Cambridge A Level Thinking Skills 9694 — 2023 May/June Paper 1 · Variant 1

This document has 16 pages. Any blank pages are indicated. [Turn over Cambridge International AS & A Level * 5 0 4 9 5 6 8 9 7 7 * DC (CE/SG) 316826/2 © UCLES 2023 THINKING SKILLS 9694/11 Paper 1 Problem Solving May/June 2023 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/23 © UCLES 2023 1 In Mrs Wilson’s geography class, the student who achieves the largest increase in their test score between any two consecutive weeks of term wins a prize. Week 1 Week 2 Week 3 Week 4 Week 5 Sandra 95 93 60 77 63 Alex 92 89 62 54 59 Petro 51 52 86 86 60 Dominic 45 48 59 49 80 Hayley 98 90 56 65 92 (a) Which student wins the prize? [1] … … … … … … … … The students suggest changing the system so that the prize winner is the student who achieves the largest increase in their test score across three consecutive weeks of term (for example, the difference between Week 2 and Week 4). (b) Which student would win the prize using this system? [1] … … … … … … …

3 9694/11/M/J/23 © UCLES 2023 [Turn over 2 Donald hires a van for delivery jobs to various cities. The cost of hire is $90 per day plus the cost of the fuel he will use. The van can travel 6 km for each litre of fuel used and the fuel costs $1.20 per litre. This week, Donald hires the van for three days for the following job: • On Monday, Hondmarket to Targhill • On Tuesday, Targhill to Kingburg • On Wednesday, Kingburg to Hondmarket The distances in km between cities are shown in the table. Hondmarket 153 Targhill 212 245 Newton 413 400 193 Kingburg Donald picks up the van in Hondmarket on Monday and returns it on Wednesday (also in Hondmarket). If he gets paid $600 for the whole job, how much profit will he make? [4] … … … … … … … … … … … … … … … …

4 9694/11/M/J/23 © UCLES 2023 3 Baby Lara has a mobile over her cot. It has four coloured ducks suspended by strings from wooden bars. The bars can rotate freely on the strings. The diagram shows a side view when all the ducks are in a line. Pink White Yellow Blue Looking up when Lara woke up, she saw the mobile, from directly below. (a) Give, on the diagram below, an example of an arrangement of the colours that she would not see. [1] … … … … (b) How many arrangements of the four colours are possible with the bars as shown in (a)? [1] … … … … … … … …

5 9694/11/M/J/23 © UCLES 2023 [Turn over 4 The Langtry Theatre has 40 rows of seats with 30 seats in each row, numbered consecutively. There is a central aisle between seats 15 and 16 of each row. The ticket prices for the current production at the theatre are as follows: front 10 rows $55 each rows 11–40 $35 each There is an overall discount of $10 when tickets for two seats next to each other in the same row and on the same side of the central aisle are purchased together. All tickets for tonight’s performance have been sold. What is the smallest possible total income from ticket sales for tonight’s performance? [3] … … … … … … … … … … … … … … … …

6 9694/11/M/J/23 © UCLES 2023 5 Sylvie sells cakes. Small cakes cost $3 each, medium cakes cost $5 each and large cakes cost $7 each. Adam has $41 to buy 11 cakes for his work colleagues. He will buy the cakes from Sylvie and will spend all the money. (a) List all the possible combinations of cakes that Adam could buy. [3] … … … … … … … … … … … Bernice intends to spend exactly $120 on cakes from Sylvie. She will buy twice as many small cakes as large cakes. (b) How many medium cakes will Bernice buy? [2] … … … … … … … … … … …

