Cambridge A Level Thinking Skills 9694 — 2021 Oct/Nov Paper 1 · Variant 2

This document has 16 pages. Any blank pages are indicated. Cambridge International AS & A Level THINKING SKILLS 9694/12 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 [ ]. * 3 5 4 5 5 4 4 7 9 2 * DC (MB) 205583/2 © UCLES 2021 [Turn over

2 9694/12/O/N/21 © UCLES 2021 1 A local government allocated budgets to sectors of education as shown in the table. Sector of Education Budget for year 2000 Budget for year 2010 Primary $9 000 000 $12 000 000 Secondary $12 000 000 $15 000 000 Higher $6 000 000 $9 000 000 (a) Which sector of education received the greatest percentage increase in its budget from 2000 to 2010? [1] … … … … … … In 2020, the local government returned the budgets back to the proportions the sectors had in 2000. The Primary sector received a $3 000 000 increase in 2020 compared with 2010. (b) How much money did Secondary and Higher each receive in the 2020 budget? [2] … … … … … … … … … …

3 9694/12/O/N/21 © UCLES 2021 [Turn over 2 I have three different shirts (blue, black and brown) and four different hats (brown, white, red and yellow). I will wear my blue shirt with any hat except the white one and my brown shirt with any hat except the yellow one. I will not wear my white hat with my black shirt, but any other combination is possible. (a) How many combinations of shirt and hat can I wear? [1] … … … … … … I am going to give away one of my hats. (b) Giving away which hat would make the smallest reduction to the number of combinations of shirt and hat that I can wear? [1] … … … … … …

4 9694/12/O/N/21 © UCLES 2021 3 George starts making breakfast at 07:00 every morning. His toaster makes 2 slices of toast at a time. It takes the toaster 4 minutes to make 2 slices of brown toast or 3 minutes to make 2 slices of white toast. After the toaster has been used once, it is warm, and, from then on, takes 1 minute less than these times to make subsequent pairs of slices of toast. (a) George has only this one toaster. (i) If George makes only white toast, how many more slices can he make by 07:13 than if he makes only brown toast? [2] … … … … … … (ii) What is the earliest time by which George can make 6 slices of white toast and 6 slices of brown toast? [1] … … … … … … (b) George buys a second identical toaster. What is now the earliest time by which he can make 6 slices of white toast and 6 slices of brown toast? [1] … … … … … … …

5 9694/12/O/N/21 © UCLES 2021 [Turn over 4 Amandeep has a number of tasks that he needs to complete at home this weekend. The tasks and the amount of time that he needs to complete each task are shown in the table below. Task Time required Other information Clean kitchen 2 hours Must be done on Saturday Wash car 1 hour 30 minutes Write report 1 hour Assemble wardrobe 2 hours 15 minutes Must be done on Sunday Practise on drums 1 hour 45 minutes Amandeep also plays for his local cricket team and must attend a practice session on Saturday. He will need to leave home at 11:15 and will arrive back home at 15:15. On each day Amandeep will not start any tasks until 10:00 and he will take a 15-minute break after he completes any task before starting the next. Once he has started any task he will work on the task until it is completed. (a) If Amandeep leaves as many of the tasks as possible until Sunday, what is the earliest time that he could complete the final task on Sunday? [2] … … … … (b) Amandeep decides that he will not work on any tasks after 19:00 on Saturday and wants to make sure that the tasks that remain for Sunday will take the smallest total time possible. Which tasks will Amandeep complete on Sunday? [3] … … … … … … … … …

6 9694/12/O/N/21 © UCLES 2021 5 Cups are sold in 3 different sizes: small, medium and large. Small cups cost $3, medium cups cost $5 and large cups cost $7. I bought some cups and spent a total of $69. (a) If I bought 6 small cups, how many medium and large cups must I have bought? [2] … … … … … … (b) If I bought 5 small cups, how many medium and large cups could I have bought? State all the possibilities. [2] … … … … … …

7 9694/12/O/N/21 © UCLES 2021 [Turn over 6 Suppose the date today is 1 June 2020. In Illyria this is written as a six-digit string: 010620 (day-month-year). In Lilliput this is written as a six-digit string: 060120 (month-day-year). (a) In Illyria, what will be the next date that reads the same from left to right as right to left? [1] … … … … (b) In Lilliput, what will be the next date that reads the same from left to right as right to left? [1] … … … … (c) A six-digit string is ‘ambiguous’ if it represents a valid but different date in each country. What is the next date that is represented by an ambiguous six-digit string in which all six digits are different? [2] … … … … … … … …

