Cambridge A Level Thinking Skills 9694 — 2015 Oct/Nov Paper 3 · Variant 3

This document consists of 9 printed pages, 3 blank pages and 1 insert. IB15 11_9694_33/3RP © UCLES 2015 [Turn over *6319686168* Cambridge International Examinations Cambridge International Advanced Level THINKING SKILLS 9694/33 Paper 3 Problem Analysis and Solution October/November 2015 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 2015 9694/33/O/N/15 1 The Qualis? magazine uses a five-star rating in its reports on consumer goods: 1 star indicates barely adequate; 5 stars indicate perfection. Items which would get no stars in at least one category are simply not listed. Jack and Jill are considering which bucket to purchase. The available choices are: Name Capacity Handle Pouring Base Price kova 5 litres






$11 pail 5 litres








$12 seau 4 litres








$11 emmer 6 litres




$13 ndoo 5 litres







$15 kopp 6 litres









$14 Jack’s priorities are to have both the largest capacity and the best handle. (a) Which one would Jack select if he ignored other considerations? [1] Jill wants to pay the minimum, but also wants the pouring to be the best available. (b) (i) What stops Jill having both her priorities? [1] (ii) Which one would she select if her main requirement were cost, and then she would look for best pouring given minimum price, ignoring Jack’s preferences? [1] Jack and Jill make a joint decision, and agree to take a bucket that gives the best available score for at least one of Jack’s priorities and at least one of Jill’s. (c) Which one do they select? Explain why. [2] Mervyn suggests that the best way to look at the information in the table is by showing each option as a pentagon, where the five ratings are displayed on five axes. For example: Handle Pouring Base Price Capacity It is normal to arrange the ratings along the axes so that being further away from the centre represents being ‘better’. Here, having a larger capacity is considered to be better. (d) Since a lower price is a better price, suggest what to do with the rating for price. [1]

3 © UCLES 2015 9694/33/O/N/15 [Turn over (e) (i) Bucket A is better than bucket B in precisely two categories and bucket B is better than bucket A in precisely two categories. Sketch, on one set of axes, two possible pentagons for buckets A and B. [1] (ii) If the pentagon for bucket C touches but does not go outside that of bucket D, would any customer be disadvantaged if bucket C were no longer available? Explain your answer. [1] (f) Give an example of ratings for a seventh bucket, the spand, which doesn’t have the worst rating of any of the buckets in the table for any factor, but which nobody would choose to buy based on the Qualis? assessment. Explain why they would not. [2]

4 © UCLES 2015 9694/33/O/N/15 2 The following details of the suspects for a crime are available to Detective Inspector Rory Kilmartin. Suspect A Suspect B Suspect C Suspect D Suspect E Gender Female Female Female Male Male Eye colour Blue Brown Green Blue Brown Handedness Left Right Right Right Left Hair Dark Dark Dark Dark Dark DI Kilmartin wants to know the height of the suspects, but is only able to access summary data, because of a technical problem in the database. He is able to get the median height of any group referred to by a descriptor in the table (e.g. the median height of the blue-eyed suspects). Below is the summary data that is accessible to DI Kilmartin: Median (Female) = 168 Median (Male) = 181 Median (Blue) = 185 Median (Green) = 155 Median (Brown) = 170 Median (Left) = 176 Median (Right) = 168 Median (Dark) = 172 He realises that only one suspect has green eyes and so is able to deduce that the height of suspect C is 155 cm. (a) DI Kilmartin believes that the fact that the median (Female) and the median (Right) are both 168 must mean that suspect B has a height of 168 cm. (i) What alternative hypothesis about some suspects’ heights would be consistent with these two medians? [1] (ii) Identify one of the other medians which confirms that DI Kilmartin was in fact correct. [1] (b) DI Kilmartin uses another median to conclude the height of suspect E. State which median he uses and the height of suspect E. [2] (c) Explain how the heights of the remaining two suspects can be found, stating clearly which medians are used. [2]

