Cambridge A Level Thinking Skills 9694 — 2022 Oct/Nov Paper 1 · Variant 1

This document has 16 pages. [Turn over Cambridge International AS & A Level DC (CE) 303236/2 © UCLES 2022 * 8 8 1 7 7 9 5 9 3 1 * THINKING SKILLS 9694/11 Paper 1 Problem Solving October/November 2022 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/O/N/22 © UCLES 2022 1 A gardener works in my garden 7 days each week. She charges me $6 if the weather is completely dry, but if it rains during any part of the day she instead charges me $8. (a) The gardener charged me $54 for one week’s work. How many days that week were completely dry? [2] … … … … … … … … … … The gardener changes her pricing structure so that on the first day of the week that it rains she charges me $8, and on any subsequent days that it rains she charges me $7. She continues to charge $6 when the weather is completely dry. (b) Following this change, she charged me $47 for one week’s work. How many days that week were completely dry? [1] … … … … … … … … … … …

3 9694/11/O/N/22 © UCLES 2022 [Turn over 2 Mark has been asked to write 2 short, 2 medium, and 1 long question for an exam paper according to the following specification. Question type Parts Total marks for question Short 1 1–4 Medium 2 or 3 3–6 Long 3 or 4 7–9 (a) What is the maximum total number of marks that the five questions could have? [1] … … … … … … (b) What is the maximum number of marks that a single part of a question could have? [1] … … … … … … (c) This is one of Mark’s questions. Why has he included this part? [1] … … … … … …

4 9694/11/O/N/22 © UCLES 2022 3 The Star Centre is open from Monday to Friday inclusive each week. It offers sessions in various activities. Information about these activities is given in the following table. Activity Days available Start times Duration (in minutes) Baking Monday, Tuesday 10:00, 12:15, 14:30, 16:45 120 Computers Monday, Wednesday, Friday 10:30, 12:30, 15:30, 18:00 90 Pottery Every day except Monday 11:00, 14:15, 17:30 150 Art Tuesday, Thursday 09:00, 12:00, 14:30, 17:00 100 Singing Tuesday, Wednesday, Thursday 10:30, 12:30, 14:30, 16:30, 18:30 75 Anyone who does two or more activities in a day must allow at least 30 minutes between sessions. Robbie has retired and he does a different activity on each of Monday, Tuesday, Wednesday and Friday. His activities are Computers, Pottery, Art and Singing. (a) On which day does Robbie do each of his activities? [1] … … … … … Annabel does Art and then Baking on the same day. She has chosen the start times of her sessions so that the amount of time from the beginning of the Art session to the end of the Baking session is as small as possible. (b) What is this amount of time? [2] … … … … … … …

5 9694/11/O/N/22 © UCLES 2022 [Turn over Annabel realises that if she had done the Baking session before the Art session then she could have reduced the total time. (c) Show that Annabel’s realisation is correct. [1] … … … … … … 4 A cake shop will write messages on top of the cakes that it produces. The cost depends on the difficulty of writing the letter and whether the letter occurs more than once in the message. Letters Cost for first or only occurrence of the letter Cost for any repeats of the letter Easy letters: IJLOTUVX $0.20 $0.15 Moderately-difficult letters: CEFHKNPSWZ $0.30 $0.20 Difficult letters: ABDGMQRY $0.40 $0.35 What is the cost of the message WELL DONE? [2] … … … … … … … … … …

6 9694/11/O/N/22 © UCLES 2022 5 Mr and Mrs Jones have four children. The names and dates of birth of the children are as follows. Name Date of birth Lottie 30 June 2001 Max 2 October 2002 Nia 21 August 2005 Ollie 5 August 2011 The Jones family visited a theme park on Nia’s birthday in 2016. The entry charges were as follows. Entry charge per person Adult (16 years and over) $40 Child 12 years old – 15 years old $36 Child 5 years old – 11 years old $25 Child under 5 years old $21 (a) How much did the Jones family pay for their entry to the theme park? [2] … … … … … … The entry charges were unchanged in 2017. (b) How much more would the total cost of the entry charges be on Nia’s birthday in 2017? [1] … … … … … …

