AQA Level 1/Level 2 Certificate in Use of Mathematics. Practice Papers

Transcription

1 AQA Level 1/Level 2 Certificate in Use of Mathematics Practice Papers

2 43503H Core Unit (Higher tier)* [Practice Paper] 4981 Money Management [9981/W, June 2010] 4982 Using Spatial Techniques [9982/W, June 2008] 4983 Using Data [9983/W, June 2010] 4984 Financial Calculations [9984, June 2009] 4985 Shape and Space [9985, June 2009] 4986 Data Handling [9986, June 2009] 4988 Algebra and Graphs* [9988, June 2010] * No Report on the Examination available

3 Centre Number Surname Other Names Candidate Number For Examiner s Use Examiner s Initials Candidate Signature Use of Mathematics Core Certificate in Use of Mathematics Higher Level Practice Question Paper For this paper you must have: a clean copy of the Data Sheet (enclosed) a ruler a calculator H Question TOTAL Mark Time allowed 1 hour 15 minutes Instructions Use black ink or black ball-point pen. Pencil should only be used for drawing. Fill in the boxes at the top of this page. Answer all questions. You must answer the questions in the spaces provided. Do not write outside the box around each page. Do all rough work in this book. Cross through any work that you do not want to be marked. You may not refer to the copy of the Data Sheet that was available prior to this examination. A clean copy is enclosed for your use. Information The marks for questions are shown in brackets. The maximum mark for this paper is 50. You are expected to use a calculator where appropriate. Advice In all calculations, show clearly how you work out your answer H

4 2 Do not write outside the box Section A Answer all questions in the spaces provided. Use Rob s lakeside café on page 2 of the Data Sheet. 1 (a) For the first 5 customers, what is the mean amount paid per customer? Answer... (2 marks) (b) Explain why your answer to part (a) might not be a good estimate for the typical amount paid by a customer (1 mark) (c) Rob needs to employ a fifth waiter. He needs 3 waiters working in the café at any one time. Between what times will Rob need the new waiter to work in the café? Start... Finish... (2 marks) (d) Ben s rate of pay is 7.20 per hour Calculate Ben s weekly wage Answer... (2 marks)

5 3 Do not write outside the box (e) In one day a total of 120 burger meals and pizza meals were sold. The numbers of burger meals and pizza meals sold were in the ratio 2:3. Work out the number of burger meals sold that day Answer... (2 marks) (f) Sarah s rate of pay is R per hour. Express her weekly wage in terms of R Answer... (2 marks) (g) Claire and Sarah have the same rate of pay. Sarah earns 48 more than Claire each week. What is Sarah s rate of pay? Answer... (4 marks) 15

6 4 Do not write outside the box Section B Answer all questions in the spaces provided. Use Size Matters on page 3 of the Data Sheet. 2 (a) Find the area of the tennis service box Answer...m 2 (1 mark) (b) Write down this area in cm 2. Answer...cm 2 (1 mark) (c) Which of the initial assumptions would not hold for a slower serve? (1 mark) 3

7 5 Do not write outside the box 3 (a) Show how the equation x x leads to 1.79 x = (3 marks) (b) Consider a fast serve from a height of 2.7 m which hits the ground 6.40 m from the net. Use similarity to work out how high the ball is when it passes over the net (4 marks) 7

8 6 Do not write outside the box Section C Answer all questions in the spaces provided. Use Darts on page 4 of the Data Sheet. 4 (a) Alan scores a treble 20, double 17 and a bull. Find Alan s score.... Answer... (1 mark) (b) Ben needs to score 161 to win a game, with 3 darts. He scores treble 20 with his first dart. He then wins the game with his next two darts. Find the value of each of his two darts Second dart... Third dart... (2 marks) (c) Caroline needs 92 to win a game and she has two darts to achieve this. One way she could achieve this score is treble 14 followed by bull. Find the other two ways that Caroline could score 92 with her two darts to win the game One way... Second way... (3 marks)

9 7 Do not write outside the box (d) Diane is going to play Eddie who is of a similar ability to her. She says I ll give you a better chance this game. Each of your scores will be doubled. (i) What is the highest score Eddie can make with one dart?... Answer... (1 mark) (ii) Explain who should win this game (1 mark) 8

