General Certificate of Secondary Education Higher Tier

Transcription

1 Centre Number Surname Other Names Candidate Number For Examiner s Use Examiner s Initials Candidate Signature General Certificate of Secondary Education Higher Tier Pages Mark Mathematics Unit 1 Higher Tier Practice Paper Set 2 Specification 4360 For this paper you must have: a calculator mathematical instruments. mathematical instruments. Time allowed 1 hour 43601H H TOTAL Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. Fill in the boxes at the top of this page. Answer all questions. You must answer the questions in the space provided. Do not write outside the box around each page or on blank pages. Do all rough work in this book. Cross through any work that you do not want to be marked. Information The marks for questions are shown in brackets. The maximum mark for this paper is 54. The quality of your written communication is specifically assessed in questions 1, 2 and 6. These questions are indicated with an asterisk ( ) You may ask for more answer paper and graph paper. These must be tagged securely to this answer booklet. Advice In all calculations, show clearly how you work out your answer. Practice Paper Set 2/43601H

2 2 Do not write outside the box Answer all questions in the spaces provided people cycle to work. Their journey times in minutes are shown below (a) Draw an ordered stem-and-leaf diagram to show the data. Remember to complete the key. Key : represents... minutes (4 marks) 1 (b) A new person cycles to work. When her journey time is included in the data, the range increases by 3 minutes. What are the two possible values of her journey time?... Answer...minutes or...minutes (2 marks)

3 3 1 (c) The local council is doing a survey to find opinions on a new cycle route. Give two reasons why these cyclists would not make a good sample. Reason Reason (2 marks) 2 Zara makes 150 birthday cards. It costs 1.25 to make each card. She keeps one-fifth of the cards to give to family and friends. She sells 70% of the rest for the full price of 4. She sells the others at half price. How much profit does Zara make? Answer... (6 marks) 14 Turn over

4 4 Do not write outside the box 3 In 2009 the Wimbledon ladies singles champion won (a) In 2009 the total prize money for the ladies singles was Work out the percentage of the prize money won by the champion. Give your answer to one significant figure. Answer...% (3 marks) 3 (b) The ratio for 2008 to 2009 of the champion s prize money is 15 : 17 Work out the champion s prize money in Answer... (2 marks)

5 5 4 Ajay collects data about the number of MP3 players in different families. Number of MP3 players Number of families The number of families with one MP3 player is missing. The families own 70 MP3 players in total. 4 (a) Calculate the mean number of MP3 players in each family. Answer... (4 marks) 4 (b) Ajay wants to test this hypothesis: Families with higher incomes own more MP3 players. Use the data handling cycle to write a plan for Ajay. (3 marks) Turn over 12

6 5 Charlie joins an archery club. 6 Do not write outside the box Each week she fires 50 arrows. The graph shows the relative frequency of her arrows hitting the target Relative frequency of hitting the target Number of arrows 5 (a) How many of Charlie s first 50 arrows hit the target? Answer... (2 marks)

7 7 Do not write outside the box 5 (b) Work out the number of Charlie s arrows that hit the target in the fifth week. Answer... (3 marks) 5 (c) Charlie fires an arrow. Estimate the probability that she hits the target. Answer... (1 marks) 6 The table shows a summary of the waiting times of 120 people who telephone a London call centre. Time, t Frequency (seconds) 0 < t < t < t < t < t < t Turn over

8 8 6 (a)(i) Draw a cumulative frequency graph for the data. Cumulative frequency Time, t (seconds) (3 marks) 6 (a)(ii) The call centre manager sets the following target. 95% of calls should have a waiting time less than 1 minute 50 seconds. Do you think this target is met? You must show your working. (2 marks)

9 9 6 (b) The box plot shows information about the waiting times for a Glasgow call centre Time, t (seconds) 120 The Glasgow and London call centres have the same target for waiting times. Compare the waiting times for the London call centre with the Glasgow call centre. (5 marks) 10 Turn over

10 10 7 (a) Ewan works in a factory with two production lines, A and B. On Monday and Tuesday workers are randomly selected to work on line A or line B. Each day the probability of working on line A is (a(i) What is the probability Ewan works on line A on both days? Answer... (2 marks) 7 (a)(ii) What is the probability Ewan works on line A on at least one of the two days? Answer... (3 marks)

11 11 7 (b) Line A makes bags containing 10 chocolates. Each chocolate has either a soft centre or hard centre. Two chocolates are chosen at random from a bag. The probability that both chocolates have a soft centre is Complete the tree diagram. first chocolate second chocolate... soft... soft hard soft... hard... hard (4 marks) 9 Turn over

12 12 8 Population density is the average number of people per square kilometre. The population of the UK is 62 million to the nearest million. The area of the UK is km 2, correct to 3 significant figures. Calculate the maximum population density in the UK. You must show your working. Answer... people per km 2 (3 marks) END OF QUESTIONS Copyright 2010 AQA and its licensors. All rights reserved 3

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