Cambridge A Level Thinking Skills 9694 — 2020 May/June Paper 1 · Variant 1

Cambridge International AS & A Level DC (JC/CT) 188390/1 © UCLES 2020 [Turn over This document has 16 pages. Blank pages are indicated. * 4 5 7 3 7 4 7 8 3 1 * THINKING SKILLS 9694/11 Paper 1 Problem Solving May/June 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 [ ].

2 9694/11/M/J/20 © UCLES 2020 1 Brian’s birthday is on 10 January and he is having a party that day. Five days before this, he is meeting his brother for lunch and ten days after his birthday he is meeting his sister for lunch. Both of these lunch meetings are at the weekend (i.e. on Saturday or Sunday). On which day of the week is Brian’s birthday? [1] … … … … … … … … … … 2 A venue holds a concert on the last Saturday of each month. Tickets go on sale on the Sunday before the concert, with a decrease in price each day, as shown in the following table. Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Ticket price $100 $90 $80 $70 $60 $50 $40 There are 500 tickets available for each concert. Sometimes the tickets sell very quickly. In January, 50 tickets were sold each day from Sunday to Friday and the remaining tickets were sold on the Saturday. (a) What was the total income from the ticket sales? [1] … … … … … … … …

3 9694/11/M/J/20 © UCLES 2020 [Turn over In February, the last available ticket was sold on the Wednesday. (b) (i) What was the greatest possible income from the ticket sales? [1] … … … … (ii) What was the least possible income from the ticket sales? [1] … … … … In March, all tickets were sold by the end of the Thursday. Each day the number of tickets sold was 40 fewer than the previous day. (c) How many tickets were sold on the Thursday? [2] … … … … … … … …

4 9694/11/M/J/20 © UCLES 2020 3 There are ten teams in the Rodentian Football League. During each season every team plays two matches against each of the other teams; once at home and once away from home. Points are awarded as follows: Win away from home 4 points Win at home 3 points Draw away from home 2 points Draw at home 1 point Loss 0 points Two days ago the league table was as shown below. Team Played Won Drawn Lost Goals scored Points For Against Squirrels 9 6 2 1 18 10 24 Jerboas 9 5 3 1 21 11 22 Porcupines 9 5 2 2 17 10 22 Agoutis 9 6 0 3 19 16 20 Marmots 9 3 4 2 19 13 17 Lemmings 9 4 1 4 16 12 15 Beavers 9 2 3 4 14 17 12 Coypus 9 3 1 5 13 19 11 Hamsters 9 0 4 5 11 22 8 Gophers 9 0 2 7 6 24 3 Three matches were played yesterday afternoon and this is the updated table. Team Played Won Drawn Lost Goals scored Points For Against Porcupines 10 6 2 2 19 11 25 Squirrels 9 6 2 1 18 10 24 Jerboas 10 5 3 2 22 14 22 Agoutis 9 6 0 3 19 16 20 Marmots 9 3 4 2 19 13 17 Beavers 10 3 3 4 17 18 16 Lemmings 10 4 1 5 17 14 15 Coypus 10 3 2 5 14 20 12 Hamsters 9 0 4 5 11 22 8 Gophers 10 0 3 7 7 25 5

5 9694/11/M/J/20 © UCLES 2020 [Turn over (a) What is the total number of matches that have been drawn so far this season, including yesterday’s results? [1] … … … … (b) How many matches have the Agoutis won away from home so far this season? Justify your answer. [2] … … … … … … … … … … (c) Which team did the Porcupines beat yesterday to go to the top of the table? Justify your answer. [2] … … … … … … … … … …

6 9694/11/M/J/20 © UCLES 2020 4 Bill and Mary Jones will be staying in a hotel in Townsville on Friday night. The prices and facilities at the four hotels in Townsville are shown in the following table. Hotel Single room, per night Double room, per night Gym Sauna Wi-Fi Room only Breakfast included Room only Breakfast included Plaza $140 $150 $190 $210 Yes Yes Yes Village $90 $100 $155 $160 Yes No No Garden $150 $165 $195 $205 Yes No Yes Coral $120 $125 $175 $195 No Yes Yes Bill and Mary want a double room, with breakfast included. They do not mind whether or not there is a gym or sauna, but do want Wi-Fi. (a) Which hotel should Bill and Mary choose in order to pay the least possible for their stay? [1] … … … … Bill and Mary’s son Euan has decided to come with them to Townsville. Euan must stay in the same hotel as his parents. He wants a single room, a gym and Wi-Fi, but does not want breakfast. The Joneses will choose the cheapest hotel that meets all of their requirements. (b) What is the least possible that the Jones family will now have to pay for their holiday? [2] … … … … … … … …

