Cambridge A Level Thinking Skills 9694 — 2016 Oct/Nov Paper 1 · Variant 2

This document consists of 19 printed pages and 1 blank page. IB16 11_9694_12/2RP © UCLES 2016 [Turn over *7328507460* Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level THINKING SKILLS 9694/12 Paper 1 Problem Solving October/November 2016 1 hour 45 minutes Additional Materials: Multiple Choice Answer Sheet Soft clean eraser Soft pencil (type B or HB is recommended) READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. There are 30 questions on this paper. Answer all the questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in pencil on the separate answer sheet. Read very carefully the instructions on the answer sheet. Ignore responses numbered 31 – 40 on the answer sheet. DO NOT WRITE IN ANY BARCODES. INFORMATION FOR CANDIDATES Each correct answer will score one mark. A mark will not be deducted for a wrong answer.

2 © UCLES 2016 9694/12/O/N/16 1 48 competitors entered the men’s 100 metres freestyle event at this year’s Muscan Swimming Championships. They were divided randomly into 6 heats, with the fastest 16 qualifying for the semi-finals. These are the results of the 6 heats. Heat 1 Heat 2 Heat 3 Name Time (s) Name Time (s) Name Time (s) Vic Richmond 52.67 Neil Trenton 52.29 Connor Hartford 52.60 Mitch Lansing 52.75 Wynn Cheyenne 52.37 Noel Halifax 52.63 Ted Austin 52.79 Corey Colima 52.55 Sonny Pierre 52.83 Orville Salem 53.06 Noah Bismarck 52.70 Miles Jackson 52.94 Archie Phoenix 53.15 Ilya Springfield 53.31 Yuri Merida 53.20 Vernon Xalapa 53.84 Gene Atlanta 53.69 Declan Dover 53.38 Michael St Paul 54.58 Milton Morelia 55.64 Morgan Helena 54.14 Neville Lincoln 55.90 Norris Raleigh 56.41 Wayne Olympia 55.36 Heat 4 Heat 5 Heat 6 Name Time (s) Name Time (s) Name Time (s) Karl Topeka 52.19 Alan Edmonton 52.51 Wes Charleston 52.54 Colin Saltillo 52.38 Carlos Sacramento 52.77 Terry Nashville 52.82 Ioan Desmoines 52.61 Mark Augusta 52.99 Scott Regina 52.98 Alex Juneau 52.73 Nelson Concord 53.45 Alvin Montgomery 53.11 Rhodri Providence 52.88 Conan Denver 53.89 Kevin Frankfort 53.52 Matt Boston 52.90 Idris Boise 53.96 Duane Durango 53.77 Ned Albany 53.63 Sol Columbia 54.30 Arthur Littlerock 54.86 Hiram Pachuca 54.97 Peter Harrisburg 56.73 Will Madison 56.28 From which heat was there only one qualifier for the semi-finals? A Heat 1 B Heat 3 C Heat 5 D Heat 6

3 © UCLES 2016 9694/12/O/N/16 [Turn over 2 The ingredients on a jar of mincemeat are in order of content by weight and are as follows: Sugar; Apples (26%); Vine fruit (26%); Candied mixed peel (4%); Vegetable suet; Treacle; Acetic Acid; Mixed spices (0.3%); Citric Acid; Antioxidant (Ascorbic Acid). To the nearest 1%, what is the possible range of sugar content? A 26% to 43% B 26% to 44% C 31% to 43% D 31% to 44% 3 Tom needs to save some money to buy himself a new car. At the start of January there is $400 in his savings account. He is able to add $100 to the account at the end of each month. In April he knows that he will be paid a bonus and have an increase in his salary, so he expects to add $500 to his account at the end of April and then $150 each month after that. Which of the following graphs represents the total money that he will have in his savings account at the end of each month? Jan Feb Mar Apr May Jun Jan Feb Mar Apr May Jun Jan Feb Mar Apr May Jun Jan Feb Mar Apr May Jun A B C D 1600 1400 1200 1000 800 600 400 200 0 $ 1600 1400 1200 1000 800 600 400 200 0 $ 1600 1400 1200 1000 800 600 400 200 0 $ 1600 1400 1200 1000 800 600 400 200 0 $

