Cambridge A Level Thinking Skills 9694 — 2021 Oct/Nov Paper 1 · Variant 3

This document has 16 pages. Any blank pages are indicated. Cambridge International AS & A Level DC (DH/CB) 205578/2 © UCLES 2021 [Turn over * 6 7 1 6 0 9 3 7 0 7 * THINKING SKILLS 9694/13 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 [ ].

2 9694/13/O/N/21 © UCLES 2021 1 The table below shows the prices of insurance for a learner driver. Calendar Months Price 1 $90 2 $164 3 $240 This insurance only applies before the test is passed. At that stage it ends, with no refund given. Alice has booked a test in four months’ time. She thinks she is very likely to fail the test. If she does not pass, then she can take another test two months later. (a) What are the four different total possible costs of insurance for all of the first four months? [2] … … … … … … … … Alice is considering two options for her insurance: 1) Pay for four months now, and pay for another two months later if she fails the test. 2) Pay for insurance for six months in advance. (b) If she does fail the first test, which option is cheaper, and by how much? [2] … … … … … … … … …

3 9694/13/O/N/21 © UCLES 2021 [Turn over 2 A knitter needs two balls of yarn to knit a scarf 1.5 metres long, and three balls to knit a scarf 3 metres long. How many balls of yarn will they need to be sure that they can knit a scarf 4.75 metres long? [1] … … … … … … … … … … 3 Blackbeard sailed due south across the ocean until he arrived at a beach on one of a small group of islands. Here he buried the treasure and then sailed off over the horizon due west into the sunset. Show, by marking on the map below, all the parts of the coast or coasts where the treasure could be. [2] N S W E

4 9694/13/O/N/21 © UCLES 2021 4 The following table gives information about the classes held at Shane’s gym. Type of class Length (minutes) Start times Days available Cost per session Spin 40 10:00, 11:00, 14:00, 15:00, 17:00 Monday, Wednesday, Friday $9 Aerobics 45 12:00, 13:15, 14:30 Monday, Tuesday, Wednesday $12 Pilates 60 10:00, 11:30, 13:00, 14:30 Every day $15 Zumba 30 11:00, 13:00, 15:30 Tuesday, Friday $8 All classes start on time. Anyone who wishes to do more than one class needs to allow 20 minutes between the end of one class and the beginning of the next class. Annabel wants to do a Spin class and a Zumba class next Friday. She can start her first class any time after 10:30. (a) (i) If Annabel does the Spin class first, what is the earliest time that she will be able to leave Shane’s? [1] … … … … (ii) If Annabel does the Spin class first, what is the shortest possible time between her arriving at and leaving Shane’s? [1] … … … … … Annabel thinks that if she does the Zumba class first she will spend less time at Shane’s. (b) Show that Annabel is correct in her thinking. [2] … … … …

5 9694/13/O/N/21 © UCLES 2021 [Turn over Belinda intends to visit Shane’s one day next week. She wants to do three different classes and she wants the total cost to be as small as possible. (c) Which day should she choose, and how much will it cost her? [1] … … … … Charlie will visit Shane’s next Friday. She will do three different classes but she cannot arrive before 10:30. (d) (i) Explain why Charlie cannot do the classes in the order Zumba, Spin, Pilates. [2] … … … … … (ii) Charlie wants the least possible time between the beginning of the first class and the end of the third class. What is the least possible time that she can be at Shane’s? State which classes she should choose. [2] … … … … … … … … … …

6 9694/13/O/N/21 © UCLES 2021 5 A shop has three different offers on its video games. These offers are shown in the following table. Offer Details of the offer X Buy 3 games, get the cheapest one at half-price Y Buy 2 games, get the cheaper one at half-price Z Buy 1 game, get any second game for $11 Carrie wishes to buy four games which cost $12, $16, $20 and $26. (a) What is the least amount that Carrie will need to pay? Show how this is achieved. [2] … … … … … … Bill wishes to buy three games. Using offer Z, the least that Bill could pay in total is $39. (b) What is the combined cost of the two cheapest games that Bill wishes to buy? [1] … … … Using offer X, Bill would pay $42 in total. Using offer Y, the least that he could pay in total is $40. (c) What are the costs of each of the three games that Bill wishes to buy? [2] … … … … … … … …

