Cambridge A Level Thinking Skills 9694 — 2016 Oct/Nov Paper 3 · Variant 1

This document consists of 7 printed pages, 1 blank page, and 1 insert. IB16 11_9694_31/2RP © UCLES 2016 [Turn over *8621638591* Cambridge International Examinations Cambridge International Advanced Level THINKING SKILLS 9694/31 Paper 3 Problem Analysis and Solution October/November 2016 2 hours Additional Materials: Electronic Calculator READ THESE INSTRUCTIONS FIRST An answer booklet is provided inside this question paper. You should follow the instructions on the front cover of the answer booklet. If you need additional answer paper ask the invigilator for a continuation booklet. Answer all the questions. Show your working. Marks may be awarded for correct steps towards a solution, even if the final answer is not correct. Marks may be lost if working needed to support an answer is not shown. Calculators should be used where appropriate. The number of marks is given in brackets [ ] at the end of each question or part question.

2 © UCLES 2016 9694/31/O/N/16 1 Kate is planning the layout of her new restaurant. To make the plans easier, she thinks of the dining area as a grid of squares as shown below: 1 2 3 4 5 6 7 8 9 10 A B C D E F G The shaded squares (at grid references G1 and G10) represent the entrance to the dining area and the access to the kitchen, so both of these squares must be empty. Each table in the restaurant consists of one or more units. Each unit takes up one square and each chair will occupy a square adjacent to one of the units. Every unit must have exactly two chairs next to it, on opposite sides of the unit. A table is described as a table for the maximum number of customers who could be seated at it; so, for example, two units positioned next to each other would be a table for 4. There must always be a route of empty squares to reach any of the chairs in the restaurant from both the entrance and the access to the kitchen. Chairs for different tables can only be in adjacent squares if they are back to back. Chairs for one table can never be adjacent to any of the units of another table. (a) Explain why it would not be possible to place units at A2 and B2 to form a table for 4. [1] (b) How many different positions are there for a table for 6? [3] Kate is considering having only tables for 4 in the restaurant. (c) What is the largest number of tables for 4 that could be fitted into the room? Give an example of the positions for the tables which achieves this, by listing the grid references. [3] Kate wants a layout which does not include any tables for more than 6, but does include at least one table for 2, 4 and 6. (d) Show, by listing the grid references of the tables, that it is possible to fit 26 customers in the room. [3]

3 © UCLES 2016 9694/31/O/N/16 [Turn over 2 A codon is a genetic code, represented by three letters, which determines the nature of a building block used in the production of proteins. There are four possibilities (U, C, A or G) for each letter in a codon. The 64 possible codons and the building blocks they produce are as follows: UUU → phe UUC → phe UUA → leu UUG → leu UCU → ser UCC → ser UCA → ser UCG → ser UAU → tyr UAC → tyr UAA → stp UAG → stp UGU → cys UGC → cys UGA → stp UGG → trp CUU → leu CUC → leu CUA → leu CUG → leu CCU → pro CCC → pro CCA → pro CCG → pro CAU → his CAC → his CAA → gln CAG → gln CGU → arg CGC → arg CGA → arg CGG → arg AUU → ile AUC → ile AUA → ile AUG → met ACU → thr ACC → thr ACA → thr ACG → thr AAU → asn AAC → asn AAA → lys AAG → lys AGU → ser AGC → ser AGA → arg AGG → arg GUU → val GUC → val GUA → val GUG → val GCU → ala GCC → ala GCA → ala GCG → ala GAU → asp GAC → asp GAA → glu GAG → glu GGU → gly GGC → gly GGA → gly GGG → gly For example, if the codon is ACU, the building block thr is made. A mutation occurs when a single letter of the code is changed, e.g. if ACA is changed to ACU. (a) How many possible mutations are there for each codon? [1] A silent mutation is one where the resulting building block stays the same. For example, CAA changed to CAG still produces gln. (b) List all the possible silent mutations of the codon CUG. [2] (c) Give four examples of codons with exactly two possible silent mutations. [3] A sequence of codons produces a sequence of building blocks, which makes up a protein. For example: GAG AGA AUA AAA GAA CUA AGA… produces glu arg ile lys glu leu arg… It is useful to be able to identify which company has produced a particular protein. To achieve this, a ‘watermark’ can be extracted from a sequence of codons. Each company is assigned its own watermark. Since there are many different sequences of codons that would produce the same protein, the company is usually able to choose a sequence of codons that bears its watermark. The watermark can be read by looking at the third letter in each codon: • if it is either U or A then a 0 is read; • if it is either C or G then a 1 is read. (d) Give a sequence of codons which would produce the sequence of building blocks in the example above (glu arg ile lys glu leu arg) and bear the watermark 1010101. [3] (e) Which two building blocks, if needed, might not have a codon which would fit the desired watermark? [1]