10 8 Do not write outside the box 5 (a) Find the difference in area between the area of the front surface of the dartboard and the area of the scoring sections Answer... (4 marks) (b) Find the difference in area as a percentage of the area of the front surface of the dartboard Answer... (2 marks) (c) The rule for the size of the scoring sections allows for the diameter to be 340 mm to 3 significant figures. What is the difference between the largest possible diameter and the smallest possible diameter?... Answer... (2 marks) 8

11 9 Do not write outside the box Section D Answer all questions in the spaces provided. Use Conetto on page 5 of the Data Sheet. 6 The diagram shows a small Sicilian ice-cream called a conetto. It comprises of a cone filled with ice-cream, and a scoop of ice-cream on top. The scoop is in the shape of a hemisphere. The scoop of ice-cream is covered in chocolate. All dimensions are in millimetres. 25 mm Scoop Cone (a) (i) Find the volume of the scoop giving your answer to 3 significant figures, in mm (ii) Write your answer to part (a)(i) in cm 3. Answer... (2 marks)... Answer... (1 mark)

12 10 Do not write outside the box (b) Find the surface area that must be covered by chocolate. (You may assume that there is no chocolate on the cone.) Answer... (3 marks) (c) Given that the volume of ice-cream in the cone is exactly the same as the volume of ice-cream in the scoop, find the height of the cone Answer... (3 marks) END OF QUESTIONS 9 Copyright 2010 AQA and its licensors. All rights reserved

13 Certificate in Use of Mathematics Higher Level Use of Mathematics 43503H/PM Core Preliminary Material Data Sheet Practice Data Sheet To be opened and issued to candidates one to three weeks prior to the examination REMINDER TO CANDIDATES YOU MUST NOT BRING THIS DATA SHEET WITH YOU WHEN YOU SIT THE EXAMINATION. A CLEAN COPY WILL BE MADE AVAILABLE H/PM

14 2 Rob s lakeside café Rob has recently opened a café on the edge of the Lake District National Park. The table shows the amounts paid by the first 5 customers on one day. Customer Amount Paid The café is open from 11:00 am to 6:00 pm from Monday to Saturday. Four waiters work in the café. The staff timesheet shows the hours worked each day by the waiters. Andy Ben Claire Sarah 11 am 12 noon 1 pm 2 pm 3 pm 4 pm 5 pm 6 pm This is the formula Rob used for working out staff weekly wages. Weekly wage = Rate of pay per hour number of hours worked per day 6

15 3 Size matters In championship tennis, it is extremely important for a player to get a high proportion of their first serves into play. A mathematical model of a tennis serve can help us to answer questions such as the following. Why do players noted for the high speed of their serves tend to be tall? Why do players usually have much slower second serves? For a singles tennis match, the dimensions of the court are as shown below. Baseline Net Baseline A 4.11 m Service box B 6.40 m m Consider a player standing at B and serving down the centre of the court, along the line BA. The net is at a height of 0.91m and a typical male tennis player strikes the ball at a height of 2.7 m. A fast tennis serve can travel at more than 60 m/s and, at this speed, the ball can be considered to travel in a straight line until it hits the ground. Suppose such a serve passes just over the net and hits the ground x m from the net. D A x m B 0.91 m C m E 2.70 m Triangle ADE is an enlargement of triangle ABC. x x Thus, This leads to 1.79 x = and therefore x = 6.04 Thus, the length to which our typical tennis player must hit the ball, can only vary by = 0.36 m. A slightly shorter player would have an even smaller margin of error. One of the simplest ways for a player of any size to increase their chance of getting the ball into play is to use a slower serve. Can you see which of the initial assumptions would not hold for such a serve?

