Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier January 2013 Pages 2 3 4 5 Mark Applications of Mathematics (Linked Pair Pilot) Unit 1 Finance and Statistics Thursday 17 January 2013 9.00 am to 10.30 am For this paper you must have: l mathematical instruments. You may use a calculator. 93701H H 6 7 8 9 10 11 12 13 14 15 16 17 18 19 TOTAL Time allowed l 1 hour 30 minutes Instructions l Use black ink or black ball-point pen. Draw diagrams in pencil. l Fill in the es at the top of this page. l Answer all questions. l You must answer the questions in the spaces provided. around each page or on blank pages. l Do all rough work in this book. Cross through any work that you do not want to l be marked. If your calculator does not have a π button, take the value of π to be 3.14 unless another value is given in the question. Information l The marks for questions are shown in brackets. l The maximum mark for this paper is 80. l The quality of your written communication is specifically assessed in Questions 3 and 10. These questions are indicated with an asterisk (*). l You may ask for more answer paper, graph paper and tracing paper. These must be tagged securely to this answer booklet. l You are expected to use a calculator where appropriate. Advice l In all calculations, show clearly how you work out your answer. (JAN1393701H01) 93701H
2 Answer all questions in the spaces provided. 1 This spreadsheet is used to work out monthly pay. A B C D E 1 Name Annual pay Taxable income Tax Monthly pay 2 Jim 17000 =B2 7600 =0.2*C2 =(B2 D2)/12 Jim s annual pay is 17 000 1 (a) What is the value in cell C2? Answer... (1 mark) 1 (b) What is the value in cell E2? Answer... (3 marks) (02)
3 2 Flags-4-U Paving slabs 4 each + Delivery 20 2 (a) Write down a formula for the cost, C, of buying x paving slabs and having them delivered. C =... (2 marks) 2 (b) Stones-R-Us Paving slabs 2.50 each + Delivery 35 James wants to buy some paving slabs and have them delivered. The total cost is the same from both companies. How many paving slabs does he want to buy? Answer... (3 marks) 9 Turn over (03)
4 3 A smoothie recipe uses banana, kiwi and yoghurt in the ratio 4 : 1 : 3 by weight. 3 (a) A smoothie is made using 280 g of banana. How much kiwi and yoghurt are needed? Kiwi... g Yoghurt... g (3 marks) (3 marks) (3 marks) 3 (b) Express the weight of kiwi as a percentage of the weight of the smoothie. Answer... % (2 marks) *3 (c) Each smoothie costs 72p to make. 3 (c) (i) The smoothies are sold at the school fayre. The school wants to make at least 30% profit on each smoothie. Work out the cheapest selling price to do this. Answer... (4 marks) (04)
5 3 (c) (ii) The cost of banana for one smoothie is 15p. The price of bananas increases by 40%. Work out the percentage increase in the cost of making a smoothie. Answer... % (4 marks) Turn over for the next question 13 Turn over (05)
6 4 A music shop manager wants to know whether people buy music from shops or websites. 4 (a) One of the questions he asks is Do you use music shops? Write down one criticism of the question. (1 mark) 4 (b) Write a suitable question to find whether people buy music from shops or websites. You should include a response section. (2 marks) (06)
7 4 (c) The manager decides to survey the first 20 customers entering his shop on a Monday morning. Give one reason why this sample is likely to be biased. (1 mark) 4 (d) How should the manager choose a sample? (2 marks) Turn over for the next question 6 Turn over (07)
8 5 Here are the shop and website prices of some books. Shop price ( ) 5 6 8 8 8 9 10 13 13 17 Website price ( ) 2.90 3.50 2 4 4.50 4.50 5.40 7.20 8.00 9.80 5 (a) The first six points have been plotted on this scatter diagram. Complete the scatter diagram. (2 marks) 10 8 Website price ( ) 6 4 2 0 0 4 6 8 10 12 14 16 Shop price ( ) 18 (08)
