Cambridge A Level Thinking Skills 9694 — 2022 Oct/Nov Paper 1 · Variant 3

This document has 20 pages. Any blank pages are indicated. [Turn over Cambridge International AS & A Level DC (CE/CT) 303237/3 © UCLES 2022 THINKING SKILLS 9694/13 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 [ ]. * 4 6 2 2 7 0 5 6 1 1 *

2 9694/13/O/N/22 © UCLES 2022 1 Driving to work takes me 15 minutes, whereas walking the same route takes me 30 minutes. If my average driving speed is 5 km / h greater than my average walking speed, how far away must my workplace be? [2] … … … … … … … … … … … … …

3 9694/13/O/N/22 © UCLES 2022 [Turn over 2 Sarah’s dog Goldy eats the recommended 2.5% of his weight in food per day. However, he is overweight and so needs to reduce the amount of food he eats until he reaches a more healthy weight. His new diet will be to eat 800 g of food each day, which is 2% of his current weight, until he has reached his target weight. (a) What is Goldy’s current weight? [1] … … … … … … After 3 months, Goldy has reached a healthy weight of 35 kg. Sarah increases Goldy’s activity to make sure he does not become overweight again. She will now need to feed Goldy 3% of his weight each day to take into account the more active lifestyle. (b) How much more dog food will Sarah need to buy each week, compared with when Goldy was on his 2% diet, to maintain this healthy weight? [2] … … … … … … … … … … … …

4 9694/13/O/N/22 © UCLES 2022 3 When Nat visits his friend he travels by bus. His nearest bus stop is at Delta Street, from where he can take a number 5 or a number 11 bus. These are the only two bus routes that serve Delta Street. Depending upon which bus he takes, he has to change to a number 7 at either India Road or Bravo Lane. The relevant bus timetables are as follows: 5 Oscar Station → Kilo Market 11 Foxtrot Precinct → November Place Oscar Station 07:00 22:45 Foxtrot Precinct 07:30 22:30 Lima Gardens 07:08 and 22:53 Mike Grove 07:36 and 22:36 Delta Street 07:12 every 22:57 Delta Street 07:44 every 22:44 Sierra Crescent 07:19 15 23:04 Romeo Drive 07:51 20 22:51 India Road 07:24 minutes 23:09 Echo Hill 07:59 minutes 22:59 Charlie Avenue 07:29 until 23:14 Victor Close 08:06 until 23:06 Uniform Rise 07:35 23:20 Bravo Lane 08:15 23:15 Kilo Market 07:42 23:27 November Place 08:21 23:21 7 Quebec Yard → Hotel Row Quebec Yard 07:00 22:30 Alfa Corner 07:04 22:34 India Road 07:11 and 22:41 Golf Course 07:18 every 22:48 Bravo Lane 07:23 10 22:53 Papa Bridge 07:30 minutes 23:00 Tango Park 07:36 until 23:06 Juliett Way 07:43 23:13 Hotel Row 07:48 23:18 His friend meets him at the Tango Park bus stop. (a) What is the shortest time period between the scheduled arrival times of any two buses at Delta Street bus stop? [2] … … … … …

5 9694/13/O/N/22 © UCLES 2022 [Turn over It is 14:17 and Nat is at Delta Street bus stop. He intends to board the first bus that arrives. (b) Show that, by taking the second bus instead, he could arrive at Tango Park 10 minutes earlier. [2] … … … … … … … … … … … … 4 Since just the date of birth is generally used for age it is possible for a person to be legally older than someone born over 24 hours earlier in another part of the world. The local time at a particular point in the year can vary from 14 hours ahead of GMT (e.g. in Samoa) to 11 hours behind GMT (e.g. in American Samoa). What is the greatest difference between the actual times of birth for two people with the same date of birth? [1] … … … … … … … …

6 9694/13/O/N/22 © UCLES 2022 5 A tribe has a tradition that the favourite child of a father is the youngest daughter, or, if there is no daughter, the eldest son. Mothers favour the eldest daughter, otherwise the youngest son. (Assume that there are no twins or deaths.) (a) Give an example where the second child is the favourite of both parents at the same time. [1] … … … … … … (b) How many children does a family need to have before there might be a child who is never either parent’s favourite? Give the simplest example. [1] … … … … … … Bonnie is the middle of three sisters, and they have three brothers. All six are or have been the favourite. (c) How many of the children are younger than Bonnie? Explain your answer. [2] … … … … … … … …