5 © UCLES 2015 9694/33/O/N/15 [Turn over A colleague working on another crime has five suspects with the following data, and there is the same problem with the raw data of their heights. Suspect H Suspect I Suspect J Suspect K Suspect L Gender Male Female Male Male Male Eye colour Blue Blue Brown Blue Brown Handedness Left Right Right Right Left Hair Dark Fair Fair Dark Dark Median (Female) = 181 Median (Male) = 182 Median (Blue) = 181 Median (Brown) = 177 Median (Left) = 173 Median (Right) = 186 Median (Dark) = 178 Median (Fair) = 183.5 (d) Suspect K is the tallest of the five. Explain why it is not possible to deduce his height from the medians. [1] (e) Deduce the heights of the other four suspects. [3]

6 © UCLES 2015 9694/33/O/N/15 3 The Bulominski highway runs from the town of Kavieng to Namatanai. It is served by buses whose price and capacity are controlled, but the departure times are not, although they may only run during daylight hours – from 06:00 to 18:00. The population is spread thinly along the highway, but all the shops and offices are in Kavieng, so most people using the buses want to go to or from the Kavieng terminus. The highway is split into 9 zones and there are many buses. Each bus is registered in one of the zones, and only travels from the far end of its registered zone to the Kavieng terminus and back. Anyone starting in zone 1 has to pay the price to the registered zone of the bus. For all other journeys the passenger pays the fare set for travel from the zone they start in to the zone they go to and the fare is the same in each direction. Journeys entirely within any single zone cost the same, regardless of which zone they are in. Each bus can take at most 15 passengers. Drivers do not know where a passenger intends to get off. All fares are one-way and paid at the end of the journey. 1 2 3 4 5 6 7 8 9 ZONES Kavieng terminus Namatanai terminus Not to scale (a) Buses from how many zones might pick up someone travelling from zone 6 to zone 5? [1] (b) What is the maximum possible number of different fares? [2] A resident of zone 4 would pay the same amount to travel to zone 1 whatever bus they took. On the return journey the price varies according to the registered zone of the bus (the higher the zone number, the higher the price). (c) Explain how this helps the bus system to run more efficiently. [1] As they aim to get the maximum income from fares, drivers starting at the Kavieng terminus usually wait until the bus is full, but they have to leave in time to get to the far end of their destination zone by 18:00. Assume that all buses travel at the same constant speed at all times. The last buses need to leave the Kavieng terminus by To Zone 1 2 3 4 5 6 7 8 9 17:40 17:25 17:10 16:40 16:25 16:10 15:45 15:20 15:00 (d) After what time is there no chance that there will be a bus to take someone to Namatanai from the border of zones 6 and 7? [2] The distance from Kavieng terminus to the other end of zone 1 is 20 km. (e) (i) What is the distance from Kavieng terminus to the far end of zone 4? [1] (ii) Show that the distance from the middle of zone 5 to the middle of zone 7 is 35 km. [2]

7 © UCLES 2015 9694/33/O/N/15 [Turn over One proposal is to set the fare for a journey by adding two components: a fixed amount that is charged for all journeys and an additional amount per kilometre from the middle of the starting zone to the middle of the destination zone. Under this proposal, the fare from zone 5 to zone 7 is $4.30 and the fare from zone 3 to zone 2 is $3.10. (f) What is the fare from zone 8 to zone 3? [4] An alternative proposal is to have a fixed amount for all journeys and an additional amount per zone travelled in. Under this proposal, the fare from zone 5 to zone 7 is still $4.30 and the fare from zone 3 to zone 2 is still $3.10. (g) What is the fare from zone 8 to zone 3 under this alternative proposal? [2]