4 © UCLES 2016 9694/12/O/N/16 4 A question-master asks each of four contestants up to 15 questions. The process is repeated again for a second round. The ‘score’ is the number of questions answered correctly. The scores after each round are announced in ascending numerical order. After the first round of a contest the scores were 8, 10, 11, and 14. After the second round the total scores for the contestants were 13, 18, 20, and 24. What was the largest possible score achieved in the second round of this contest? A 10 B 11 C 14 D 16 5 A rectangular piece of paper is folded in half and then folded in half the other way to produce a rectangle with sides half the lengths of those of the unfolded paper. Three corners of this folded paper are then cut off and the paper unfolded. Which one of the following could not be a representation of the paper when unfolded again? A B C D

5 © UCLES 2016 9694/12/O/N/16 [Turn over 6 A display showing the 24-hour time (0000 to 2359) uses some or all of seven lights for each digit as follows: What is the greatest number of lights on at any time? A 25 B 26 C 27 D 28 7 My family – 2 adults and 2 children – are planning to go to an amusement park. Tickets are priced as follows: Adult $45.00 Child $35.00 Family Ticket 2 adults 2 children $150.00 However, there are various offers available: • 10% off the cost of each ticket if you book in advance • $7.00 off individual tickets with a Dollarland Stores loyalty card • with vouchers from a newspaper, one child can be admitted for $7.50 when two adults take two children and buy individual tickets • $120.00 plus a $16.50 booking fee for a family ticket if you book online. Only one offer can be used at a time. What is the lowest price we can pay to go to the amusement park? A $132.00 B $132.50 C $135.00 D $136.50

6 © UCLES 2016 9694/12/O/N/16 8 In her first five weekly shopping trips on Saturdays, Angela spends $14, $7, $14, $7, $7 respectively to ensure that she has enough stock of her new daily vitamin pill to last for the week, without spending more than she needs to. Which one of the following would explain this variation? A The pills are sold in packets of 4 B The pills are sold in packets of 5 C The pills are sold in packets of 6 D The pills are sold in packets of 7 9 Four members of an online community construct a diagram to show whether they have ever met in real life. Each person is represented by a dot and two dots are joined together with a line if those two people have ever met in real life. The diagram looks like this: Each member of the group then makes a table, showing with a tick when two people have ever met in real life. Shaded cells show people linked to themselves. Which person’s table is wrong? A B C D

7 © UCLES 2016 9694/12/O/N/16 [Turn over 10 People employ Mo to cut and trim their lawns. His charges are: • 20 cents per square metre of area that he cuts • 20 cents per metre of lawn edge that he trims However, he has a minimum total charge of $12 per lawn. Which of the following graphs shows how Mo’s charge for cutting and trimming the whole of a square lawn varies with the length of its sides? A Charge ($) Length of side (m) B Charge ($) Length of side (m) C Charge ($) Length of side (m) D Charge ($) Length of side (m)

8 © UCLES 2016 9694/12/O/N/16 11 The table below shows the price (in dollars) per person of travelling on a ferry boat from Revod to Olamst or the reverse journey from Olamst to Revod. The price depends upon the accommodation chosen and the time of year the journey is made. Accommodation type October to April May and September June, July and August 2-berth outside cabin 105 119 140 2-berth inside cabin 95 108 125 3-berth outside cabin 98 116 129 3-berth inside cabin 86 104 117 2-berth inside cabin (no shower or w.c.) 76 86 103 No cabin – reclining seats 45 55 65 Simple passage 35 45 56 A family of five plan to go by ferry from Revod to Olamst in May returning in June. The parents wish to travel both ways in a 2-berth outside cabin, and are willing to pay for the children to enjoy a 3-berth inside cabin on both journeys. The three children think all members of the family should take the cheapest (even if most uncomfortable) fare available, and use the savings made as compared to the parents’ plan for special holiday treats. How much would the family save in total on the ferry crossing if the children’s plan was adopted compared to the parents’ plan? A $379 B $650 C $676 D $1181