7 9694/11/M/J/23 © UCLES 2023 [Turn over 6 Twelve teams are taking part in a football tournament at a stadium next Saturday. The twelve teams are arranged into four groups with three teams in each group. In each of the four groups, each team will play the other members of the group once. In the semi-finals, the winner of the first group will play the winner of the second group, and the winner of the third group will play the winner of the fourth group. The winners of these two matches will play in the final. Each match will last for 20 minutes; but if the teams are level, they will continue to play for an extra 10 minutes. If they are then still level, the winner will be decided by the toss of a coin. All of the matches will be played consecutively in the order: first group, second group, third group, fourth group, semi-finals, final. There will be a 15-minute break between each match. The tournament will start at 09:00. (a) What is the earliest time that the tournament could end? [2] … … … … … … Jimmy is a member of one of the teams in the tournament and he will play in all their matches. (b) (i) What is the greatest length of time that Jimmy could need to be at the stadium? [1] … … … … (ii) What is the latest time that Jimmy’s first match could start? [3] … … … … … … …

8 9694/11/M/J/23 © UCLES 2023 7 Alex’s computer has a strange fault. It performs calculations correctly, but, when it displays the calculation, every digit displayed is either one higher or one lower than the correct digit. On Monday, the computer display showed a complete calculation as: 34 + 58 = 63 Alex realised that this could result from three possible correct calculations. (a) What are the three possible correct complete calculations? [3] … … … … … … … … On Tuesday, the computer display showed a complete calculation as: 67 × 8 = 413 Alex realised that this could result from two possible correct calculations. (b) What are the two possible correct complete calculations? [2] … … … … … … … … … …

9 9694/11/M/J/23 © UCLES 2023 [Turn over 8 Shopping is delivered to my house every week in plastic carrier bags. During each delivery, the person delivering my shopping will receive any bags that I return to them from past deliveries, up to a maximum number equal to the number of bags used for last week’s delivery, or 25 bags, whichever is smaller. I receive 5 cents for every bag I return, and each week I return the maximum number of bags permitted. The number of bags used to deliver my shopping, since I began having my shopping delivered, are shown in the table below. I could not return any bags in Week 1, as I did not have any. Week Number of bags 1 17 2 20 3 12 4 27 5 10 6 41 7 16 (a) How many bags do I have at home after Week 3’s delivery? [1] … … … … (b) How many bags do I have at home after Week 7’s delivery? [2] … … … … (c) How much money have I received in total so far for all of the returned bags? [2] … … … …

10 9694/11/M/J/23 © UCLES 2023 9 In a game, each of the first seven letters of the alphabet (A, B, C, D, E, F, G) is paired with a number from 1 to 7, in some order. Each letter is paired with a different number. Words are formed from these letters. The score for each word is the sum of the numbers that are paired with the letters in the word. In one game, FEE scores 19, ACE scores 16 and CAB scores 10. (a) (i) Explain why F must be paired with 5. [2] … … … … … (ii) What are the possible scores for the word CAD? [2] … … … … … … The remaining letters of the alphabet are also paired with numbers as follows: H I J K L M are paired with the numbers 8 to 13, in some order N O P Q R S T are paired with the numbers 14 to 20 in some order U V W X Y Z are paired with the numbers 21 to 26 in some order (b) What is the least possible score for the word ACUTELY? [1] … … … … … …

11 9694/11/M/J/23 © UCLES 2023 [Turn over The word FOOT scores 56 and the word TOFFEE scores 57. (c) Which number is T paired with? [2] … … … … … …

12 9694/11/M/J/23 © UCLES 2023 10 A 180 g bag of Sporties contains a combination of chocolate basketballs and chocolate volleyballs. The total weight of chocolate in a bag is always at least 178 g and never more than 182 g. Each basketball is 11 g and each volleyball is 8 g. The total number of balls in a bag is always 19 or 20. The bag of Sporties I bought last week contained 7 basketballs and 13 volleyballs. (a) What are the other three combinations of basketballs and volleyballs that a bag of Sporties may contain? [3] … … … … … … … … … … … The makers of Sporties intend to add footballs, weighing 9 g each, to the combination of balls in the near future. The weight of a basketball and a volleyball will not change and the total weight of chocolate in a bag will still be between 178 g and 182 g. The total number of balls in a bag will still be 19 or 20. There will be at least 5 of each type of ball in every bag. (b) Find a combination of basketballs, volleyballs and footballs that will result in a different number of each type in a bag. [2] … … … … … … …