7 9694/13/O/N/21 © UCLES 2021 [Turn over 6 Clive has decided to paint three rooms in his house. He will need 10 litres of red paint for one of the rooms, 12 litres of pink paint for another room and 16 litres of orange paint for the final room. Paint is sold in 2 litre tins and normally costs the same for any colour. However, there is a special offer on red paint, reducing the price of each tin by $3. Clive is considering buying red, white and yellow paint and then mixing it to make the pink and orange paint that he needs. He will make the pink paint by mixing red and white paint in the ratio 2 : 1. He will make the orange paint by mixing equal quantities of red and yellow paint. How much money will Clive save by doing this instead of buying red, pink and orange paint? [3] … … … … … … … … … … … … … … … … … … … … … …

8 9694/13/O/N/21 © UCLES 2021 7 Every morning from Monday to Friday Chris buys a bottle of water, a packet of tuna sandwiches and a packet of plain crisps from the local shop. The amounts that he spent on each day in the last two weeks are shown in the table below. Monday Tuesday Wednesday Thursday Friday Week 1 $2.80 $2.80 $2.80 $2.60 $2.60 Week 2 $2.90 $2.90 $2.00 $2.20 $2.20 The individual full prices of the items have not changed, but there have been offers in place on some of the days: In the first week bottles of water were half price. From Wednesday to Friday of the second week packets of sandwiches were half price. Packets of crisps were reduced in price by the same amount on five of the ten days. (a) Which was the first day on which packets of crisps were reduced in price? [1] … … … … (b) If there were no offers in place on a particular day, what would be the full price for Chris’s items? [2] … … … … … … … … … … … … …

9 9694/13/O/N/21 © UCLES 2021 [Turn over 8 In the game of Snoobill, points are scored by hitting coloured balls. A player continues making attempts until they either fail to hit a ball, hit a ball of a colour they have already hit, or have succeeded in hitting all of the different colours. A red ball scores 1 point, orange 2, yellow 3, green 4, blue 5, violet 6 and black 7. A player’s total score is obtained by adding the points for each colour of ball they have hit. (a) What is the largest total score a player can achieve? [1] … … … … Suppose a player hits 3 colours and scores a total of 12 points. (b) List all the different combinations of the colours of the three balls that would give this score of 12 points. [2] … … … … … … In one game Al and Bert each hit 3 colours, but Al’s total score was 11 points greater than Bert’s. One of the colours Bert hit was yellow (3 points). (c) Which colours did Al hit? [2] … … … … … … … …

10 9694/13/O/N/21 © UCLES 2021 9 A local shop sells spring water in bottles of three different sizes. The sizes and prices of the bottles are shown in the following table. Bottle size 1 litre 2 litres 5 litres Price $8 $15 $35 There is a special offer: any 4 bottles of the same size for the price of 3. (a) What is the least possible cost of buying 5 litres of this water? [1] … … … … (b) What is the least possible cost of buying exactly 15 litres of this water? [2] … … … … … … … … … … (c) How could 15 litres of this water be obtained more cheaply from this shop? [1] … … … … … …

11 9694/13/O/N/21 © UCLES 2021 [Turn over 10 Buses run regularly between Garton and Hendy. They leave Garton on the hour and at 30 minutes past the hour from 07:00 until 22:30. They leave Hendy at 10 and 40 minutes past each hour from 07:10 until 22:10. The journey in either direction takes 75 minutes. When a bus arrives at Garton or Hendy, it leaves again for the return journey after a break of at least 5 minutes and it becomes the next bus in the other direction. No other buses travel between Garton and Hendy. (a) At what time will the 07:00 bus from Garton to Hendy leave Garton for the second time? [1] … … … … (b) How many times in a day will the bus that makes the 07:00 journey from Garton to Hendy leave Garton? [1] … … … … Bill is driving the 08:40 bus from Hendy to Garton. (c) How many buses will he pass that are travelling from Garton to Hendy? State the times that these buses leave Garton. [2] … … … … (d) How many buses are required to provide the return bus service between Garton and Hendy? Explain your answer. [2] … … … … … …