7 9694/11/M/J/20 © UCLES 2020 [Turn over 5 My 6-digit passcode for internet banking is made up of: my house number; followed by half my house number, minus one; followed by double my house number, plus one. All six digits are different. The first number of my passcode is 2. What is my full passcode? [2] … … … … … … … … … … … … … … … … … … … … … … … … …

8 9694/11/M/J/20 © UCLES 2020 6 When I arrived at Barnoff railway station yesterday evening I noticed that the clocks on platforms 1 and 2 were displaying different times, as follows: Platform 1 Platform 2 A few seconds later they both changed, simultaneously, to: After watching them both for several minutes, I concluded that the last digit of the platform 2 clock was faulty, with one element that was permanently on and one element that was permanently off. For how many minutes altogether during each hour are the displays on both of these clocks identical? [3] … … … … … … … … … … … … … … …

9 9694/11/M/J/20 © UCLES 2020 [Turn over 7 The following table gives the cost of tickets for entry into the Penguin Theme Park. Type of ticket Cost Adult $40 Child $25 Family (2 adults and 2 children) $120 Group (up to 10 people) $350 Tickets can only be used on the day on which they are bought. Every child must be accompanied by an adult; each adult can only be responsible for one child. Last Saturday, the total money taken in ticket sales was $18 000. (a) What was the least possible number of people that entered the park last Saturday? [1] … … … (b) What was the greatest possible number of people that entered the park last Saturday? [2] … … … … Last Monday, 279 adults and 160 children visited the park. (c) What was the least possible amount that was taken in ticket sales last Monday? [3] … … … … … … … … …

10 9694/11/M/J/20 © UCLES 2020 8 I am on holiday in Dolbania. Five different denominations of coin are in circulation here. I know they are worth 5¢, 10¢, 25¢, 50¢ and $1, but I don’t know which is which and the values are not marked on them. One of the coins has a star on it, one has a tree, one has a cat, one has a bird and one has a fish. I visit the same cafe every morning. Normally I buy a cup of coffee and a slice of carrot cake. The cost is $3.20 and I pay with a $5 note. On the first morning I received 3 ‘fish’ coins and 3 ‘cat’ coins as change; on the second morning my change was 5 ‘fish’ coins, 5 ‘bird’ coins and 1 ‘star’ coin. (a) What is the value of the ‘cat’ coin? [2] … … … … … … … … … … Today I had my usual cup of coffee but I ordered two slices of carrot cake. Once again I paid with a $5 note, and this time my change was a single ‘cat’ coin. (b) How much does my cup of coffee cost? [1] … … … … … … …

11 9694/11/M/J/20 © UCLES 2020 [Turn over 9 Six students sat tests in Mathematics, English and Science. Their scores in English and Science were plotted against their scores for Mathematics in a scatterplot. By mistake, the dots do not distinguish between the English and Science scores. However, each dot is plotted correctly, and no students were absent for any test. 10 9 8 7 6 5 4 3 2 1 00 1 2 3 4 5 Mathematics 6 7 8 9 10 The scatterplot showing just English and Science scores is shown below. Science 10 9 8 7 6 5 4 3 2 1 00 1 2 3 4 5 English 6 7 8 9 10 (a) How many students obtained a higher score in Mathematics than they did in English? State the scores in these two subjects for each of these students. [3] … … … … … … (b) Explain why there are only 11 dots rather than 12 dots in the first scatterplot. [1] … …

12 9694/11/M/J/20 © UCLES 2020 10 Dave can drive from Abdet to Bentall by two routes. The old route goes in roughly a straight line while the new faster route is 26% longer. Dave’s average speed on the new faster route is 40% higher than his average speed on the old route. (a) By what percentage is Dave’s journey time reduced by taking the new route compared to the old? [2] … … … … … … … … This time saving is actually 6 minutes and Dave’s average speed on the new route is 70 km per hour. (b) How many kilometres longer is the new route than the old route? [3] … … … … … … … … … … … …