7 9694/13/O/N/22 © UCLES 2022 [Turn over 6 Six teams are taking part in a hockey tournament. Each team will play each of the other teams once. (a) How many matches will there be? [1] … … … … … … In each match the teams play for 20 minutes. If the scores are equal after 20 minutes, they continue to play for a further 10 minutes. There is a 5-minute interval between each match. Last Saturday the tournament started at 09:00 and ended at 17:10. (b) In how many matches were the scores equal after the first 20 minutes of play? [3] … … … … … … … … … … … … … … …

8 9694/13/O/N/22 © UCLES 2022 7 The graphs below show the examination scores for 8 students in 3 school subjects. Ana Bernie Callum Daya Erin Felix Gunter Hugo Maths 100 80 60 40 20 0 Ana Bernie Callum Daya Erin Felix Gunter Hugo English 100 80 60 40 20 0 Ana Bernie Callum Daya Erin Felix Gunter Hugo Science 100 80 60 40 20 0 The head teacher tries to make a scatter plot for Maths and English, but neglects to label the axes. 0 0 20 40 60 80 10 30 50 70 90100 10 20 30 40 50 60 70 80 90 100 He also accidentally interchanges one student’s Maths and English marks. (a) Which student’s Maths and English marks have been interchanged on the scatterplot? [1] … …

9 9694/13/O/N/22 © UCLES 2022 [Turn over Next, the head teacher tries to make a scatter plot for Maths and Science, again neglecting to label the axes. 0 0 20 40 60 80 10 30 50 70 90 100 10 20 30 40 50 60 70 80 90 100 This time he accidentally interchanges two students’ Science marks. (b) Which two students’ Science marks have been interchanged on this scatter plot? [2] … … … … 8 Every sunny day, a plant increases in weight by 5 grams. On days which are not sunny the plant decreases in weight by 3 grams. Over a total of 16 days, overall the plant increased in weight by 8 grams. How many sunny days were there? [2] … … … … … … … … …

10 9694/13/O/N/22 © UCLES 2022 9 The Swirler is a ride at the Bolandian Theme Park. The Swirler car starts from The Point, travels round a track and finishes back at The Point. The car can carry up to 12 people at the same time. The car leaves The Point on the hour and every 6 minutes thereafter. The ride lasts for 5 minutes. Boarding and disembarking takes 1 minute. Each day, the first ride on the Swirler begins at 10:00 and the final ride ends at 18:00. (a) What is the greatest number of people who can ride on the Swirler each day? [1] … … … … The Swirler is very popular and at The Point there is always a queue of people waiting to ride. When Jacob joined the queue at 10:20, there were already 53 people ahead of him in the queue. (b) At what time did Jacob begin his ride on the Swirler? [2] … … … … Last Thursday, there were never more than 60 people in the queue when the Swirler left The Point. (c) What is the latest time that a person could have joined the existing queue and been certain to ride on the Swirler that day? [1] … … … … … … …

11 9694/13/O/N/22 © UCLES 2022 [Turn over On Saturdays, visitors can pay more and obtain a Priority Pass. This pass allows the visitor to jump to the front of the queue for the Swirler. At most two visitors with these passes are allowed on any one ride. Last Saturday, Lee joined the queue for the Swirler at 11:27. He did not have a Priority Pass. There were already 72 people in the queue. (d) What is the earliest time that Lee could be certain to begin his ride? [2] … … … … … … … …

12 9694/13/O/N/22 © UCLES 2022 10 Every month the glass in a very large greenhouse must be cleaned. When the cleaning is undertaken by more than one person, each person works at the same rate as if they were working by themselves. If Hans does it by himself it takes him 4 hours; Iago takes 5 hours, Nelson 6 hours and Zinedine 20 hours. (a) How long will it take to clean the glass if Hans, Iago, Nelson and Zinedine all work together? [2] … … … … … … … … … … (b) Sheena joins the cleaning team and when she works with the other four it takes exactly 1 hour to clean the glass. How long would it take Sheena to clean the glass by herself? [1] … … … … … … … …