13 9694/11/M/J/23 © UCLES 2023 [Turn over 11 Peter, Kirsty and Laura all have some books. Peter gives 2 of his books to Kirsty, and Kirsty gives 3 of her books to Laura. Laura now has 8 more books than Peter and 1 more book than Kirsty. Everyone has at least 1 book. (a) What is the smallest total number of books there could be? [1] … … … … … … There are at most 100 books in total. (b) What is the largest number of books that Kirsty could have now? [2] … … … … … … … … … … … … … … … …

14 9694/11/M/J/23 © UCLES 2023 12 Wayne is driving from Burada to Orada. He still has 126 km to go, but he has stopped for a rest after driving for three hours. He travelled 34 fewer kilometres during the second hour than during the first hour because of heavy traffic. As a result, he was 41 km short of halfway through his journey at the end of the second hour. During the third hour he travelled 88 km. How far did Wayne travel during the second hour of his journey? [3] … … … … … … … … … … … … … … … … … … … … … …

15 9694/11/M/J/23 © UCLES 2023 BLANK PAGE

16 9694/11/M/J/23 © UCLES 2023 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 9 printed pages. © UCLES 2023 [Turn over Cambridge International AS & A Level THINKING SKILLS 9694/11 Paper 1 Problem Solving May/June 2023 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 May/June 2023 series for most Cambridge IGCSE, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components.

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 2 of 9 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 2023 © UCLES 2023 Page 3 of 9 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 dep mark depends on earlier, asterisked (*), mark 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 2023 © UCLES 2023 Page 4 of 9 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

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 5 of 9 Question Answer Marks 1(a) Petro 1 1(b) Hayley 1 Question Answer Marks 2 Hire of van for three days, $90  3 = $270 [1] Distances 153, 400, 413 [1] so total 966 km Cost of fuel = 966/6  $1.2 = $193.20 [1] Total cost, $270 + $193.20 = $463.20 Profit on job, $600 – 463.20 = $136.80 4 Question Answer Marks 3(a) Diagram must show all 4 colours with Pink and White on different bars. 1 3(b) 8 1 Question Answer Marks 4 The minimum would occur when 28 seats in each row (14 pairs on either side of the central aisle) are sold at a discount [1] Smallest total for front 10 rows is 10  (28  $50 + 2  $55) = $15 100 Smallest total for rows 11–40 is 30  (28  $30 + 2  $35) = $27 300 Total discount = $5600 1 mark for any one of these three Smallest total income is $42 400 OR The minimum would occur when 2 seats in each row (1 on either side of the central aisle) are sold without a discount [1] If discount is applied to all seats, extra income from non-discounted 80 aisle seats = 40  $10 = $400 [1] Smallest total income = (300  $50 + 900  $30) + $400 = $42 400 3

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 6 of 9 Question Answer Marks 5(a) 9 small, 2 large 8 small, 2 medium, 1 large 7 small, 4 medium 1 mark for each Allow any clear notation, e.g. 33333333377 3 5(b) At least two trials to find total cost using twice as many small cakes as large OR 3  2L + 5M + 7L = 120 OR Search to find a multiple of 13 plus a multiple of 5 giving $120 1 mark for any of these Number of medium cakes = 11 SC: 1 mark for answer of 7 2 Question Answer Marks 6(a) 1 mark for Number of matches to be played = 15 OR time to first semi-final start = 420 minutes (7 hours) OR first semi-final starts at 16:00 Least total duration = 15  20 + 14  15 = 510 minutes = 8 hours 30 minutes. Tournament ends at 17:30 2 6(b)(i) Jimmy is at stadium for 15  30 + 14  15 = 660 minutes or 11 hours 1 6(b)(ii) For latest start time, Jimmy must play in the 2nd match in the 4th group Number of matches already played = 10 1 mark for either Greatest duration 300 minutes + 10 breaks [1] = 450 minutes = 7 hours 30 minutes Jimmy’s first match could start as late as 16:30 SC: 1 mark for final answer of 16:15 3