4 © UCLES 2016 9694/31/O/N/16 3 Traffic officers are modelling the flow of traffic on busy multi-lane highways in situations where lanes are closed. They envisage a simple scenario involving 9 cars on a 3-lane highway where two of the lanes are being closed. The traffic filters into the lane on the left, where it passes a camera. This is shown in the diagram below. L 1 2 4 7 3 5 8 6 9 a b c d e M R camera direction of traffic The flow of traffic is modelled by updating the diagram to represent the position one second later. Each second, each car can move one cell up or left, but there can never be two cars in the same cell. When car 1 moves up past the camera, there are several possibilities for how the other cars could move during the same second. For example, car 2 could move to La, car 4 to Lb, car 5 to Lc, car 8 to Mc and car 9 to Md. (a) What is the shortest amount of time that it could take for car 6 to pass the camera? [1] (b) Which of the nine cars could be the last to pass the camera? List all of them. [2] When two lanes of traffic merge, the traffic slows. The officers now assume that a car moving left takes a second longer than moving up. This is modelled as a second of delay after the car has moved into its new lane. (c) Show that car 4 could pass the camera in 5 seconds, if it allows car 3 to leave in front of it. You should use diagrams to show the positions of the relevant cars at the end of each second. [3] (d) What is the shortest time that car 6 could take to pass the camera? State a possible order of cars passing the camera that would enable this to happen, including any gaps where no cars passed during that 1-second time interval. [2] (e) Consider a case where the nine cars in the diagram pass the camera in the minimum total time. State a possible order of the cars passing the camera, including any gaps. [2] (f) If there were 30 cars on the highway, using all three lanes, what is the shortest amount of time in which all of them could pass the camera? [2]

5 © UCLES 2016 9694/31/O/N/16 [Turn over The traffic officers are considering what really happens when two cars could both move into the same space (one moving up, one moving left). They now assume that, in this case, the car moving to the left always takes priority over the car moving up. They model this situation, considering only the nine cars shown on the original diagram. (g) Given this assumption, state the order in which the nine cars would pass the camera, including any gaps. [3]

6 © UCLES 2016 9694/31/O/N/16 4 In the Nyneskwaird Sudoku Tournament competitors attempt six sudoku puzzles. The difficulty level of the puzzles increases as the tournament progresses and each puzzle has a time limit. Points are awarded to the first three competitors to complete a puzzle as follows: First 12 points Second 8 points Third 5 points Upon successfully completing a puzzle, all competitors have their times recorded as the number of minutes (with the seconds ignored). Each competitor scores a number of points equal to the difference between the time limit and the time recorded. For instance, if a puzzle has a time limit of 50 minutes, a competitor who successfully completes it in 42 minutes 59 seconds scores 8 points. The points for the recorded time and any points for finishing in the first three are added to give the competitor’s score for that puzzle. Each competitor’s final score is the sum of their five best scores from the six puzzles. Ahmed, Ben, Chloe, Darren, Ekta, Fleur, Gavin and Hazel are the eight competitors taking part in this year’s tournament. The scoreboard after the times for the fifth puzzle had been entered is shown below. Due to a technical error, however, Fleur’s time for puzzle 4, which she did complete within the time limit, is missing from the display. Puzzle 1 Puzzle 2 Puzzle 3 Puzzle 4 Puzzle 5 Puzzle 6 Total score Time limit 30 mins 45 mins 55 mins 60 mins 75 mins 90 mins Ahmed 17 mins 38 mins 44 mins 47 mins 60 mins 77 Ben 22 mins 34 mins 37 mins 49 mins 59 mins 89 Chloe 18 mins 29 mins 40 mins 51 mins 62 mins 82 Darren 28 mins 33 mins 38 mins 53 mins 61 mins 68 Ekta 25 mins 36 mins 45 mins 48 mins 57 mins 71 Fleur 12 mins 43 mins 41 mins 63 mins 64 Gavin 23 mins 35 mins 43 mins 44 mins 65 mins 67 Hazel 14 mins 36 mins 45 mins 52 mins 64 mins 62 They have now all completed the final puzzle, with the following results: Hazel 67 minutes Darren 71 minutes Gavin 72 minutes Chloe 73 minutes Ahmed 75 minutes Ekta 75 minutes Fleur 76 minutes Ben 77 minutes When these times are entered into the scoreboard, the total scores will automatically adjust to display the sum of the best five scores for each of the competitors.