8 9694/12/O/N/21 © UCLES 2021 7 In Richard’s cake shop, there are two sizes of cake but only one size of box. The box can contain exactly: • 4 large cakes, OR • 3 large cakes and 2 small cakes, OR • 2 large cakes and 3 small cakes, OR • 5 small cakes. All boxes must be filled in one of these ways; for example, it is not possible to put just 3 small cakes in a box, as they could slide around and get damaged. (a) What is the smallest possible number of boxes that are needed for 10 large cakes and 13 small cakes? State the way in which the boxes should be filled. [2] … … … … … … … … Richard says, “Yesterday, I packed 17 cakes into 4 boxes.” Judy says, “There are 3 different ways in which you could have done that.” (b) State the three different ways. [2] … … … … … … … … …

9 9694/12/O/N/21 © UCLES 2021 [Turn over 8 In Bolandia 50¢ coins weigh 7 grams and 20¢ coins weigh 4 grams. Marc lives in Bolandia. Each day he puts 50¢ coins and 20¢ coins into a jar. At the end of every month he empties the jar and pays the money he has saved into his savings account. On each of the 30 days of last month Marc put at least two 50¢ coins and two 20¢ coins into the jar. When he emptied the jar he discovered that the total weight of the coins was exactly 900 grams. (a) What is the minimum amount that Marc could have saved last month? [2] … … … … … … … … … (b) What is the maximum amount that Marc could have saved last month? [3] … … … … … … … … …

10 9694/12/O/N/21 © UCLES 2021 9 Amir sells stationery supplies to businesses. He has set his price for paper at $8 per box, but, for ‘large’ orders, he offers a discounted rate of $6 per box. The discounted rate applies to all boxes in the order. As a result of this offer it is possible to reduce the total cost of an order by $72, by adding one extra box of paper to the order. What is the smallest number of boxes there can be in a ‘large’ order? [3] … … … … … … … … … … … … … … … … … … … … … … …

11 9694/12/O/N/21 © UCLES 2021 [Turn over 10 A single-track tramline runs for 9.0 kilometres between Beelo and Hiyar. There are no stations in between. It is uphill all the way from Beelo to Hiyar and downhill in the opposite direction. There is a passing place halfway between the two stations. The downhill tram stops at the passing place for 2.5 minutes. It travels at the same constant speed during both halves of its journey, arriving at Beelo 20.5 minutes after departing from Hiyar. The uphill tram travels at a constant speed that is 20% slower than that of the downhill tram and does not stop at all during its journey. How many minutes after departing from Beelo does the uphill tram arrive at Hiyar? [3] … … … … … … … … … … … … … … … … … … … … …

12 9694/12/O/N/21 © UCLES 2021 11 The World Cup for teams playing Flogit is conducted as follows. In the first stage of the tournament, the 24 teams are divided into 4 leagues of 6. In each league each team plays every other team once. The teams coming first and second in each league proceed to the next stage of the tournament, which is a knockout stage. There are four quarter-final matches; the winners of these progress to the semi-finals, followed by the final. (a) How many matches does the winning team play? [1] … … … … … … (b) How many matches in total are there in the tournament? [2] … … … … … … … … …

13 9694/12/O/N/21 © UCLES 2021 [Turn over There are 9 players in each team in any match. No player is allowed to play more than 5 matches in succession. (c) What is the fewest number of players that could have played for the winning team? [2] … … … … … … … … … … … … … … … … …

14 9694/12/O/N/21 © UCLES 2021 12 Assetguarder is a Financial Services Company with nine offices around the world. All nine offices are open for business from 09:00 to 17:00 local time from Monday to Friday each week. The company has an IT Support department, run from the London office. This department must have someone on duty whenever at least one of the offices is open for business. Richard joined the IT Support department at the beginning of February. The local times at the locations of the other offices, compared to London, were as follows during the whole of February: Auckland +13 hours Melbourne +11 hours Singapore +8 hours Cape Town +2 hours Frankfurt +1 hour London – Buenos Aires –3 hours New York –5 hours Vancouver –8 hours Consequently there had to be someone on duty at all times from the first opening time at the beginning of each week to the last closing time at the end of the week. (a) On weekdays during Richard’s first month: (i) which office opened at the same time as the New York office closed? [1] … … … … (ii) for which one-hour period, in London time, was only one of the offices open for business? [3] … … … … … … … …

15 9694/12/O/N/21 © UCLES 2021 (iii) for which one-hour period, in London time, were five of the offices open for business simultaneously? [2] … … … … … … (b) For what length of time was the IT Support department able to close down each weekend during Richard’s first month? [2] … … … … … … … … …

16 9694/12/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 9694/12 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.

9694/12 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.