7 9694/11/O/N/22 © UCLES 2022 [Turn over In 2018, all single-person entry charges were increased by 10% on the 2016 charges. The theme park also introduced a Family Ticket costing $150. This allowed entry to the park for two adults and two children of any age on any day in July or August. The Jones family visited the theme park in 2018 on Lottie’s birthday. (c) How much could they have saved by going on Ollie’s birthday instead of Lottie’s birthday? [3] … … … … … … … … … … … …

8 9694/11/O/N/22 © UCLES 2022 6 At a soccer match between the Reds and the Blues, half of the crowd support the Reds, one quarter of the crowd support the Blues and the rest support neither the Reds nor the Blues. One third of the Reds-supporters are wearing red hats and one quarter of the Blues-supporters are wearing blue hats. Half of the people who support neither the Reds nor the Blues are wearing black hats. All of the remaining members of the crowd are not wearing a hat. What proportion of the people wearing hats are Reds-supporters? [3] … … … … … … … … … … … … … … … … … … … … … …

9 9694/11/O/N/22 © UCLES 2022 [Turn over 7 An old calendar used years of 365 days, but inserted an extra day into every year that was divisible by four to keep the calendar synchronised to the observed seasons, calling a year with 366 days a leap year. (a) If leap years were abolished, how long would it take for the calendar to return to agreement with the old calendar? [1] … … … … … … A modern calendar also uses this system of leap years, except that if a year is divisible by one hundred it will not be a leap year, unless it is also divisible by four hundred, in which case it is. (b) If leap years had been abolished in 2000 (which was a leap year), how long would it have taken for the calendar to return to agreement with the modern calendar? [3] … … … … … … … … … … … … … … …

10 9694/11/O/N/22 © UCLES 2022 8 Gilmesh and Hercules plan to run along a long road for 20 minutes. They will start together. Gilmesh will run 300 metres in the first minute, but in every successive minute he will run 10 metres less than in the previous minute. Hercules will run 200 metres in the first minute, but in every successive minute he will run 5 metres more than in the previous minute. At the end of each minute, a record will be taken of which runner is ahead and by how far. (a) (i) At the end of which minute will the record show Gilmesh to be ahead by the greatest distance? [2] … … … … … … … … (ii) What is this greatest distance? [1] … … … … … … (b) At the end of which minute will the record first show Hercules to be ahead? [1] … … … … … …

11 9694/11/O/N/22 © UCLES 2022 [Turn over 9 I have two cousins and the three of us share the same birthday. I am 8 years younger than my older cousin and 11 years older than my younger cousin. At present the sum of our ages is 120. (a) How old am I? [2] … … … … … … … … (b) What will my age be when our three ages and their sum comprise all the digits from 1 to 9? [2] … … … … … … … … … … … … … …

12 9694/11/O/N/22 © UCLES 2022 10 In the vast outer reaches of the universe, there are three kinds of particles: red, green and blue. • When two particles of the same colour collide they produce 1 unit of energy. • When two particles of different colours collide they produce 2 units of energy and a particle of the third colour. For example: blue + blue → 1 unit of energy red + green → blue + 2 units of energy (a) What is the final result, after all possible collisions have happened, when starting with 6 blue particles? [1] … … … … … … … … (b) What is the maximum number of units of energy that can be produced when starting with 3 blue particles and 3 red particles? Give an example showing all the collisions and what is produced by them. [2] … … … … … … … … … …

13 9694/11/O/N/22 © UCLES 2022 [Turn over (c) What is the maximum number of units of energy that can be produced when starting with 2 blue particles, 2 red particles and 2 green particles? [1] … … … … … … … … (d) What is the maximum number of units of energy that can be produced when starting with 8 particles? [1] … … … … … … … …