7 © UCLES 2016 9694/31/O/N/16 (a) (i) Who is the only competitor who took less time to complete one of the puzzles than the previous puzzle? [1] (ii) Which competitor’s times have increased by the same amount, from one puzzle to the next, throughout the tournament? [1] (b) (i) Gavin was the first competitor to complete puzzle 4. What was his score for this puzzle? [2] (ii) Each puzzle was completed first by a different competitor. Which two competitors were not the first to complete any of the puzzles? [1] Although Fleur’s time for puzzle 4 is missing, the score of 64 for her first five puzzles is correct. (c) What time should be displayed on the scoreboard for Fleur’s puzzle 4? [3] After being the last to complete puzzle 6, Ben is worried that he has failed to stay in the lead. However, when the scoreboard is updated it will show that he has won the tournament, finishing just 1 point ahead of Darren. (d) (i) The score for which puzzle will not count towards Ben’s final score? [2] (ii) What is Ben’s final score? [1] (iii) Give the order in which the other competitors have finished behind Ben and Darren. [4]

8 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 International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. © UCLES 2016 9694/31/O/N/16 BLANK PAGE

® IGCSE is the registered trademark of Cambridge International Examinations. This document consists of 10 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International Advanced Level THINKING SKILLS 9694/31 Paper 3 Problem Analysis and Solution October/November 2016 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 will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 31 © UCLES 2016 1 (a) Explain why it would not be possible to place units at A2 and B2 to form a table for 4. [1] Because there would have to be a chair at A1 and it would not be possible to get to it. Condone solutions which state/imply that A1 and B1 can’t be served, OR A1 and A3 can’t be served. (b) How many different positions are there for a table for 6? [3] 54 (full marks for this value, or equivalent expression) If the tables are positioned in a horizontal row then they cannot be on row A, B, F or G. It would be possible to access positions all around the table for any of the 8 positions on any of the other rows. Similarly, if the tables are positioned in a vertical column then they cannot be on column 1, 2 or 9 or 10 and any of the 5 positions on any of the other columns could be accessible. Total number of possibilities is 3 × 8 + 6 × 5. Partial credit: • Identifying either that rows A, B, F and G or that columns 1, 2, 9 or 10 are not useable. Or that C,D,E possible/3,4,5,6,7,8 possible [1] .Allow ‘only 3 rows possible’ or ‘only 6 columns possible’ • Correct number of tables for any individual row or column [1] • Calculation of either 3 × 8 OR 6 × 5 [2] (c) What is the largest number of tables for 4 that could be fitted into the room? Give an example of the positions for the tables to achieve this, by listing the grid references.[3] 6 For example, tables could be placed at B2–C2, E2–F2, B5–B6, E5–E6, B8–B9 and E8–E9. The rules for placement of tables mean that each individual table must lie in a 3 × 2 grid of squares which cannot contain any part of other tables and the three squares on each side of the long edge must be empty. Therefore a maximum of three tables can be placed on any row across the diagram and there can be at most two rows (regardless of the orientation of the tables). The maximum possible is therefore 6 and it is then easy to find a working example. 1 mark for ‘all tables can be accessed from both exits’ [5 or more tables] 1 mark for ‘diners can be seated without adjacency infringements’ [5 or more tables] 1 mark for a viable arrangement of 6 tables

Page 3 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 31 © UCLES 2016 (d) Show, by listing the grid references of the tables, that it is possible to fit 26 customers in the room. [3] For example: • Two tables for 6: D1–3, D5–7 • One table for 4: D9–10 • Five tables for 2: A2, A5, A9, G3, G7 1 mark for ‘all tables can be accessed from both exits’ [at least one 4 and 6 : 24 or more diners] 1 mark for ‘diners can be seated without adjacency infringements’ [at least one 4 and 6 : 24 or more diners] 1 mark for an arrangement tables for 26 which satisfies all constraints (including a table for 2)