16 4 Darts The standard dartboard is divided into 20 numbered sectors. Double Points Triple Points Outer bull Inner bull A dart landing in either of the two large portions of each numbered sector scores that number of points. A dart landing in the thin inner portion of a numbered sector scores triple that number of points. A dart landing in the thin outer portion of a numbered sector scores twice that number of points. A dart landing in the inner bull scores 25. A dart landing in the outer bull scores 50. A dart landing outside these portions of the board scores nothing. The highest possible score with three darts is therefore 180, obtained when all three darts land in triple 20. The standard game of darts is a contest between two players who take it in turns to throw three darts. Each player starts with a score of 501 and the scores of their darts are used to reduce this to precisely 0. In achieving this, the last dart thrown must be a double or the inner bull. A throw that reduces a players score to 1 or a negative number is invalid the player s turn ends and their score is reset to what it was before that turn. The scoring area of a standard dartboard is a circle of diameter 340 mm. The entire front surface of a standard dartboard has a diameter of 451 mm.

17 5 Conetto Conettos are small ice-cream filled cones that are a speciality desert from Sicily. They are small cones filled with ice-cream, with a scoop of ice-cream on top.the scoop is in the shape of a hemisphere. The scoop of ice-cream is covered in chocolate. They are bought by weight and are put on trays straight from the freezer. People in the UK will be more familiar with Cornetto, which are much larger. In general a person would only eat one Cornetto, as an ice-cream. 25 mm Scoop Cone The volume of sphere of radius r is The surface area of the sphere is 4 π 3 3 r. 2 4π r. The volume of a cone of base radius r and height h is 1 π 2. 3 r h END OF DATA SHEET ACKNOWLEDGEMENT OF COPYRIGHT HOLDERS AND PUBLISHERS Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyrightholders have been unsuccessful and AQA will be happy to rectify any omissions of acknowledgements in future papers if required. Copyright 2011 AQA and its licensors. All rights reserved

18 AQA Certificate in Use of Mathematics Core - Higher (43503H) Answers and Marking Scheme Practice Paper Core Higher 43503H AQA Certificate in Use of Mathematics Mark Scheme Practice Paper Q Solution Marks Total Comments (a) M1 adding and dividing by A1 2 cao (b) (c) Criticising time period or suggesting sampling during the whole day 1.00 (pm) or (pm) or E1 1 M1 A1 2 cao Identifying times, e.g. notes on diagram or for 1 answer given (implied process) (d) M1 M1 substitution into formula A1 2 A1 cao gets M1 A0 (e) M1 48 A1 2 A1 cao (f) 5 6 R = 30 R M1A1 2 M or seen (g) 30 R R M1A1 8 per hour M1A1 4 Total 15 2(a) 26.3 m 2 B1 1 (b) cm 2 B1 1 (c) Straight line assumption B1 1 Total 6 2.7x 0.91 x M1A1 2.7x 0.91x A1 3 3(a) (b) h M1A h M m A1 4 (3 cm above the net) Total 7 1

19 Core Higher 43503H AQA Certificate in Use of Mathematics Mark Scheme Practice Paper 4(a) B1 1 (b) 51, 50 M1A1 2 (c) M1A A1 3 (d)(i) 120 B1 1 (ii) Diane, Eddie can never score odd values E1 1 5(a) Total π225.5 or π 170 M1A1 Either area Difference = mm 2 M1A1 4 Answer to(a) (b) 43.2% 2 M1A1 2 π225.5 (c) = 1 mm M1A1 2 6(a)(i) Total π M mm 3 A1 2 (ii) 4.09 cm 3 B1f 1 (b) (c) Area = 4π 2 2 M1A1 = 982 mm 2 A1f π h M1A mm A1 3 Total 9 TOTAL MARK FOR PAPER 50 2

20 Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Free-Standing Mathematics Qualification Foundation Level June 2010 Money Management (Pilot) 9981/W Unit 1 Wednesday 26 May 2010 For this paper you must have: * a clean copy of the Data Sheet (enclosed) * a protractor * a ruler * a calculator am to am Question TOTAL Mark Time allowed * 1 hour Instructions * Use black ink or black ball-point pen. Pencil should only be used for drawing. * Fill in the boxes at the top of this page. * Answer all questions. * You must answer the questions in the spaces 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 you do not want to be marked. * You may not refer to the copy of the Data Sheet that was available prior to this examination. A clean copy is enclosed for your use. Information * The marks for questions are shown in brackets. * The maximum mark for this paper is 40. * You are expected to use a calculator where appropriate. Advice * In all calculations, show clearly how you work out your answer. (JUN109981/W01) P28634/Jun10/9981/W 6/6/ 9981/W