8 © UCLES 2015 9694/33/O/N/15 4 Claddem is a game for two players, played over a number of rounds. The equipment for playing the game consists of two identical cards (one for each player), 20 numbered tiles, a bag and a scoring rack. One of the cards and the tiles are shown below. 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 In each round both players attempt to form three 2-digit numbers on their cards that add up to 150. At the beginning of a round all the tiles are placed in the bag and the bag is shaken. The players then take turns to withdraw three tiles at a time from the bag, at random. The players decide what to do with each set of their three tiles: • One must be placed on a square on the player’s own card, from where it may not subsequently be moved. • One must be given to the other player to be placed by that player later. • One must be placed on the scoring rack. After they have both had three turns, each player has three tiles already in place on their card and three tiles that they have received from the other player. These tiles are now placed on the remaining squares on the cards, and the player who forms the three 2-digit numbers whose sum is closer to 150 wins the round. The number of points scored by the winner of a round is the sum of the six numbers on the tiles placed on the scoring rack during the round. A player whose three-number sum is exactly 150 also scores a bonus of 10 points. If there is a tie, the player with the highest single 2-digit number wins. Doug and Sally are playing a game of Claddem. At the end of the first round the tiles left in the bag were numbered 4 and 9, and their completed cards were as follows: 0 2 3 4 5 7 Doug’s card 3 1 2 7 8 5 Sally’s card

9 © UCLES 2015 9694/33/O/N/15 (a) (i) Who won this round? Justify your answer. [1] (ii) How many points did the winner score? [2] Sally has just made the final withdrawal of three tiles from the bag in the second round. She now has to decide what to do with tiles numbered 0, 2 and 9. This is how the cards look at present. 6 3 7 Doug’s card 8 3 Sally’s card Doug has given Sally tiles numbered 1, 4 and 6. Sally has given Doug tiles numbered 2 and 5 so far. The sum of the numbers on the tiles on the scoring rack so far is 27. (b) How close to 150 can Sally get if she keeps (i) the 0 tile? [1] (ii) the 2 tile? [1] (iii) the 9 tile? [1] (c) What must Sally do with these tiles in order to win this round? Explain your answer in detail. [3] (d) What are the numbers on the two tiles that are left in the bag? [3] The maximum amount that can be scored by the winner of a round of Claddem is 58 points. (e) Explain how it is possible for 58 points to be scored, and give an example of a completed card that could score 58 points. [3]

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® IGCSE is the registered trademark of Cambridge International Examinations. CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Advanced Level MARK SCHEME for the October/November 2015 series 9694 THINKING SKILLS 9694/33 Paper 3 (Problem Analysis and Solution), maximum raw mark 50 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 2015 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 2015 9694 33 © Cambridge International Examinations 2015 1 (a) Which one would Jack select if he ignored other considerations? [1] Only emmer and kopp have the largest capacity; kova, seau and kopp have the best handle, so kopp is only choice for best of both. (b) (i) What stops Jill having both her priorities? [1] None of the lowest price has the best pouring. OR The best pourer does not have the lowest price. OR The best pourer has highest price. OR There’s no overlap between best pourer and lowest price. (ii) Which one would she select if her main requirement were cost, and then she would look for best pouring given minimum price, ignoring Jack’s preferences? [1] Kova and seau are the lowest price, but she would take the better pourer: kova. (c) Which one do they select? Explain why. [2] Emmer, kova, seau and kopp are all acceptable for Jack; Jill would accept ndoo, seau or kova. That leaves kova or seau as possible. But kova has both the larger capacity and the better pouring. Hence kova 1 mark for answer, 1 mark for explanation including use of secondary criteria (capacity and pouring). OR 1 mark total for seau with explanation that it is acceptable to both. OR 1 mark for identification of choice between kova and seau. (d) Since a lower price is a better price, suggest what to do with the rating for price. [1] Any decreasing function of price (over range $11–$15). e.g. $20 – price, 1/price. Accept non-technical descriptions of the transformation, e.g. ‘draw it the other way around’, ‘take from outside’. (e) (i) Bucket A is better than bucket B in precisely two categories and bucket B is better than bucket A in precisely two categories. Sketch, on one set of axes, two possible pentagons for buckets A and B. [1] Any correct diagram. (ii) If the pentagon for bucket C touches but does not go outside that of bucket D, would any customer be disadvantaged if bucket C were no longer available? Explain your answer. [1] No. Whatever the customer’s priorities, bucket D is always as good or better (for each consideration).