Page 4 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 31 © UCLES 2016 2 (a) How many possible mutations are there for each codon? [1] 3 + 3 + 3 = 9 (or equivalent expression) (b) List all the possible silent mutations of the codon CUG. [2] CUA, CUC, CUU [1 mark] UUG [1 mark] Any additional codons: no marks awarded (c) Give four examples of codons with exactly two possible silent mutations. [3] AUU AUC AUA UAA AGA AGG UUA UUG Deduct one mark for any incorrect judgment – ignore any surplus correct codons. E.g. 2 correct and 2 incorrect makes 2 judgment errors: 1 mark 3 correct codons, makes 1 judgment error: 2 marks (d) Give a sequence of codons which would produce the sequence of building blocks in the example above (glu arg ile lys glu leu arg) and bear the watermark 1010101. [3] There are several options. For example: GAG AGA AUC AAA GAG CUA AGG glu arg ile lys glu leu arg 1 0 1 0 1 0 1 GAG AGA AUC AAA GAG CUA AGG CGU UUA CGG CGA CUU CGC Partial credit: 1 mark getting the correct watermark 1 mark for six codons correct (from the table) (e) Which two building blocks, if needed, might not have a codon which would fit the desired watermark? [1] AUG and UGG are the only codons with no silent mutations, so met and trp. Accept codons instead of building blocks. No marks awarded if any extras given.

Page 5 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 31 © UCLES 2016 3 (a) What is the shortest amount of time that it could take for car 6 to pass the camera? [1] 5 seconds. (b) Which of the nine cars could be the last to pass the camera? List all of them. [2] 3, 5, 6, 7, 8, 9 1 mark for 3, 5 1 mark for 6, 7, 8, 9 Withhold 1 mark for each extra car (c) Show that car 4 could pass the camera in 5 seconds, if it allows car 3 to leave in front of it. You should use diagrams to show the positions of the relevant cars at the end of each second. [3] 1 mark for diagrams which clearly show a delay when 3 moves sideways. 1 mark for demonstrating that 5 seconds are represented/needed (dep) 1 mark for a correct sequence of diagrams 1 2 4 3 t = 0 2 3 4 t = 1 3 4 t = 2 3 4 t = 3 4 t = 4 t = 5

Page 6 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 31 © UCLES 2016 (d) What is the shortest time that car 6 could take to pass the camera? State a possible order of cars passing the camera that would enable this to happen, including any gaps where no cars passed during the 1-second time interval. [2] 7 seconds 1 – 2 – 4 – gap – 5 – gap – 6 OR 1 – 2 – gap – 3 – 5 – gap – 6 OR 1 – 2 – gap – 3 – 4 – gap – 6 1 mark for a correct list; 1 mark correct time (dep) Award 1 mark for one inappropriate insertion or omission of gap OR description of car movements + correct time, but no clear description of gaps Possible time frames shown below (not needed for full mark answer) 1 2 4 7 3 5 8 6 9 2 4 5 7 3 6 8 9 4 5 7 3 6 8 9 5 6 7 3 8 9 5 6 7 3 8 9 6 7 3 8 9 6 7 3 8 9 7 3 8 9

Page 7 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 31 © UCLES 2016 (e) Consider a case where the nine cars in the diagram pass the camera in the minimum total time. State a possible order of the cars passing the camera, including any gaps. [2] The cars can exit in 11 seconds. Simplest method is 2 synchronised lane changes, in which all the cars in the middle lane move into the left-hand lane, at the same time as the right-hand cars move into the middle lane. These introduce 2 gaps in the sequence. Cars would leave in the following order: 1 – 2 – 4 – 7 – gap – 3 – 5 – 8 – gap – 6 – 9 (taking 11 seconds). 1 mark for a solution with a gap after 7 or 8 OR a feasible exit strategy with gaps after . For example: 1 – 2 – gap – 3 – 4 – gap – 5 – 7 – gap – 6 – 8 – gap – 9 : 13 seconds 1 – 2 – 3 – gap – 5 – gap – 4 – gap – 8 – gap – 6 – gap – 7 – 9 : 14 seconds 1 2 4 7 3 5 8 6 9 2 4 7 3 5 8 6 9 4 7 3 5 8 6 9 7 3 5 8 6 9 3 5 8 6 9 5 8 6 9 8 6 9 6 9 6 9 9 3 5 8 6 9