13 9694/13/O/N/22 © UCLES 2022 [Turn over 11 Gino is taking part in a 775 km walk challenge to raise money for charity. He will start his walk on Tuesday 1 August and he wants to finish on 31 August. He will walk 20 km on Wednesdays and 30 km on all other days except Saturdays, when he will have a day off. He will walk whatever distance is left on 31 August. (a) How far will Gino need to walk on 31 August? [2] … … … … … … … … … Kim is also taking part in the challenge. She will walk for 5 consecutive days, have a day off, walk for another 5 consecutive days, have a day off, and will continue with this pattern until she completes the distance. She will alternate between walking 25 km and 15 km on the days that she walks. Kim starts her walk on Tuesday 1 August and walks 25 km. (b) On what day and date will she complete the walk, and how far will she walk on the final day? [3] … … … … … … … … … …

14 9694/13/O/N/22 © UCLES 2022 12 An office worker must post 30 letters. 10 letters will be sent 1st class, which costs 40¢ per letter. 10 letters will be sent 2nd class, which costs 25¢ per letter. The other 10 letters can be sent either 1st class or 2nd class. The cost of the postage can be made up using any number of stamps. The office worker has the following numbers of stamps in stock to choose from. Stamp value Stamps in stock 40 cent 5 30 cent 4 25 cent 10 10 cent 10 5 cent 16 (a) The manager tells the office worker that he must use stamps to the exact value required for each letter. What is the highest number of letters that could be posted? [3] … … … … … … … … … … … … … … … …

15 9694/13/O/N/22 © UCLES 2022 [Turn over (b) The office worker realises that he could send more letters if he ignores the manager’s instruction and chooses to use stamps to a higher value than is necessary for some letters. What is now the highest number of letters that could be posted? [2] … … … … … … … … … …

16 9694/13/O/N/22 © UCLES 2022 13 Every week Li collects an entry fee of $3 from each of the attendees at his local games club. Usually, most people pay using three $1 coins, but some pay with either a $5 or $10 note and require change. Since Li collects the money when everyone has arrived, he can usually give everyone the change that is needed from the money that is paid to him. Two weeks ago 34 people attended the club and many of them paid with notes. This meant that Li did not collect enough coins to give everyone the correct change. (a) What is the smallest number of people who might have paid with notes two weeks ago? [3] … … … … … … … … Li collected money from as many people as possible as long as he could give change. There were three people who did not pay, but who agreed to pay $6 the next time they attended. All three of these attended last week and each paid with a $10 note. There were again 34 attendees at the club. Last week Li was able to give everyone the correct change from the coins that he collected last week. (b) What is the largest number of people who might have paid with notes last week? [3] … … … … … … … … … …

17 9694/13/O/N/22 © UCLES 2022 Today, when one person paying with a $5 note apologised for not having the correct change, Li claimed that it was useful as he would be able to use the $5 note when giving change to someone else paying with a $10 note and so would not run out of $1 coins as quickly. (c) Explain why Li is wrong, using calculations to support your reasoning. [2] … … … … … … … … … … … …

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20 9694/13/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. BLANK PAGE

This document consists of 8 printed pages. © UCLES 2022 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/13 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.

9694/13 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.

9694/13 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

9694/13 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

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 5 of 8 Question Answer Marks 1 My driving speed must be double my walking speed. So I must walk at 5 km/h and drive at 10 km/h. [1] So my work must be 2.5 km away. 2 Question Answer Marks 2(a) Goldy’s new diet is 800 g, which is 2% of her weight. Her weight is 0.8  100/2 = 40 kg 1 2(b) New amount is 1050 g per day Which is 250 g more per day / 7350 g total per week [1] 250  7 = 1750 g per week 2 Question Answer Marks 3(a) Buses arrive at Delta street at the following minutes past the hour: #5: 12 27 42 57 # 11: 04 24 44 1 mark for either Smallest gap is 2 minutes 2 3(b) First bus 14:24; arrives Bravo Lane at 14:55. 15:03 from Bravo Lane arrives Tango Park at 15:16. [1] Second bus 14:27; arrives India Road at 14:39. 14:41 from India road arrives Tango Park at 15:06. [1] 2 Question Answer Marks 4 00:00 to 23:59 in day + 25 hours time zone so 49 hours 1 Question Answer Marks 5(a) Son then daughter 1 5(b) 2: Daughter then son. 1 5(c) Just one (sister) [1] The sons must all be older than the first daughter [1] 2