9 © UCLES 2016 9694/12/O/N/16 [Turn over 12 Below is a table containing information about unemployment figures in seven countries. Total 25 – 54 unemployment (%) 2000 2001 2002 2003 2004 2005 Australia 5.30 5.00 5.10 4.80 4.00 3.90 Canada 5.70 6.20 6.50 6.40 5.90 5.70 Czech Republic 7.70 7.50 6.50 7.00 6.00 7.40 Estonia 12.90 11.80 10.00 9.40 8.90 7.50 Finland 8.00 7.40 7.30 7.30 7.20 6.80 France 8.80 8.10 8.30 8.90 10.00 9.10 Germany 7.30 7.50 8.20 9.50 9.00 10.40 Which two countries experienced the same change in unemployment between 2001 and 2004? A Australia and Germany B Czech Republic and Germany C France and Germany D Australia and the Czech Republic

10 © UCLES 2016 9694/12/O/N/16 13 12 1 2 3 4 5 6 7 8 9 10 11 X Y Z The diagram shows three wheels meshed together so that when wheel X is turned, wheel Y turns, and this turns wheel Z. There is no slipping or sliding when the wheels are turned. The diameters of wheels X, Y and Z are 10 cm, 30 cm and 60 cm respectively. Starting from the position in the diagram, wheel X is turned four times round in a clockwise direction. After these four revolutions, what will the number be at the top of wheel Z? A 2 B 4 C 8 D 10

11 © UCLES 2016 9694/12/O/N/16 [Turn over 14 The Green Road car park has a capacity of 150 cars. It is open from 8 am to 6 pm and cars are not allowed to stay overnight. It is mainly used by commuters and shoppers. About half the capacity is used by commuters, who mainly stay for the whole day. Shoppers generally come after 9 am and leave before 5 pm, but only stay for the morning or afternoon. Given the above information, which of the statements A – D is the most likely description of the graph shown below? Number of cars Time (hour) A The number of cars arriving in the car park during each hour B The number of cars leaving the car park during each hour C The number of cars in the car park at the end of each hour D The number of spaces in the car park at the end of each hour

12 © UCLES 2016 9694/12/O/N/16 15 Petra receives three job offers. She will only work 35 hours a week (excluding breaks) and for no more than 9 hours a day (including breaks). She will only work five days each week, but she wants to earn the highest salary possible. Her current post at Ripemoff Limited fits her time conditions perfectly and she earns $10 per hour with a fixed bonus of $25 per week. She is offered a post at Hardwork Products. She would have to work four half days (08:00 to 14:00) and one full day (08:00 to 17:30 with a lunch break of 1 hour), and would be paid $70 for each of her four half days and $140 for her full day. Another post is at Slavedrivers Incorporated. She would have to work 09:00 to 16:00 for three days and 09:00 to 18:00 for the other two, with half an hour lunch break every day. She would be paid $11 per hour. The third post is at Poundoflesh Partners. She would have to work 08:30 to 16:30 (with two breaks of half an hour each) five days a week, and would be paid $9 per hour and a fixed bonus of $14 per day. None of the companies pays its employees for their breaks. Which option should Petra choose? A Stay at Ripemoff Limited B Move to Hardwork Products C Move to Slavedrivers Incorporated D Move to Poundoflesh Partners