9694/12 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

9694/12 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

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 5 of 8 Question Answer Marks 1(a) Higher 1 1(b) Secondary: $20 m [1] Higher: $10 m [1] 2 Question Answer Marks 2(a) 9 1 2(b) White 1 Question Answer Marks 3(a)(i) 4 Award 1 mark for either 8 brown or 12 white seen. 2 3(a)(ii) 07:16 1 3(b) 07:09 1 Question Answer Marks 4(a) Total length of tasks in hours is 1.5 + 1 + 2.25 + 1.75 = 6.5 hours [1] There will be three breaks of 15 minutes each. 7 hours 15 minutes after 10:00 is 17:15 SC: 1mark for 17:30 as final answer. 2 4(b) Before going to cricket, Amandeep writes the report. [1] After cricket, Amandeep cleans the kitchen and washes the car [1] Assemble wardrobe and Practise on drums If 0 scored, award 1 mark for a final answer of Assemble wardrobe, Practise on drums and Write report 3 Question Answer Marks 5(a) 69 – (6 × $3) = $51 [1] 6 medium, 3 large 2 5(b) 8 medium and 2 large or 1 medium and 7 large 1 mark for two correct in a list of no more than three OR one correct in a list of no more than two 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 6 of 8 Question Answer Marks 6(a) 021120 1 6(b) Cannot be 021120 because that is before current date. Hence 121121 1 6(c) 12 May 2034 1 mark for 5 December 2034 OR 051234 OR 120534 2 Question Answer Marks 7(a) 5 boxes are needed [1] 2 with 4 large cakes, 1 with 2 large cakes and 3 small cakes, and 2 with 5 small cakes [1] 2 7(b) List of ways 3 boxes with 4 large cakes and 1 box with 3 large cakes and 2 small cakes 3 boxes with 4 large cakes and 1 box with 2 large cakes and 3 small cakes 3 boxes with 4 large cakes and 1 box with 5 small cakes. 2 marks for all three correct and no extras 1 mark for any two correct from the list with no more than one incorrect OR for all three correct from the list and one extra incorrect. 2 Question Answer Marks 8(a) Two of each type of coin per day produces a total value of 30 × 140¢ = 4200¢ and a total weight of 30 × 22 grams = 660 grams. [1] The minimum amount saved would be if the remaining 900 – 660 = 240 grams consisted entirely of 60 × 20¢ coins, giving a total of 4200¢ + 1200¢ = 5400¢. 2 8(b) The extra 240 grams needs to consist of as many 7 grams as possible. [1] The optimum is 32 × 7 grams + 4 × 4 grams. [1] The maximum amount saved is 4200¢ + 1600¢ + 80¢ = 5880¢. 3

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 7 of 8 Question Answer Marks 9 Total saving needs to be $72 plus the $6 spent on an additional box $72 + $6 = $78 [1] Saving on each box is $2 per box 78 ÷ 2 = 39 [1] 40 OR 1 mark for comparison of correct costs for any number of boxes (at least 30) and 1 more than ‘30’. 1 mark for a second comparison of correct costs for a pair of consecutive numbers closer to 39. 40 OR 1 mark for 8x = 6(x + 1) + 72 oe 1 mark for x = 39 40 3 Question Answer Marks 10 Speed of the downhill tram is (9 ÷ 18 =) 0.5 km/min [1] (so) speed of the uphill tram is (80% of 0.5 =) 0.4 km/min [1] Journey time of the uphill tram is (9 ÷ 0.4 =) 22.5 minutes Alternatively: Speed of the downhill tram is (9 ÷ 18/60 =) 30 km/hour [1] (so) speed of the uphill tram is (80% of 30 =) 24 km/hour [1] Journey time of the uphill tram is (9/24 hours =) 22.5 minutes 3 Question Answer Marks 11(a) 5 matches in the league then 3 in the knockout stages, so 8. 1 11(b) 15 matches in each of four leagues [1] 15 × 4 + 7 = 67 SC: 1 mark for 127 (double-counts league matches) 2 11(c) It is possible to use just 2 substitutes with appropriate rotation, making a total of 11 players. 1 mark for a complete scheme for 8 matches or their number of matches from 11a, provided it is greater than 5, shown using fewer than 18 players OR for evidence establishing that 10 is insufficient. 2

9694/12 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2021 © UCLES 2021 Page 8 of 8 Question Answer Marks 12(a)(i) The Melbourne office. 1 12(a)(ii) Singapore [1] 06:00.[1] The Singapore office is the only one open from 06:00 to 07:00. 3 12(a)(iii) 14:00 to 15:00 1 mark for 14:00 OR Cape Town, Frankfurt, London, Buenos Aires and New York 2 12(b) The Vancouver office closed at 01:00 on Saturday (London time) and the Auckland office opened at 20:00 on Sunday [1] so the IT Support department was able to close down for 43 hours. 2