12 9694/13/O/N/21 © UCLES 2021 11 A box for the secure storage of keys has 11 buttons: digits 0–9 and Reset. 0 1 2 3 4 5 6 7 8 Reset 9 The box is opened by pressing Reset, entering a code and then pulling a lever. The code must have between one and five different digits (inclusive). The physical mechanism used means that it is not possible to press both of a pair of digits on a row, and the order in which the digits are pressed does not make any difference. This means that Reset 1 9 2 7 and Reset 1 2 7 9 are the same, but Reset 1 9 2 8 is not possible. (a) How many 5-digit codes are there? [1] … … … (b) How many different codes are possible? [3] … … … … … … … … (c) Give one reason why the makers recommend selecting 3- or 4-digit codes rather than 5-digit ones. [1] … … …

13 9694/13/O/N/21 © UCLES 2021 12 On a shopping trip, Mr Alexander took with him twice as much money as Mrs Alexander took with her. During the trip, Mrs Alexander spent twice as much money as Mr Alexander spent. When they returned home, Mr Alexander had three times as much money left as Mrs Alexander did. (a) If Mr Alexander spent $7, how much money did Mrs Alexander return home with? [2] … … … … … … (b) If Mrs Alexander returned home with $33, how much money did Mr Alexander spend? [1] … … … … … …

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16 9694/13/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. BLANK PAGE

This document consists of 8 printed pages. © UCLES 2021 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/13 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.

9694/13 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.

9694/13 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

9694/13 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

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 5 of 8 Question Answer Marks 1(a) 1 + 1 + 1 + 1: $90 + 90 + 90 +90 = $360 2 + 1 + 1: $164 + 90 + 90 = $344 2 + 2: $164 + 164 = $328 3 + 1: $240 + 90 = $330 1 mark for any three correct 2 1(b) Option 1: $164 + $164 + $164 = $492 ft Option 2: $240 + 240 = $480 1 mark for either correct total Option 2 is cheaper by $12 2 Question Answer Marks 2 5 1 Question Answer Marks 3 1 mark for any two marked correctly No incorrect additions for 2 marks 2 Question Answer Marks 4(a)(i) Spin: 11:00 to 11:40, Zumba: 13:00, ending at 13:30 1 4(a)(ii) Spin: 14:00 to 14:40, Zumba: 15;30 to 16:00, so 2 hours 1 4(b) Zumba: 13:00 to 13:30, Spin: 14:00 to 14.40 [1] so 1 hour 40 minutes which is less than 2 hours 2 4(c) Friday, $32 1 4(d)(i) 2 marks for a clearly expressed correct answer 1 mark for correct answer that omits the time for Spin She cannot start the Spin class earlier than 14:00, so will be too late for last Pilates class at 14:30. OR The latest Pilates class starts at 14:30, so she cannot start the Spin class earlier than 11:00. 2 4(d)(ii) Pilates 11:30 [1] Zumba 13:00 and Spin 14:00 3 hours 10 minutes [1] 2