Page 3 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2015 9694 33 © Cambridge International Examinations 2015 (f) Give an example of ratings for a seventh bucket, the spand, which doesn’t have the worst rating of any of the buckets in the table for any factor, but which nobody would choose to buy based on the Qualis? assessment. Explain why they would not. [2] e.g. Capacity 5 litre, Handle

, Pouring

, Base

, Price $14 [1 mark] Kopp or pail (as appropriate) is no worse in any category and is better in some. [1 mark]

Page 4 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2015 9694 33 © Cambridge International Examinations 2015 2 (a) (i) What alternative hypothesis about some suspects’ heights would be consistent with these two medians? [1] a = 168 AND d = 168 OR a = d. (ii) Identify one of the other medians which confirms that DI Kilmartin was in fact correct. [1] Median (Blue) OR Median (Dark) (b) DI Kilmartin uses another median to conclude the height of suspect E. State which median he uses and the height of suspect E. [2] Median (Brown) + B’s height: [1 mark] E’s height is 172 [1 mark] (c) Explain how the heights of the remaining two suspects can be found, stating clearly which medians are used. [2] Median (Male) + E’s height allows suspect D’s height to be deduced Median (Blue) + D’s height allows suspect A’s height to be deduced OR Median (Left) + E’s height allows suspect A’s height to be deduced Median (Blue) + A’s height allows suspect D’s height to be deduced OR Median (Male) + E’s height allows suspect D’s height to be deduced Median (Left) + E’s height allows suspect A’s height to be deduced Award 2 marks for reference to a pair of appropriate medians and which height obtained. Award 1 mark for E’s height and appropriate median OR Award 1 mark for a pair of appropriate median. (d) Suspect K is the tallest of the five. Explain why it is not possible to deduce his height from the medians. [1] For each descriptor Suspect K is one of a group of at least three. SC1: generic observation that medians typically do not address outliers (such as tallest).

Page 5 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2015 9694 33 © Cambridge International Examinations 2015 (e) Deduce the heights of the other four suspects. [3] I = 181 (because she is the only female) J = 186 (because he and suspect I are the only fair-haired suspects) L = 168 (J & L are brown-eyed) H = 178 (because of median dark-haired, or L&H left-handed, or by elimination as all medians of odd-sized sets (female blue right dark) must be attained.) Award 1 mark I’s height, 1 mark for J, 1 mark for both L and H.

Page 6 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2015 9694 33 © Cambridge International Examinations 2015 3 (a) Buses from how many zones might pick up someone travelling from zone 6 to zone 5? [1] 4 (from 6, 7, 8 or 9) (b) What is the maximum possible number of different fares? [2] All single zone fares are the same (zero distance). From 9 to 8 but same in both directions so 1 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 37. Award 1 mark for 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 soi (36 or 45 or 73) (c) Explain how this helps the bus system to run more efficiently. [1] It discourages people from getting on buses which could take others further but would likely end up with empty seats for parts of the journey. To Zone 1 2 3 4 5 6 7 8 9 18:00 17:40 17:25 17:10 16:40 16:25 16:10 15:45 15.20 15:00 20 15 15 30 15 15 25 25 20 20 35 50 80 95 110 135 160 180 (d) After what time is there no chance that there will be a bus to take someone to Namatanai from the border of zones 6 and 7? [2] It takes 25 + 25 + 20 minutes for all of zones 7–9, but they must arrive by 18:00, so 16:50. 1 mark for 70 minutes OR 110 minutes seen OR a correct method with arithmetic error. (e) (i) What is the distance from Kavieng terminus to the far end of zone 4? [1] 80 km (ii) Show that the distance from the middle of zone 5 to the middle of zone 7 is 35 km. [2] 15/2 + 15 + 25/2 = 35 OR (135 + 110)/2 – (95 + 80)/2 OR (Mid 5 to mid 6) 15 + (mid 6 to mid 7) 20 1 mark for 15/2 OR 25/2 OR (135 + 110)/2 OR (95 + 80)/2 OR associated times