9 5 (b) Describe the type of correlation shown on the scatter diagram. (1 mark) 5 (c) A book has a shop price of 15. Estimate its website price. You must show your working.... (2 marks) 5 (d) The shop manager thinks that one of the prices on the website is incorrect. Circle this point on the graph. Give a reason for your answer. (2 marks) Turn over for the next question 7 Turn over (09)
10 6 These interest rates are paid on investments. Investment Interest rate (percent per year) Less than 10 000 0.8 10 000 to 19 999 1.2 20 000 or more 1.5 This flow chart can be used to work out the interest, I, earned on an investment of x. Start Input x Yes Is x < 10 000? No Is x < 20 000? Yes I = x 0.008 No I = x 0.015 I = x 0.012 Output I Stop (10)
11 6 (a) Phil makes an investment of 2000. How much interest does Phil earn?... (2 marks) 6 (b) Sam makes an investment of 36 000. How much interest does Sam earn?... (2 marks) 6 (c) Megan s investment earns 225 interest. How much was her investment?... (3 marks) 7 Turn over (11)
12 7 Dan and Jane take it in turns to drive to work. The table shows information about 40 journeys when Dan drives. Time, t (minutes) Frequency 10 t 20 8 20 t 25 10 25 t 30 14 30 t 45 8 7 (a) Draw a cumulative frequency diagram to show this information on the grid. 40 30 Cumulative frequency 20 10 0 0 10 20 30 Time, t (minutes) 40 50 (4 marks) (12)
13 7 (b) Use your graph to estimate the median journey time. Answer... minutes (1 mark) 7 (c) Use your graph to estimate the interquartile range. Answer... minutes (2 marks) 7 (d) The -and-whisker plot shows information about 40 journeys when Jane drives. 0 10 20 30 40 50 Jane says, My times are quicker and more consistent than Dan s. Comment on Jane s statement. Time, t (minutes) (4 marks) 11 Turn over (13)
14 8 Some boys share a bag of sweets. If each boy has 6 sweets, there will be 5 sweets left in the bag. If there were 3 more sweets in the bag, each boy could have exactly 7 sweets. How many sweets were in the bag? Answer... (4 marks) 9 In 2008, the number of visitors to the Lake District was 8.3 10 6 These visitors spent a total of 1.171 10 9 On average, how much did each visitor spend? Give your answer to the nearest pound.... (3 marks) (14)
15 *10 Here is a sign by a wishing well. A formula for estimating the depth, d metres, of a well is d = 5t 2 where t is the time in seconds taken by an object to reach the water at the bottom of the well. A coin is dropped into the well. It takes 2.8 seconds, to the nearest tenth of a second, to reach the water. Does this information support the statement on the sign? You must show your working. (5 marks) 12 Turn over (15)
16 11 The table shows information about the time, t (minutes), 100 people spend visiting a castle. Time, t (minutes) Frequency 10 t 40 12 40 t 60 36 60 t 80 24 80 t 150 28 11 (a) Draw a histogram to represent this information. 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time, t (minutes) (3 marks) (16)
17 11 (b) The table shows information about the time, t (minutes), 80 people spend visiting a stately home. Time, t (minutes) Frequency 10 t 40 15 40 t 60 25 60 t 80 22 80 t 150 18 Naz says, The median time at the castle is almost 2 minutes more than the median time at the stately home. Is he correct? You must show your working. (5 marks) Turn over for the next question 8 Turn over (17)
18 12 A joiner makes two types of garden table. Deluxe tables each cost 400 to make. Economy tables each cost 200 to make. She decides to l spend no more than 3000 l make at least two of each type of table l make no more than 10 tables altogether. 12 (a) One inequality for this information is d + e 10 Explain what the letters d and e stand for. (1 mark) 12 (b) Use the information above to show that 2d + e 15 (1 mark) 12 (c) The joiner makes a profit of 80 on each deluxe table sold. She makes a profit of 50 on each economy table sold. The lines d = 2 and 2d + e =15 are drawn on the graph opposite. Complete the graph to show all the information and work out the maximum profit she can make.... (5 marks) (18)
19 16 e d = 2 14 12 10 8 6 4 2 0 0 2 4 6 2d + e = 15 8 10 12 14 d END OF QUESTIONS 7 (19)
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