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 7 of 9 Question Answer Marks 7(a) 23 + 49 = 72 [1] 25 + 47 = 72 [1] 25 + 49 = 74 [1] If 4 answers are given, award 1 mark for 3 correct with 1 incorrect No marks if more than 4 answers given 3 7(b) 56  9 = 504 [1] 58  9 = 522 [1] If 3 answers are given, award 1 mark for 2 correct with 1 incorrect No marks if more than 3 answers given 2 Question Answer Marks 8(a) 12 1 8(b) In week 5 I am limited to returning 25 bags (not 27) [1] So I still have 12 bags at the end of week 5 After week 7 delivery I have 43 – 25 + 16 = 34 bags 2 8(c) I have returned 109 bags [1] $5.45 SC: 1 mark for $5.55 (from returning 12 in week 6) 2 Question Answer Marks 9(a)(i) Difference between E and B is 6, so E = 7 (and B = 1) [1*] F scores 19 – 2  7 = 5 [1dep] AG OR Max value of F is 7, so E must be 6 or 7. If E = 6, A + C = 10 and B = 0 which is not possible, so E = 7 [1*] F scores 19 – 2  7 = 5 [1dep] AG OR FEE = 19 means either E = 6 or 7. If E = 6, A + C + E = 16 implies A + C = 10, but 6 and 7 are taken, (so A + C < 10,) so E = 7 [1*] F scores 19 – 2  7 = 5 [1dep] AG 2 9(a)(ii) 11 [1] 13 [1] If 3 answers are given, award 1 mark for 2 correct with 1 incorrect No marks if more than 3 answers given If 0 scored, award 1 mark for A and C are 3 and 6 (or 6 and 3) 2 9(b) ACE scores 16. Least scores for U, T, L, Y are 21, 14, 8, 22, total 81 1

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 8 of 9 Question Answer Marks 9(c) 2 O’s and 1 T score (56 – 5 =) 51 1 O and 1 T score (57 – (2  5 + 2  7)) = 33 1 mark for either O = 51 – 33 = 18 and T = 15 OR TOFFEE (57) – FOOT (56) = FEE – O = 1.[1] FEE is 19 so O is 18. From FOOT, T = 56 – 5 – 18 – 18 = 15 2 Question Answer Marks 10(a) 6 basketballs; 14 volleyballs [1] 9 basketballs; 10 volleyballs [1] 10 basketballs; 9 volleyballs [1] If 4 answers are given, award 1 mark for 3 correct with 1 incorrect No marks if more than 4 answers given 3 10(b) 2 marks for any correct final answer or a set of final answers ALL of which are correct 8 basketballs; 5 volleyballs; 6 footballs 8 basketballs; 6 volleyballs; 5 footballs 6 basketballs; 5 volleyballs; 8 footballs 5 basketballs; 8 volleyballs; 7 footballs 5 basketballs; 9 volleyballs; 6 footballs If 2 marks for correct final answer (or a set of final answers ALL of which are correct) not awarded, award max of 1 mark for any response in a list of no more than 3 that is worth 1 mark or 2 marks, but not given as a final answer. 1 mark for an answer with a total of 19 or 20 but with (limited) violation of one other condition: Weight no more than 2g outside the required range Only 4 of one type of Sportie More than one Sportie of the same quantity No marks if more than 3 answers are given 2

9694/11 Cambridge International AS & A Level – Mark Scheme PUBLISHED May/June 2023 © UCLES 2023 Page 9 of 9 Question Answer Marks 11(a) 18 1 11(b) 35 1 mark for final answer 36 OR 1 mark for a correct set with a total in the range 90 to 108 with K = P + 7, L = P + 8 or equivalent OR 1 mark for a correct algebraic equality/inequality, e.g. P + P + 7 + P + 8 < 101 2 Question Answer Marks 12 (Halfway is 126 + 88 – 41 =) 173 (km) [1] (Distance travelled during the first two hours is 173 – 41 =) 132 (km) [1] Distance travelled during the second hour is 49 km OR x + x + 34 + 41 = ½ (2x + 34 + 88 + 126) oe [2] x = 49, Distance travelled during the second hour is 49 km 3