21 2 Do not write outside the box Section A Answer all questions in the spaces provided. Use Bank statement on page 2 of the Data Sheet. 1 (a) Describe in full the transaction which took place on 3 May. (1 mark) 1 (b) What was the total amount of the withdrawals from cashpoints? 1 (c) (i) How many cheques are shown on the statement? Answer... (1 mark) Answer... (1 mark) 1 (c) (ii) What was the total value of the cheques shown on this statement? Answer... (2 marks) 5 (02) P28634/Jun10/9981/W

22 3 Do not write outside the box Section B Answer all questions in the spaces provided. Use Toy sale on page 3 of the Data Sheet. 2 (a) Sean bought a board game. The usual price of the board game was 24. How much did Sean pay? 2 (b) A Meccano set costs 31 before the sale. Fiona bought a Meccano set in the sale. How much did Fiona pay for the Meccano set? Answer... (3 marks) Answer... (3 marks) 6 3 Remote-control cars were imported from Norway and each cost 530 Norwegian Krone. The exchange rate was Norwegian Krone to 1. Calculate the cost of each car in pounds. Answer... (3 marks) 3 Turn over s (03) P28634/Jun10/9981/W

23 4 Do not write outside the box 4 Ivan is completing a jigsaw puzzle which has 800 pieces. He has fitted 360 pieces. 4 (a) What fraction of the jigsaw puzzle has Ivan completed? Give your fraction in its simplest form. 4 (b) Give your answer to part (a) as a percentage. Answer... (2 marks) Answer... (1 mark) 3 5 (a) Lily spent on toys in the sale. She paid with two 20 notes. How much change did she receive? Answer... (2 marks) 5 (b) The shop assistant gave Lily her change using the smallest possible number of notes and coins. What notes and coins did he give Lily? Answer: notes... Answer: coins... (1 mark) 3 (04) P28634/Jun10/9981/W

24 5 Do not write outside the box Section C Answer all questions in the spaces provided. Use Increase in cost of food on page 4 of the Data Sheet. 6 The data are reproduced below. A B C D E 1 Item Cost in July 2007 (pence) Cost in July 2008 (pence) 2 Baked beans Cornflakes Eggs, 12 medium free-range Milk, semi-skimmed, 6 pints Pure corn oil White loaf (800 grams) Increase in cost (pence) Increase as a percentage of cost in (a) Complete the spreadsheet. Give the percentages to the nearest whole number. Space for working (5 marks) 6 (b) Write down a formula which would give the content of cell E2. Answer... (1 mark) Turn over s 6 (05) P28634/Jun10/9981/W

25 6 Do not write outside the box 7 Mike and Naomi have bought 24 eggs. They agree to divide the eggs in the ratio 3:1 with Mike having more. How many does Mike have? Answer... (3 marks) 3 (06) P28634/Jun10/9981/W

26 7 Do not write outside the box Section D Answer all questions in the spaces provided. Use Cans of cola on page 4 of the Data Sheet. 8 Pack Number of cans Cost of the pack (pence) Single can 1 Small 6 Standard 10 Large 24 Special offer 20 Cost per can (pence) 8 (a) Complete the table, giving the cost per can to one decimal place. (5 marks) Space for working 8 (b) Which of the five packs gives the best value for money? 8 (c) Why would a person not necessarily buy this size of pack? Answer... (1 mark) Answer... (1 mark) 7 Turn over s (07) P28634/Jun10/9981/W

27 8 Do not write outside the box Section E Answer all questions in the spaces provided. Use Bank accounts on page 5 of the Data Sheet. 9 Pete deposits 3000 in the County Saver account for 9 months. It earns compound interest at the rate of 0.72% paid every 3 months. Starting value ( ) Interest ( ) Final value ( ) First 3 months Second 3 months Third 3 months Complete the table above. (4 marks) Space for working 4 END OF QUESTIONS ACKNOWLEDGEMENT OF COPYRIGHT-HOLDERS AND PUBLISHERS Section C: mysupermarket.co.uk Copyright Ó 2010 AQA and its licensors. All rights reserved. (08) P28634/Jun10/9981/W