13 9694/11/M/J/20 © UCLES 2020 [Turn over 11 Trains run between Carrow and Dinton, which are 280 km apart. Trains leave Carrow for Dinton on the hour and at 30 minutes past each hour. Trains leave Dinton for Carrow at 15 and 45 minutes past each hour. The journey in either direction takes 3 hours 30 minutes. Elias catches the 12:00 train from Carrow to Dinton. (a) What time did the first train that passes Elias leave Dinton? [1] … … … … (b) How many trains travelling from Dinton pass Elias during his journey? [1] … … … … All trains travel at a constant speed. (c) How far from Carrow will the 10:00 train from Carrow be when it passes the 10:15 train from Dinton? [2] … … … … … … … … … … … …

14 9694/11/M/J/20 © UCLES 2020 12 Marian runs a small company that makes picture frames. She takes 5 hours to make one frame. Marian employs only Beth and Carrie and they make simpler types of frame. Beth takes 3 hours to make one frame and Carrie takes 4 hours to make one frame. The company has sufficient orders to ensure that there are always frames of each type to be made. Marian, Beth and Carrie work from 09:00 to 17:00 every day of the week except Sunday. They have a lunch break each day from 12:00 to 13:00. As soon as each person finishes a frame, she starts the next one. Marian, Beth and Carrie each started making a new frame on Monday at 09:00. (a) How many frames has Marian completed by 17:00 on Saturday of the same week? [1] … … … … (b) Show that, after the women have all been working for 60 hours, 47 frames have been made. [1] … … … … (c) At what time on which day is the 20th frame completed? [3] … … … … … … … … … … …

15 9694/11/M/J/20 © UCLES 2020 (d) (i) Who makes the 60th frame to be completed? [2] … … … … … … … … … (ii) How many hours has she been working when the 60th frame is completed and how many frames has she made? [2] … … … … … …

16 9694/11/M/J/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 9694/11 Paper 1 Problem Solving May/June 2020 MARK SCHEME Maximum Mark: 50 Published Students did not sit exam papers in the June 2020 series due to the Covid-19 global pandemic. This mark scheme is published to support teachers and students and should be read together with the question paper. It shows the requirements of the exam. The answer column of the mark scheme shows the proposed basis on which Examiners would award marks for this exam. Where appropriate, this column also provides the most likely acceptable alternative responses expected from students. Examiners usually review the mark scheme after they have seen student responses and update the mark scheme if appropriate. In the June series, Examiners were unable to consider the acceptability of alternative responses, as there were no student responses to consider. Mark schemes should usually be read together with the Principal Examiner Report for Teachers. However, because students did not sit exam papers, there is no Principal Examiner Report for Teachers for the June 2020 series. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the June 2020 series for most Cambridge IGCSE™ and Cambridge International A & AS Level components, and some Cambridge O Level components.

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 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.

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 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

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 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

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 5 of 8 Question Answer Marks 1 Since the two birthdays are 15 days apart, it must be that the first lunch is on a Saturday and the second lunch is on a Sunday. 5 days after a Saturday is a Thursday. 1 Question Answer Marks 2(a) ( ) ( ) 50 100 90 80 70 60 50 200 40 × + + + + + + × = $30 500 1 2(b)(i) 499 $100 $70 × + = $49 970 1 2(b)(ii) 500 $70 × = $35 000 1 2(c) Total number sold = 5 times the number sold on Sunday, less 40 + 80 + 120 + 160. [1] 5 times number sold on Sunday = 500 + (40 + 80 + 120 +160) = 900, So number sold on Sunday = 180 and number sold on Thursday = 20 OR ( ) ( ) ( ) ( ) 40 80 120 160 500 x x x x x + − + − + − + − = oe [1] 5 900, 180 x x = = Number sold on Thursday = 20 2 Question Answer Marks 3(a) The ‘Drawn’ column of the current table adds up to 24. Each drawn match features twice in this column, so the number of drawn matches is 12. 1 3(b) 20 points, 6 wins, 0 draws [1] 20 = 2 × 4 + 4 × 3, so 2 wins away from home [1] 2 3(c) Porcupines scored 2 goals and had 1 goal scored against them. [1] Only Lemmings scored 1 goal and had 2 goals scored against them. [1] 2 Question Answer Marks 4(a) The restrictions only prevent them from staying at the Village hotel. The next cheapest for a double room with breakfast is Coral. 1 4(b) Coral is no longer acceptable as it does not have a gym. Plaza: $210 + $140 = $350. Garden: $205 + $150 = $355. So the least they could pay is $350 1 mark for identifying the Plaza and the Garden are the two possibilities. 2