14 9694/11/O/N/22 © UCLES 2022 11 The company that manufactures the chocolate bar Quasar is currently running a promotion with prizes of $10, $100 and $1000. While stocks last, each Quasar bar has a letter of the alphabet printed on the inside surface of the wrapper. Cash prizes of the relevant number of dollars can be claimed by sending in collections of wrappers that spell one of the following: TEN; HUNDRED; THOUSAND. Every wrapper issued in connection with this promotion has one of the ten letters that make up the prize-winning words printed inside. Exactly 80% of these wrappers have the letter N. The numbers of wrappers with each of the other letters are as follows. A 200 D 1250 E 18000 H 7500 O 500 R 1000 S 50 T 12000 U 7500 (a) What was the total number of wrappers issued with a letter printed inside? [1] … … … … (b) What is the largest total amount that the company could have to pay out in prize money? [3] … … … … … … … … … … …

15 9694/11/O/N/22 © UCLES 2022 [Turn over 12 Hobart bus tickets have numbers from 000000 to 999999. The number on the first ticket for each bus is random, with subsequent ticket numbers going up by one each time. In the rare event of going past 999999, the next number is 000000. A lucky ticket is one where the sum of the digits is 21. (a) What is the average sum of the digits on a ticket? [1] … … … … (b) List all the possible differences between the sums of the digits on consecutive tickets. [3] … … … … … … … … Jim is the first person in the queue and is delighted to find that he has a lucky ticket. There are 23 people in the queue for the same bus. (c) Give an example of a possible number for Jim where there is another lucky ticket, and the ticket of another person in the queue ends 00. [1] … … … … … … [Turn over for Question 13]

16 9694/11/O/N/22 © UCLES 2022 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 Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. 13 At the car park in the city centre, tickets must be bought when entering the car park, which takes a negligible amount of time. The prices are shown in the table below. Maximum allowed length of stay Price ($) 30 minutes 1.00 1 hour 1.50 2 hours 2.00 3 hours 2.50 5 hours 3.00 8 hours 3.50 There is a total of 50 spaces in the car park and the car park opens at 08:00. If all cars are parked for the maximum amount of time paid for, what is the earliest time in the day that a total of at least $250 could have been paid for parking? Justify your answer. [3] … … … … … … … … … … … … … … … …

This document consists of 8 printed pages. © UCLES 2022 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/11 Paper 1 Problem Solving October/November 2022 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 2022 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 2022 © UCLES 2022 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 2022 © UCLES 2022 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 2022 © UCLES 2022 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 October/November 2022 © UCLES 2022 Page 5 of 8 Question Answer Marks 1(a) 6  $8 + 1  $6 = $54 The number of dry days must be 1. 1 mark for charge for any non-zero pair of wet and dry days calculated. 2 1(b) The number of dry days must be 3. 1 Question Answer Marks 2(a) 2  (4 + 6) + 9 = 29 1 2(b) 9 − (3 − 1) = 7 1 2(c) Without it there would be too many parts for Short and not enough marks for Medium. 1 Question Answer Marks 3(a) Computers on Monday Pottery on Friday Art on Tuesday Singing on Wednesday 1 3(b) Sessions giving the least gap in between are Art at 14:30 (to 16:10) and Baking at 16:45 (to 18:45) [1] Least overall time is 14:30 to 18:45, so 4 hours 15 minutes 2 3(c) She could do Baking at 14:30 (to 16:30) then Art at 17:00 to 18:40, giving total time of 4 hours 10 minutes 1 Question Answer Marks 4 2 easys (LO) with 1 repeat (L) = 2  0.20 + 1  0.15 = 0.55 3 mediums (WEN) with 1 repeat (E) = 3  0.30 + 1  0.20 = 1.10 1 difficult (D) with 0 repeats = 1  0.40 = 0.40 Total = $2.05 Award 1 mark for either of the first two totals given OR for correct amounts listed for 7 or 8 letters 2