13 © UCLES 2016 9694/12/O/N/16 [Turn over 16 Yesterday I opened a savings account and paid in the $87 500 that I recently inherited. The account that I have chosen is aimed at savers with at least $50 000 to invest. It pays no interest for two months when the account is first opened, but from the third month interest is credited to the account as follows: Balance before interest is added Monthly interest less than $50 000 0 from $50 000 to $99 999 $350 $100 000 or more $750 My intention is to leave the money in this account without making any withdrawals for at least the next five years. Which one of these bar charts shows the total interest I can expect to receive during each of the next five years? 1st year 2nd year 3rd year A 4th year 5th year 10 000 5000 Interest ($) 1st year 2nd year 3rd year B 4th year 5th year 10 000 5000 Interest ($) 1st year 2nd year 3rd year C 4th year 5th year 10 000 5000 Interest ($) 1st year 2nd year 3rd year D 4th year 5th year 10 000 5000 Interest ($)

14 © UCLES 2016 9694/12/O/N/16 17 I went shopping for presents and bought two each of three different books, and one of a fourth book. The four books were all different prices. All four prices were whole numbers of dollars. The total bill was $25. None of the books was as low as $1. Which of the following could have been the price of the book I bought only one of? A $2 B $3 C $4 D $5 18 Last year, Billy decided to save up to buy a computer. In January he saved 25% of the total cost of the computer. In each of February and March he saved 15% of the total cost. In April he saved 20% of the total cost. In May, he only managed to save 25% of what he had saved in April, but in June he was able to save the remaining amount that he needed to buy his computer. Which one of the following pie charts could represent Billy’s monthly savings? A B C D 19 John and Tanya are playing a game. Tanya has thought of a three-digit number and given John two clues to help him to work out the number. The clues that she has given him are: • The digits add up to 12. • The first digit is twice as much as the last digit. Which one of the following extra pieces of information would be sufficient to allow John to deduce the number? A The number is even B The number is odd C The difference between the largest and smallest digit is 3 D The difference between the largest and smallest digit is 8

15 © UCLES 2016 9694/12/O/N/16 [Turn over 20 Four teams – the Blues, the Greens, the Reds and the Yellows – took part in a football tournament in which several exciting goals were scored. The number of goals scored altogether by the Blues and the Reds was equal to twice the number scored by the Greens, whilst the total scored altogether by the Reds and the Yellows was equal to three times the number scored by the Greens. Which is the only one of the following statements that is definitely true? A The Blues scored more goals than the Greens B The Greens scored more goals than the Reds C The Reds scored more goals than the Yellows D The Yellows scored more goals than the Blues 21 The local science museum needs to raise a certain amount of money every week to pay its running costs. The entrance fee is $10 for adults and $8 for children. Last week 140 adults and 100 children visited the museum and the money raised from their entrance fees was just enough to cover the running costs. This week however the running costs will be $100 more than last week. Tina assumes that the same number of people will visit this week, and so has decided to increase the entrance fee to $12 for adults and $9 for children. She is also going to introduce a family ticket, which will admit 2 adults and 2 children. She predicts that 40 of these family tickets will be sold. What is the cheapest price for the family ticket that will raise the required amount of money? A $33 B $35 C $37 D $41 22 Eight students take a Physics test and their marks are 40, 35, 56, 29, 74, 61, 50 and 39. Two other students, Ron and Sam, also take the test and join the eight students to form a group of ten. Which one of the following sets of information would be sufficient to find Sam’s mark? A The mean increases by 2 marks and the median increases by 3 marks when the marks for Ron and Sam are included B The mean mark of all ten students and knowledge that Ron’s mark is 2 more than Sam’s mark C The mean mark of all ten students and the mean mark of Ron and Sam D The median mark of all ten students and the median mark of Ron and Sam