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 6 of 8 Question Answer Marks 5(a) Use offer Z twice: $26 and $12 for $23 and $16 and $20 for $27 [1] Total $50 [1] 2 5(b) $28 1 5(c) Difference in cost between two cheapest games is $4 [1] Costs are $12, $16 and $20 OR simultaneous equations: Cost (in $) x, y, z: x + y + 0.5z = 42 and x + 0.5y +z = 40 or equivalent [1] Costs are $12, $16 and $20 2 Question Answer Marks 6 The 12 litres of pink paint will require 8 litres of red and 4 litres of white. The 16 litres of orange paint will require 8 litres of red and 8 litres of yellow. 1 mark for either Therefore a total of 26 litres of red paint, 4 litres of white and 8 litres of yellow are required. An additional 16 litres of red paint will be bought compared to buying individual colours. [1] 16 litres of paint will require 8 tins. The saving will be $24 OR Mixing the pink paint will mean that an additional 8 litres of red paint will be bought instead of pink. [1] Mixing the orange paint will mean that an additional 8 litres of red paint will be bought instead of orange. [1] 16 litres of paint will require 8 tins. The saving will be $24 OR Without mixing paints, cost = $(19x – 15) [1] With mixing, cost = $(19x – 39) [1] Saving = $(39 – 15) = $24 3 Question Answer Marks 7(a) Thursday of week 1 1 7(b) The only difference between Wednesday and Thursday of week 1 is the offer starting on crisps. The reduction on packets of crisps must be 20¢ [1] The offer on crisps is the only offer in place on Monday (and Tuesday) of week 2, so the full price must be $2.90 + $0.20 = $3.10. 2

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 7 of 8 Question Answer Marks 8(a) 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 1 8(b) (R, G, Black); (O, Y, Black); (R, Blue, V); (O, G, V); (Y, G, Blue) OR (1, 4, 7); (2, 3, 7); (1, 5, 6); (2, 4, 6); (3, 4, 5) 2 marks for all five and no incorrect. 1 mark for five correct and no more than two extras OR four correct and no more than one incorrect OR three correct and no incorrect 2 8(c) green, violet, black OR (4, 6, 7) 1 mark for Bert (1, 2, 3) oe OR Al (5, 6, 7) and Bert (1, 2, 4) oe 2 Question Answer Marks 9(a) 3 × $8 + $8 = $32 1 9(b) 4 × 2l + 4 ×1l + 2l + 1l costs $(45 + 24 + 15 + 8) = $92 1 mark for any correct calculation for 15l except $105: e.g. $93, $95, $96, $98 2 9(c) 16 litres can be bought as 8 × 2l, costing 2 × $45 = $90 1 Question Answer Marks 10(a) Arrives at Hendy at 08:15, leaves at 08:40, arrives 09:55. Becomes the 10:00 1 10(b) 6 1 10(c) Passes all buses from Garton that are on their journey between 08:40 and 09:55. These are the 07:30, 08:00, 08:30, 09:00, 09:30, a total of 5 1 mark for a list with one extra/omission 2 10(d) 2 marks for 6 with a fully correct explanation 1 mark for 6 with a vague or incomplete explanation The first bus from Garton becomes the 08:40 from Hendy, so 07:10, 07:40 and 08:10 are needed. First bus from Hendy becomes the 08:30 from Garton, so 07:00, 07:30, 08:00 are needed, total number of buses needed is 6. OR Bus returns to starting point every 3 hours. 6 buses leave Garton (or Hendy) every 3 hours, so number of buses needed is 6. OR Since 5 buses are passed on the journey of one bus, and this bus becomes the ‘next’ bus, a total of 6 buses are needed. 2

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 8 of 8 Question Answer Marks 11(a) 2 × 2 × 2 × 2 × 2 = 32. 1 11(b) In each row there are three possibilities [1] (nothing, left, right), and each of the five rows is independent, but all ‘nothing’ is excluded [1]: 3 × 3 × 3 × 3 × 3 – 1 = 242 OR Number of 1 digit numbers = 10 Number of 2 digit numbers = 40 Number of 3 digit numbers = 80 Number of 4 digit numbers = 80 Number of 5 digit numbers = 32 2 marks for 4 correct OR 1 mark for 2 correct Total = 242 3 11(c) Valid reason stated sufficiently clearly, e.g. • There are more of these than 5 digit codes • The least chance of guessing comes from using the widest possible choice • Practical suggestions such as to reduce mechanical wear 1 Question Answer Marks 12(a) $21 1 mark for any pair of calculations that satisfy two of the three criteria OR 1 mark for 2x – 7 = 3(x – 14) oe OR 1 mark for $63 (the amount Mr Alexander returned home with) 2 12(b) $11 1