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 6 of 8 Question Answer Marks 5(a) Ages of children are 15, 13, 11, 5 [1] Cost = 2  $40 + 2  $36 + 2  $25 = $202 2 5(b) Ages are now 16, 14, 12, 6 so extra is $4 + $11 = $15 1 5(c) On Ollie’s birthday, ages are 17, 15, 12, 7. Use Family ticket to include Max and Nia Cost = $150 + $(40 + 25)  1.1 [1] = $150 + $71.50 = $221.50 On Lottie’s birthday, ages are 17, 15, 12, 6 Cost = (3  $40 + 2  $36 + 1  $25)  1.1 [1] = $238.70 Saving = $17.20 3 Question Answer Marks 6 From the proportions given, supposing a multiple of 12 is likely to be helpful. Suppose there are 48 people in the crowd: Of these, 24 support the Reds, 12 the Blues, 12 neither [1] 8 red hats, 3 blue hats, 6 black hats [1] Proportion of hats that are Reds = 8/(8 + 3 + 6) = 8/17 oe (47.1%) OR 1 mark for any of ½  ⅓ or ¼  ¼ or ¼  ½ 1 mark for writing the three fractions with a common denominator 3 Question Answer Marks 7(a) 365 non-leap years would have to pass, which would take 365  4 = 1460 years Ignore subsequent attempts to consider various moments of abolition 1 7(b) In a period of 100 years, there would be 24 leap years [1] In a period of 400 years there would be one extra, for 97 leap years [1] In a period of 1200 years there would be 291 leap years In 1500 years there would be 363 leap years Leaving 2 additional leap years to re-synchronise, for a total of 1508 years 3

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 7 of 8 Question Answer Marks 8(a)(i) Gilmesh will be ahead by 100 m after 1 minute, then by a further 85 m after 2 minutes, with his lead increasing by 15 m less each minute. [1] This is at a maximum after 7 minutes 2 8(a)(ii) 100 + 85 + 70 + 55 + 40 + 25 + 10 = 385 metres 1 8(b) 15 minutes 1 Question Answer Marks 9(a) 41 1 mark for sight of three ages with a difference of 8 between the higher two, a difference of 11 between the lower two OR an algebraic relationship such as x + x + 8 + x – 11 = 120 2 9(b) 64 1 mark for three ages that are the correct amount apart with six different digits, not including 0 2 Question Answer Marks 10(a) 3 units of energy 1 10(b) 2 marks for 10 units of energy with correct sequence of collisions. 1 mark for a correct sequence up to a point at which a green particle is used in a collision. 2 10(c) 9 units of energy 1 10(d) 14 units of energy 1 Question Answer Marks 11(a) 240 000 1 11(b) 1 mark for each of the following amounts (max 2) THOUSAND is constrained by S: (50  $1000 =) $50 000 HUNDRED is constrained by D: ((1250 – 50)/2  $100 =) $60 000 TEN is constrained by T: ((12 000 – 50)  $10 =) $119 500 giving a total of $229 500 3

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 8 of 8 Question Answer Marks 12(a) 27 1 12(b) 1, 8, 17, 26, 35, 44, 54 1 mark for any 2 correct, 1 mark for another 4 correct, 1 mark for the final one correct 3 12(c) Sum must be 21 and last digits not greater than 93 (because 17 drop needs at least 6 before so at most 9 after can back to 21) and not less than 78 1 Question Answer Marks 13 The earliest point possible could be achieved at a time at which all 50 spaces were occupied by cars that had paid for the most expensive ticket. 50  3.50 = $175, so the tickets bought (previously) must have cost a total of $75 [1] 50 tickets at $1 (for 30 minutes), plus an additional 25 tickets bought at 08:30 for another 30 minutes would achieve more than $75 which means that the $250 could be achieved at 09:00 [1] This could not be achieved with just $1 tickets, but 50 tickets at $1.50 (1 hour) would cost $75 [1] 09:00 3