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 6 of 8 Question Answer Marks 6(a) 15 1 6(b) Total length of intervals (‘15’ – 1)  5 = 70 [1] Total length of matches = 490 – ‘70’ = 420 [1] 420 – (15  20) = 120 minutes extra, so number of draws = 120/10 = 12 OR Total length of normal matches and intervals = 14  25 + 20 = 370 [1] Total length of day = 490 490 – 370 = 120 minutes extra [1] so number of draws = 120/10 = 12 3 Question Answer Marks 7(a) Erin 1 7(b) Bernie [1] and Callum [1] 2 Question Answer Marks 8 6 sunny days and 10 non-sunny days would result in growth of 6  5 – 10  3 = 0 grams [1]. Changing one non-sunny day into a sunny day would result in the required increase of 5 + 3 = 8 grams, so this means having 7 sunny days and 9 non-sunny days. OR Any correct calculation for a number of sunny days and a number of non- sunny days, 16 days in total, and an attempt to improve [1] For increase of 8 grams, number of sunny days = 7 2 Question Answer Marks 9(a) 960 1 9(b) 53 people in queue, so Jacob will be on the 5th ride after 10:20 [1] 10:48 2 9(c) 17:24 1 9(d) Worst scenario is 10 people per ride [1]. Lee is 73rd in queue, so he will be on the 8th ride after 11:27. This is the 12:12 ride. 2

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 7 of 8 Question Answer Marks 10(a) In one hour they will have cleaned 1/4+1/5+1/6+1/20 = 2/3 of the glass 1 mark for an attempt to add the fractions If 2/3 cleaned in one hour then cleaning all will take 1 hour 30 minutes 2 10(b) In one hour the original 4 clean 2/3 of the glass. Hence Sheena must clean the other 1/3. To clean all the glass by herself would take 3 hours 1 Question Answer Marks 11(a) Gino walks 170 km in first 7 days [1] He has walked 680 km by 28th, 730 km by 30th, so on last day he needs to walk 45 km 2 11(b) Considering weeks from Tuesday to Monday, Kim walks 120 km for the first 5 weeks [1] and 105 km in the week 6, total 705 km, leaving 70 km [1] from Tuesday 12th September. Distances 15, 25, 15, 15, So Friday 15 September 15 km SC: 2 marks for 15 September and 15 km. OR Kim walks 200 km in 12 days [1] She will finish on the 46th day OR 39 days of walking [1] 3 Question Answer Marks 12(a) For example: 9  1st class: 5  40 + (4  30 + 4  10) [1] 15  2nd class: 10  25 + 3  (2  10 + 5) + 2  (5  5) [1] 24 letters 3 12(b) By using the 30c stamps to post 2nd class letters [1] He can post two additional letters, so 26 2

9694/13 Cambridge International AS & A Level – Mark Scheme PUBLISHED October/November 2022 © UCLES 2022 Page 8 of 8 Question Answer Marks 13(a) The worst case would be where everyone paid with a $10 note. [1] For example: 3 people paying with a $10 note would require a total of $21 in $1 coins, which would require 7 people paying with coins. [1] If more than 10 people paying with $10 note, not enough $1 coins are available, so the minimum number of people is 11 SC: 2 marks for answer of 10 3 13(b) The 3 players who paid $6 must have received a total of 12 $1 coins for their change [1] For example: 3 people paying with a $5 note would require a total of $(3  2 + 12) in $1 coins, which would require 6 people paying with coins. [1] Since 34 = 7 + 5  5 + 2, the number of people paying with notes is at most 3 + 5  3 + 1 = 19 3 13(c) If a person pays with a $10 note and there is no $5 note to give in the change then 7 $1 coins are needed for the change. If a person pays with a $10 note and there is a $5 note to give in the change then: 2 $1 coins must be given in change to the person paying with the $10 note 2 $1 coins have been given to the person who paid with the $5 note. 3 $1 coins have not been collected from the person who paid with the $5 note instead of paying the exact amount. 1 mark for any two of these three. 2 + 2 + 3 = 7, so the number of coins that Li has is the same either way. 2