Page 7 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2015 9694 33 © Cambridge International Examinations 2015 (f) What is the fare from zone 8 to zone 3? [4] Middle of zone 3 to middle of zone 2 = 15 km 35 – 15 = 20 km difference $4.30 – $3.10 = $1.20 $1.20/20 = $0.06 per km Award 2 marks for $0.06 soi; 1 mark for substantially correct method. $3.10 – 15 × $0.06 = $2.20 or $4.30 – 35 × $0.06 = $2.20 is the fixed amount [1 mark] Middle of zone 8 to middle of zone 3 = 105 km $2.20 + 105 × $0.06 = $8.50 (g) What is the fare from zone 8 to zone 3 under this alternative proposal? [2] Must be $1.20 per zone, which implies $0.70 as the fixed amount [1 mark] Fare = $0.70 + 6 × $1.20 = $7.90 Award 1 mark for substantially correct method. Condone $1.90 with use of 5 zones.

Page 8 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2015 9694 33 © Cambridge International Examinations 2015 4 (a) (i) Who won this round? Justify your answer. [1] Sally. Sally’s total is 152, Doug’s total is 147. Both totals (or distances from 150) must be stated and Sally identified as the winner for the mark to be awarded. (ii) How many points did the winner score? [2] 30 If 2 marks cannot be awarded, award 1 mark for either of the following: • Identifying the tiles thrown away as 0, 1, 6, 6, 8 and 9. • Recognising that the total of the 20 tiles is 90 and attempting to subtract the total of the 12 tiles on the cards together with the 2 tiles left in the bag (correctly or incorrectly calculated). (b) How close to 150 can Sally get if she keeps (i) the 0 tile? [1] 157 (e.g. 86 + 31 + 40) OR 7 away (from 150) (ii) the 2 tile? [1] 141 (e.g. 86 + 34 + 21) OR 159 (e.g. 86 + 31 + 42) OR 9 away (from 150) (iii) the 9 tile? [1] 139 (e.g. 86 + 34 + 19) OR 11 away (from 150) (c) What must Sally do with these tiles in order to win this round? Explain your answer in detail. [3] Award 1 mark for each of the following: • She must give the 9 to Doug • so that his best total will be 158 (e.g. 73 + 56 + 29) OR if she gives him the 0 or the 2, his best total would be 149 or 151 (respectively) (e.g. 73 + 56 + 20 or 73 + 56 + 22). • She must keep the 0, (i.e. discard 2) to make 157 / to be closer to 150 than Doug. (157 may be seen in response to (b)(i) above.)

Page 9 Mark Scheme Syllabus Paper Cambridge International A Level – October/November 2015 9694 33 © Cambridge International Examinations 2015 (d) What are the numbers on the two tiles that are left in the bag? [3] 0 and 7 If 3 marks cannot be awarded: Award 1 mark for evidence of appreciation that the two numbers must add up to 90 – 27 – the sum of the other numbers in the stimulus 1 mark for recognition that the numbers that do not appear in the stimulus are 0, 1, 4, 5, 7, 8 and 9 OR 1 mark for exactly two distinct tiles from this list or from the candidate’s list. (e) Explain how it is possible for 58 points to be scored, and give an example of a completed card that could score 58 points. [3] Award 1 mark for each of the following: • the six tiles thrown away must be 7, 7, 8, 8, 9 and 9 • recognition that the winner’s three-number total must be 150 • a completed grid that totals 150, with no digit greater than 6 and no digit appearing more than twice (e.g. 64 + 52 + 34)