn over These offers are very popular, particularly for stays which include Saturday night. The manager of the Devon sees an opportunity to make more profit if he excludes Saturdays from the offers, and instead increases all the prices for Saturday by 20%. (c) What is the least possible charge that Flo would now have to pay for her stay? [2] … … … … … … … … …

10 9694/11/O/N/21 © UCLES 2021 8 Stella sells dance costumes. White costumes are priced at $10 each and all other colours are priced at $12 each. She has a special offer: 4 costumes of the same colour for the price of 3. The Belle dance group has 14 members and is performing in a show. Its costumes are bought from Stella. For the first dance, the dancers will all wear red costumes. (a) What is the least possible total cost of these 14 costumes? [1] … … … … For the second dance, 4 dancers must wear white costumes and 7 dancers must wear blue costumes. The other 3 dancers may wear white or blue costumes. (b) What is the least possible total cost of these 14 costumes? [2] … … … … … … … … … … … … … … … …

11 9694/11/O/N/21 © UCLES 2021 [Turn over Stella decides to change her prices: she removes the special offer, and reduces the price of each costume. White costumes will be priced at $3 less than any other colour costume. A customer buying 100 white and 200 blue costumes will pay the same total price now as they would have done before the change in pricing. (c) What is the new price for a blue costume? [3] … … … … … … … … … … … …

12 9694/11/O/N/21 © UCLES 2021 9 In the sport of Burgy, points are scored either by getting a snootch giving 7 points, or getting a coff giving 5 points. The local newspaper produced this table of how teams in a local league were performing after each team had played 4 games. Team Played Won Lost Total points scored Total points conceded Epsilon 4 4 0 67 36 Alpha 4 3 1 37 50 Beta 4 2 2 61 51 Gamma 4 2 2 57 47 Delta 4 1 3 42 28 Zeta 4 0 4 23 76 Unfortunately, there is a misprint in one (but only one) of the numbers in the table. (a) Which number has been misprinted? [2] … … … … … … … … (b) What should this number have been? [2] … … … … … … … …

13 9694/11/O/N/21 © UCLES 2021 [Turn over 10 Tom needs to buy some gifts to give to the guests at an event that he is organising. All of the guests will receive the same gift and he has identified four different stores from which he can buy the gifts. The prices available at each of the stores and the different special offers that are available are summarised in the table below. Store Price each Special offers A $2.00 10% off purchases of 60 or more B $1.90 None C $2.20 20% off purchases of 80 or more D $2.00 Set of 20 for $35 Tom is going to buy exactly one gift for every guest at the event. He has worked out that it will be cheaper to buy the gifts from store A than from any other store. At least how many guests are attending the event? [4] … … … … … … … … … … … … … … … … … … …

14 9694/11/O/N/21 © UCLES 2021 11 The only values of coins that are in use in the country where Max lives are worth 1¢, 2¢, 5¢, 25¢ and $1. Max always pays exactly for any purchase that he makes, if he can. If not, he makes the smallest amount of money greater than the price he can with the coins that he has and pays with this. This morning Max had 6 coins. He bought an item from the local shop worth 19¢. He was given his change for his purchase using the smallest number of coins possible. He then had a total of 10 coins. (a) Explain how we can be certain that Max must have paid with a $1 coin. [2] … … … … … … The next item that Max bought cost 32¢, but he had to pay using two 25¢ coins. (b) How much money did Max have left once he had received his change? [3] … … … … … … … … … … … … … …

15 9694/11/O/N/21 © UCLES 2021 [Turn over 12 One cup of tea, 3 cups of coffee and 2 cakes cost $15.75. One cup of tea, 2 cups of coffee and 1 cake cost $10.00. (a) What is the cost of 1 cup of coffee and 1 cake? [1] … … … … … … (b) What is the cost of 3 cups of tea, 5 cups of coffee and 2 cakes? [2] … … … … … … … … … [Turn over for Question 13]

16 9694/11/O/N/21 © UCLES 2021 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. 13 Four friends go to a gym which has four different exercise machines. Bambi, Cherry and Dolly all do 8 minutes of continuous exercise on each machine. Abigail does 10 minutes on three of the machines but only 2 minutes on the other machine. They start at the same time and there can only be one person on any particular machine at any time. What is the shortest possible time in which all four friends can complete their exercise routines? [3] … … … … … … … … … … … … … … … … … … … … …

This document consists of 8 printed pages. © UCLES 2021 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/11 Paper 1 Problem Solving October/November 2021 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 2021 series for most Cambridge IGCSE™, Cambridge International A and AS Level components and some Cambridge O Level components.

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 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.

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 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

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 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

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 5 of 8 Question Answer Marks 1 The latest that Jane could arrive at the airport is 15:30, so she must catch a train that leaves no later than 14:45 [1] The last train not later than this time leaves at 14:20. 2 Question Answer Marks 2(a) $4.50 + 4 × $0.80 + 2 × $3.60 + 2 × $1.00 = $16.90 1 2(b) 10 cupcakes and 8 muffins cost $4.50 + 4 × $0.80 + 2 × $3.60 [1] $14.90 If 0 scored, award 1 mark for $15.10 seen 2 2(c)(i) $48 1 2(c)(ii) $36 1 Question Answer Marks 3 Area needing painting is 62 – 2 × 3 [1] = 30 m2 Amount of paint needed is 30 ÷ 2.8, so 11 litres [1] Least cost is 4 × $20 + 1 × $10 = $90 OR Area needing painting is 62 – 2 × 3 = 30 m2. [1] Large cans are more economical than small cans. 4 large cans will cover 28 m2 [1] and the remaining 2 requires an extra 1 litre can. Total cost is 4 × 20 + 10 = $90 3 Question Answer Marks 4(a) The total number of points scored in the first 8 rounds is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 Kevin must have scored the remaining 36 – 19 = 17 points 1 4(b) 3 1 4(c) Since the two scores are currently very close, it must be the case that one of the players will win two rounds and the other will win one. The final difference will be smallest if the 11 is paired with the 19 [1] Kevin scores a total of 17 + 9 + 10 = 36 Harriet scores a total of 19 + 11 = 30 The difference will be 6. 2