28 Free-Standing Mathematics Qualification Foundation Level June 2010 Money Management (Pilot) 9981/PM Unit 1 Preliminary Material Data Sheet To be opened and issued to candidates between Wednesday 5 May 2010 and Wednesday 19 May 2010 REMINDER TO CANDIDATES YOU MUST NOT BRING THIS DATA SHEET WITH YOU WHEN YOU SIT THE EXAMINATION. A CLEAN COPY WILL BE MADE AVAILABLE. P28633/Jun10/9981/PM 6/6/6/ 9981/PM

29 2 Bank statement Cross Channel Bank Account Number: J.C. STEPHENSON 21, AVENUE CLOSE, CHATHAM, ME4 5FR Sheet No Sort Code: CHATHAM YOUR PRESENT OVERDRAFT LIMIT IS: 600 When overdrawn marked OD Date Payment type Details Paid out ( ) Paid in ( ) Balance ( ) 2010 Opening Balance APR Cashpoint HSBC WEST STREET, CHATHAM 15 APR Debit card CAFÉ BISTRO APR Direct Debit NATIONAL CREDIT CARD OD 16 APR Cheque OD 18 APR Cashpoint HSBC WEST STREET, OD CHATHAM 23 APR Bank Giro Credit A1 TECHNOLOGY APR Debit card MEDWAY TRAVEL AGENCY APR Cheque APR Cashpoint HSBC WEST STREET, CHATHAM 1 MAY Direct Debit PREMIER INSURANCE MAY Cheque MAY Debit card BARGAIN BOOKS MAY Debit card INDIAN CURRY HOUSE MAY Cheque MAY SUNDRY CREDIT MAY INTEREST [GROSS] MAY Fixed Serv Chrg ACCOUNT CHARGE P28633/Jun10/9981/PM

30 3 Toy sale The toy department of a large store is closing down and is advertising some special sale offers. ALL Remote-control Helicopters 2 for 25 SAVE 8 Jigsaws 2 5 OFF Meccano sets 45% OFF ALL BOARD GAMES NOW 1 3 OFF P28633/Jun10/9981/PM Turn over s

31 4 Increase in cost of food A newspaper, in conjunction with mysupermarket.co.uk, compared the costs of certain foods in July 2007 and in July Some of the data found are shown below. Item Cost in July 2007 Cost in July 2008 Baked beans 25p 31p Cornflakes 83p 86p Eggs, 12 medium free-range 1.75p 2.58p Milk, semi-skimmed, 6 pints 1.68p 2.12p Pure corn oil 49p 1.38p White loaf (800 grams) 48p 72p Cans of cola Cans of cola, each containing 330 ml of cola, can be bought in packs of different sizes. Small, containing 6 cans costing 2.53 Standard, containing 10 cans costing 3.49 Large, containing 24 cans costing 7.41 The store is also advertising a special offer of 20 cans for The cost of a single can of cola is 52p. P28633/Jun10/9981/PM

32 5 Bank accounts The Atlantic Union Bank has a number of different savings accounts. Account name Rate of interest National Saver 3.9% paid annually County Saver 0.72% paid every 3 months City Saver 1.92% paid every 6 months Instant Access 0.3% paid annually END OF DATA SHEET P28633/Jun10/9981/PM

33 6 There are no data printed on this page P28633/Jun10/9981/PM

34 7 There are no data printed on this page P28633/Jun10/9981/PM

35 8 There are no data printed on this page ACKNOWLEDGEMENT OF COPYRIGHT-HOLDERS AND PUBLISHERS Increase in cost of food: mysupermarket.co.uk Copyright Ó 2010 AQA and its licensors. All rights reserved. P28633/Jun10/9981/PM

36 Version : klm Free-Standing Mathematics Qualification June 2010 Money Management 9981/W Foundation Level Final Mark Scheme