16 © UCLES 2016 9694/12/O/N/16 23 I have a collection of 160 gold coins which I want to share between my four grandchildren. At present they are 9, 5, 4 and 2 years old, so I could share out the coins in the ratio of their ages without having to round off any figures. However, I have decided to wait until the next time their ages are such that I can share them out in the ratio of their ages without having to round off any figures. How many more coins will my youngest grandchild eventually receive than if I had decided to share them out now? A 3 B 5 C 9 D 12 24 Each day I eat lunch at my own house, my aunt’s house or my sister’s house. During the last 11 days I ate lunch at least once at each person’s house. I ate lunch twice as many times at my aunt’s house as at my own house. Which piece of information, by itself, would enable you to work out how many days I ate lunch at my sister’s house? A I ate lunch at my sister’s house more times than at my own house B I ate lunch at my sister’s house an odd number of times C I ate lunch at my aunt’s house an even number of times D I ate lunch at my sister’s house more times than at my aunt’s house 25 Widgit Inc. make gruffles and mankets. Gruffles only come in black, while mankets come in either black or white. Last week, 84% of the mankets they made were white and 37% of all the items they made were black. What percentage of the items they made last week were gruffles? A 21% B 25% C 31% D 53%

17 © UCLES 2016 9694/12/O/N/16 [Turn over 26 Fatima and Sam like to go cycling. They both ride at a constant speed but Fatima’s speed is quicker than Sam’s. Last week they set off from Applebig at the same time but Fatima got to their destination Beechwood 45 minutes before Sam. This week, their route was 20 km shorter but Fatima arrived at their destination with Sam still having 8 km to ride. Sam always cycles at a constant speed of 16 km/h. What is the constant speed at which Fatima always cycles? A 20 km/h B 24 km/h C 28 km/h D 32 km/h 27 At the end of each round of a racing competition points are awarded to each of the participants. The winner receives 5 points, the person in second place scores 3 points and all other participants score 1 point. Hilary and Jennifer have both competed in all of the rounds so far. Hilary has now scored a total of 30 points and Jennifer has a total of 38 points. What is the smallest number of rounds that could have taken place? A 8 rounds B 9 rounds C 10 rounds D 12 rounds

18 © UCLES 2016 9694/12/O/N/16 28 Orla has a loan from her bank, with slightly unusual conditions. Every month, she pays back a fixed percentage of the outstanding amount. Every month the bank loans her an extra fixed amount. No interest is payable until the end of the loan period. Which of the following graphs could not show her balance from month to month? Outstanding loan Months A Outstanding loan Months B Outstanding loan Months C Outstanding loan Months D

19 © UCLES 2016 9694/12/O/N/16 29 The manager of a train company calculates the price of a ticket by charging a fixed amount plus an extra amount per kilometre of travel. Last year, when prices needed to go up, the fixed amount was kept the same, but the cost per kilometre was increased by 2¢. This resulted in the price for a 30 kilometre journey going up by 2.5%. This year the manager has chosen to increase the fixed amount by 10% instead. The price for a 50 kilometre journey is now $2.50 more than it was before the first change. What is the cost of a ticket for a 50 kilometre journey after this latest increase? A $30.00 B $31.00 C $31.50 D $32.50 30 Tickets for a recent concert were $10 each for adults and $5 each for children. A family ticket for 2 adults and 2 children was available for $25. Tickets for all 640 seats in the theatre were sold, and the total income from ticket sales was $4780. What is the maximum number of family tickets that could have been sold? A 52 B 82 C 108 D 160

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® IGCSE is the registered trademark of Cambridge International Examinations. This document consists of 2 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level THINKING SKILLS 9694/12 Paper 1 Problem Solving October/November 2016 MARK SCHEME Maximum Mark: 30 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 AS/A Level – October/November 2016 9694 12 © UCLES 2016 Question Number Key Question Number Key 1 D 16 C 2 C 17 B 3 A 18 A 4 C 19 C 5 D 20 D 6 B 21 B 7 A 22 B 8 B 23 C 9 A 24 B 10 B 25 B 11 C 26 A 12 D 27 C 13 B 28 B 14 D 29 D 15 D 30 C