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 6 of 8 Question Answer Marks 5 20 tickets @$20, 30 tickets @$50, 50 tickets @$70, 80 tickets @$80 gives $11 800. A further $8200 needs to be raised from the $90 tickets 1 mark for $11800 or $8200 seen Requires 92 to be sold. 1 mark for division of ‘8200’ by 90 The total number of tickets is 20 + 30 + 50 + 80 + 92 = 272 3 Question Answer Marks 6 (Summer has too large a range for B. Bright would need B to come down but C cannot. Merry would need B down but A and C cannot move down.) Light [1] needs to go up one note [1]. 2 Question Answer Marks 7(a) Argyle: $(100 + 20 + 2.50 + 2) × 2 × 5 = $1245 Banton: $(90 + 25 + 4) × 2 × 5 = $1190 So Banton is cheaper by $55 1 mark for $1245 or $1190 seen or $27.50 seen or $55 without comment that Banton is cheaper 2 7(b) Cost per night = $(120 + 22 + 8) = $150 2 nights at 10% discount + 4 nights at 25% discount with attempt at both calculations [1] = $270 + $450, so $720 Award 1 mark for $765 (from 3 nights + 3 nights) 2 7(c) Split as 3 nights + 2 nights + Saturday. Charge for 3 nights at 15% discount is $382.50 OR Charge for Saturday is $150 + 20% surcharge = $180 [1] Charge for 2 nights at 10% discount is $270 Total charge = $832.50 2

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 7 of 8 Question Answer Marks 8(a) 3 $36 2 $12 × + × = $132 1 8(b) Least cost is for 6 white and 8 blue costumes = $50 + $72 = $122 1 mark for sub-optimal answers $124, $126 or $132 or indication that 8 blue is optimal. 2 8(c) Before, price of 100 white + 200 blue = 25 × $30 + 50 × $36 = $2550 [1] 300 at new price - $300 = $2550 [1] New price = $2850/300 = $9.50 3 Question Answer Marks 9(a) All entries in the points scored and conceded columns must be expressible as 7m + 5n, where m and n are whole numbers. [1] soi Zeta’s total points scored of 23 points is not. 2 9(b) The sum of the entries in the points scored and points conceded columns should be the same. [1] In the table as printed the sum of the points scored column entries is 1 less than the sum of the entries in the goals conceded column. Hence, since there is only one misprint, Zeta must have scored a total of 24 points. 2 Question Answer Marks 10 (A will be cheaper than B and C if) number of guests is at least 60 [1] A search using 60 – 79 with values found for at least A and D [1] A second search using 61 – 79 that moves closer to 76 [1] 76 SC: 3 marks for final answer of 75 OR (B will be cheaper than A if there are fewer than 60 bought and C will be cheaper than A if 80 or more are bought. Therefore) A will be cheaper than B and C in the range 60–79. [1] 60 gifts from store D would cost 3 × 35 = $105 60 gifts from store A would cost 90% of 60 × 2 = $108. [1] Each of the next 19 gifts will cost $1.80 from store A and $2 from store D, so the difference reduces by $0.2 for each extra person [1] so the prices will be equal if 75 are bought and then store A will be cheaper if there are at least 76 guests SC: 3 marks for final answer of 75 4

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 8 of 8 Question Answer Marks 11(a) He cannot have paid with four 5¢ coins, or he would have received only one coin in change OR He cannot have paid with one 25¢ coin, or he would have received only two coins in change [1] (In neither case would he now have ten coins) So he must have paid with a $1 coin. If 0 marks scored, 1 mark for showing $1 coin works with details of the five coins given in the change 2 11(b) Following his first purchase, Max must have had one 1c coin, one 5c coin and three 25c coins and an additional 5 coins. Since he would have been able to make a total of 31c exactly, he cannot have had any more coins with a value of 1c, 2c or 5c. [1] Since his first purchase had to be made with a $1 coin he cannot have had any 25c coins originally, and therefore cannot have more than three 25 coins following the first purchase. [1] Therefore the remaining 5 coins must all be $1 coins. So Max had $5.81 before his second purchase and so he now has 5.81 – 0.32 = $5.49. SC2: 2 marks for final answer of $5.81. 3 Question Answer Marks 12(a) $5.75 1 12(b) 1 tea and 1 coffee costs $4.25 [1] $15.75 + 2 × $4.25 = $24.25 OR 3 tea + 6 coffee + 3 cakes costs 3 × $10 = $30 [1] Subtract cost of 1 coffee + 1 cake = $5.75 giving $24.25 2 Question Answer Marks 13 36 minutes 1 mark for any systematic approach that yields a schedule consistent with the information for the first two ‘rounds’. OR 2 marks for answer of 38 minutes. Example giving 36 minutes: 1 C(8) B(8) (2) D(8) A(10) 2 D(8) C(8) A(10) (2) B(8) 3 A(10) D(8) (2) B(8) C(8) 4 B(8) (4) A(2) (6) C(8) D(8) 3