Page 8 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 31 © UCLES 2016 (f) If there were 30 cars on the highway, using all three lanes, what is the shortest amount of time in which all of them could pass the camera? [2] The same method as for part (e) can be applied, i.e. all the sideways movement leads to just two gaps. Therefore the additional 21 cars will add an additional 21 seconds, making a total of 32 seconds. Some explanatory work needed for 2 marks (e.g. 30 + 2) FT their (e) + 21 (except 9 + 21 = 30) Award 1 mark for evidence that the candidate has considered 2 grouped lane shifts. (g) Given this assumption, state the order in which the nine cars would pass the camera, including any gaps. [3] The order is: 1 – 2 – gap – 3 – gap – 5 – gap – 6 – gap – 9 – gap – 8 – 4 – 7 1 mark for 1, 2, 3, 5 as the first cars, listed in that order. 1 mark for 6, 9, 8, 4, 7 as the next cars, in that order. 1 mark for all the gaps in the correct places.

Page 9 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 31 © UCLES 2016 4 (a) (i) Who is the only competitor who took less time to complete one of the puzzles than the previous puzzle? [1] Fleur (41 minutes for puzzle 3, following 43 minutes for puzzle 2) (ii) Which competitor’s times have increased by the same amount, from one puzzle to the next, throughout the tournament? [1] Chloe (an increase of 11 minutes each time) (b) (i) Gavin was the first competitor to complete puzzle 4. What was his score for this puzzle? [2] 28 (60 – 44 + 12) If 2 marks cannot be awarded, award 1 mark for an answer of 16 (failing to add on the 12 points for completing the puzzle first) OR 75/55 – 44 + 12 (wrong time limit) OR an arithmetic error in the calculation of 60 – 44 + 12. (ii) Each puzzle was completed first by a different competitor. Which two competitors were not the first to complete any of the puzzles? [1] Ahmed and Darren (c) What time should be displayed on the scoreboard for Fleur’s puzzle 4? [3] 54 (minutes) 64 – 30 – 2 – 14 – 12 = 6 points. Time limit was 60 minutes. If 3 marks cannot be awarded, award 2 marks for either of the following: • sight of 6 (points for puzzle 4) • at least three correct scores for puzzles 1, 2, 3 and 5 AND a correct number of minutes 30 for puzzle 1; 2 for puzzle 2; 14 for puzzle 3; 12 for puzzle 5 If 2 marks cannot be awarded, award 1 mark for either of the following: • an answer of 42 (minutes) (which fails to take any account of the additional points awarded for being first, second or third to complete a puzzle) • an attempt to subtract an incorrect total number of points for puzzles 1, 2, 3 and 5 (max one error) from 64.

Page 10 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2016 9694 31 © UCLES 2016 (d) (i) The score for which puzzle will not count towards Ben’s final score? [2] (puzzle) 1 If 2 marks cannot be awarded, award 1 mark for at least four correct scores for the puzzles: 8 for puzzle 1; 16 for puzzle 2; 30 for puzzle 3; 11 for puzzle 4; 24 for puzzle 5; 13 for puzzle 6. SC1: 8 with no further working This mark can be awarded for sight of these figures in (d)(ii). (ii) What is Ben’s final score? [1] 94 (iii) Give the order in which the other competitors have finished behind Ben and Darren. [4] Chloe (3rd); Hazel (4th); Ahmed (5th); Gavin (6th); Ekta (7th); Fleur (8th) If 4 marks cannot be awarded, award 1 mark for 1 correct; 2 marks for 3 correct; 3 marks for 5 correct (regardless of order): Chloe 90 (points) Hazel 89 Ahmed 85 Gavin 83 Ekta 81 Fleur 76 (possible FT from (c)) OR 2 marks for the list of the 6 competitors’ total scores for all 6 puzzles OR 1 mark for any 4 correct: Ahmed 92 Chloe 99 Ekta 86 Fleur 78 (possible FT from (c)) Gavin 90 Hazel 97