GCSE Applications of Mathematics (Linked Pair Pilot) Question paper Unit 01 - Finance and Statistics January 2013

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1 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 Mark Applications of Mathematics (Linked Pair Pilot) Unit 1 Finance and Statistics Thursday 17 January am to am For this paper you must have: l mathematical instruments. You may use a calculator H H 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. (JAN H01) 93701H

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.

2 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 =B =0.2*C2 =(B2 D2)/12 Jim s annual pay is (a) What is the value in cell C2? Answer... (1 mark) 1 (b) What is the value in cell E2? Answer... (3 marks) (02)

A B C D E 1 Name Annual pay Taxable income Tax Monthly pay 2 Jim 17000 =B2 7600 =0.

3 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)

50 each + Delivery 35 James wants to buy some paving slabs and have them delivered.

4 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)

.. g (3 marks) (3 marks) (3 marks) 3 (b) Express the weight of kiwi as a percentage of the weight of the smoothie. Answer.

5 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 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)

Write down one criticism of the question.

7 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)

Give one reason why this sample is likely to be biased.

8 8 5 Here are the shop and website prices of some books. Shop price ( ) Website price ( ) (a) The first six points have been plotted on this scatter diagram. Complete the scatter diagram. (2 marks) 10 8 Website price ( ) Shop price ( ) 18 (08)

9 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 10 6 These interest rates are paid on investments. Investment Interest rate (percent per year) Less than to 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 < ? No Is x < ? Yes I = x No I = x I = x Output I Stop (10)

11 11 6 (a) Phil makes an investment of How much interest does Phil earn?... (2 marks) 6 (b) Sam makes an investment of 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)

... (2 marks) 6 (b) Sam makes an investment of 36 000.

12 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 t t t (a) Draw a cumulative frequency diagram to show this information on the grid Cumulative frequency Time, t (minutes) (4 marks) (12)

Time, t (minutes) Frequency 10 t 20 8 20 t 25 10 25 t 30 14 30 t 45 8 7 (a) Draw a

13 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 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)

.. minutes (2 marks) 7 (d) The -and-whisker plot shows information about 40 journeys when Jane drives.

14 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 These visitors spent a total of On average, how much did each visitor spend? Give your answer to the nearest pound.... (3 marks) (14)

Answer... (4 marks) 9 In 2008, the number of visitors to the Lake District was 8.

15 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)

by an object to reach the water at the bottom of the well. A coin is dropped into the well. It takes 2.

16 16 11 The table shows information about the time, t (minutes), 100 people spend visiting a castle. Time, t (minutes) Frequency 10 t t t t (a) Draw a histogram to represent this information Time, t (minutes) (3 marks) (16)

Time, t (minutes) Frequency 10 t 40 12 40 t 60 36 60 t 80 24 80 t 150 28 11

17 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 t t t 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)

Time, t (minutes) Frequency 10 t 40 15 40 t 60 25 60 t 80 22 80 t 150 18 Naz says, The median

18 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)

12 (a) One inequality for this information is d + e 10 Explain what the letters d and e stand for.

19 19 16 e d = d + e = d END OF QUESTIONS 7 (19)

GCSE Mathematics Question Paper Unit 2 March 2012

GCSE Mathematics Question Paper Unit 2 March 2012 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier March 2012 Pages 2 3 4 5 Mark Mathematics