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 6 of 8 Question Answer Marks 5 The only 6-digit number that satisfies all the conditions is 281357. 1 mark for deducing any of the numbers that follow the correct construction but do not have all digits different: 200941 221045 241149 261253 2 Question Answer Marks 6 Comparison of the two clocks before and after the change shown reveals that on the last digit of the platform 2 clock the top right element is permanently on and the bottom left element is permanently off. 1 mark for evidence of both As a result only 1,3,4,7 and 9 display correctly. [1] Allow one error, addition or omission for 1 mark. This means that the displays on both clocks are identical for 5 out of every 10 minutes and, therefore, 30 minutes of each hour. 3 Question Answer Marks 7(a) Least number when all pay maximum: All adults at $40 each: 18 000/40 = 450 people 1 7(b) Greatest number when cheapest tickets sold: All family tickets [1]: 18 000/120 = 150 groups of 4, so 600 people 2 7(c) Each child accompanied by adult, so 160 adults and 160 children: Least cost with family tickets, so need 80 [1] Leaves 119 adults: least cost with group tickets, so need 12 [1] Total = 80 × $120 + 12 × $350 = $13 800 SC: uses 9 individual adult tickets rather than 12th group ticket = $13 810 Award 2 marks 3

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 7 of 8 Question Answer Marks 8(a) My change when ordering a cup of coffee and one slice of carrot cake is $1.80. 3 ‘fish’ + 3 ‘cats’ = $1.80, so 1 ‘fish’ + 1 ‘cat’ = 60¢, which means that one of these two coins must be 50¢ and the other one must be 10¢. [1] For 5 ‘fish’ to be part of the $1.80 change on the second morning, the ‘fish’ cannot be the 50¢ coin, so the ‘cat’ coin is the 50¢. 2 8(b) The change from $5 is 1 ‘cat’ (50¢), so the cost of a cup of coffee and two slices of cake is $4.50. The cost of a slice of cake is therefore $1.30 and a cup of coffee is $1.90. FT from (a): If answer to (a) is 25¢, accept $1.65. If answer to (a) is 10¢, accept $1.50. If answer to (a) is 5¢, accept $1.45. 1 Question Answer Marks 9(a) 4 students [1] 9, 7 7, 6 4, 3 8, 7 1 mark for any two of these four specified 2 marks for any three of these four specified 3 9(b) One student obtained the same score in English and Science. 1 Question Answer Marks 10(a) Dave’s time on the new route compared to the old is 1.26/1.4 [1] = 0.9 Hence journey time reduced by 10% 2 10(b) Journey time on old route is 10 × 6 = 60 minutes and on new route is 54 minutes (0.9 hours) 1 mark for either 60 or 54 Length of old route = 0.9 × 70 = 63 km. This is 26% longer than old route which is therefore 50 km. 1 mark for either 63 or 50 Hence new route is 13 km longer than old route. 3

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 8 of 8 Question Answer Marks 11(a) First train from Dinton that arrives at Carrow after 12:00 is the 08:45. 1 11(b) All trains from Dinton that are travelling between 12:00 and 15:30. So 08:45 to 15:15, a total of 14. 1 11(c) The 10:00 will have travelled for 15 minutes longer, so distance 20 km [1] Divide 280 into two parts differing by 20, so 150 and 130, giving distance 150 km. OR: Speed of trains = 280/3.5 = 80 80T + 80(T – ¼ ) = 280 [1] T = 15/8, distance from Carrow is 80 × 15/8 = 150 km. 2 Question Answer Marks 12(a) Marian works 7 hours a day, so a total of 42 hours. Number of complete frames in this time is 8 1 12(b) Marian: 60/5 = 12; Beth: 60/3 = 20; Carrie 60/4 = 15 frames Total 47 AG 1 12(c) Marian completes after 5, 10, 15, 20, 25….hours Beth completes after 3, 6, 9, 12, 15, 18, 21, 24, 27 ….hours Carrie completes after 4, 8, 12, 16, 20, 24….hours. 27 hours [2] 1 mark for promising systematic approach 3 days and 6 hours, so Thursday at 16:00 3 12(d)(i) 47 frames in 60 hours: identify 13th frame needed [1] This is made by Beth 2 12(d)(ii) Number of hours = 78 [1] Number of frames made by Beth = 20 + 6 = 26 [1] 2