37 Mark schemes are prepared by the Principal Examiner and considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the standardisation meeting attended by all examiners and is the scheme which was used by them in this examination. The standardisation meeting ensures that the mark scheme covers the candidates responses to questions and that every examiner understands and applies it in the same correct way. As preparation for the standardisation meeting each examiner analyses a number of candidates scripts: alternative answers not already covered by the mark scheme are discussed at the meeting and legislated for. If, after this meeting, examiners encounter unusual answers which have not been discussed at the meeting they are required to refer these to the Principal Examiner. It must be stressed that a mark scheme is a working document, in many cases further developed and expanded on the basis of candidates reactions to a particular paper. Assumptions about future mark schemes on the basis of one year s document should be avoided; whilst the guiding principles of assessment remain constant, details will change, depending on the content of a particular examination paper. Further copies of this Mark Scheme are available to download from the AQA Website: Copyright 2010 AQA and its licensors. All rights reserved. COPYRIGHT AQA retains the copyright on all its publications. However, registered centres for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within the centre. Set and published by the Assessment and Qualifications Alliance. The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number ) and a registered charity (registered charity number ). Registered address: AQA, Devas Street, Manchester M15 6EX

38 Money Management 9981/W (Pilot) - AQA FSMQ Mark Scheme 2010 June series Key to mark scheme and abbreviations used in marking M m or dm A B E mark is for method mark is dependent on one or more M marks and is for method mark is dependent on M or m marks and is for accuracy mark is independent of M or m marks and is for method and accuracy mark is for explanation or ft or F follow through from previous incorrect result MC mis-copy CAO correct answer only MR mis-read CSO correct solution only RA required accuracy AWFW anything which falls within FW further work AWRT anything which rounds to ISW ignore subsequent work ACF any correct form FIW from incorrect work AG answer given BOD given benefit of doubt SC special case WR work replaced by candidate OE or equivalent FB formulae book A2,1 2 or 1 (or 0) accuracy marks NOS not on scheme x EE deduct x marks for each error G graph NMS no method shown c candidate PI possibly implied sf significant figure(s) SCA substantially correct approach dp decimal place(s) No Method Shown Where the question specifically requires a particular method to be used, we must usually see evidence of use of this method for any marks to be awarded. However, there are situations in some units where part marks would be appropriate, particularly when similar techniques are involved. Your Principal Examiner will alert you to these and details will be provided on the mark scheme. Where the answer can be reasonably obtained without showing working and it is very unlikely that the correct answer can be obtained by using an incorrect method, we must award full marks. However, the obvious penalty to candidates showing no working is that incorrect answers, however close, earn no marks. Where a question asks the candidate to state or write down a result, no method need be shown for full marks. Where the permitted calculator has functions which reasonably allow the solution of the question directly, the correct answer without working earns full marks, unless it is given to less than the degree of accuracy accepted in the mark scheme, when it gains no marks. Otherwise we require evidence of a correct method for any marks to be awarded. 3

39 Money Management 9981/W (Pilot) - AQA FSMQ Mark Scheme 2010 June series Free-Standing Mathematics Qualification Money Management (9981/W) Answers and Marking Scheme - June 2010 Question 1 (a) Paid to Bargain Books by debit card B1 (b) Total amount is 140 B1 (c)(i) 4 B1 (c)(ii) M1 = A1 TOTAL 5 Not simply copied line from statement (2 out of 3 facts) Question 2 (a) Discount is M1 = 8 A1 or 2 24 M1 3 Sean pays 16 A1 SC2 Use of % and exactly 16 (b) Discount is M1 or M1 A1 100 Question 3 Question 4 = A1 Fiona pays TOTAL 6 A1 Cost is M1 = A1 = B1 TOTAL (a) Fraction is 800 M1 SC1 9 = 20 A1 (b) 45 % B1 ft TOTAL ( 81.8 B1) 11 4

40 Money Management 9981/W (Pilot) - AQA FSMQ Mark Scheme 2010 June series Question 5 (a) Change is M1 Allow = A1 (b) Note: 10; Coins 2, 50p, 10p, 2p. B1 Question 6 TOTAL 3 A B C D E Cost in July Increase in 2008 (pence) cost (pence) 1 Item Cost in July 2007 (pence) Increase as a percentage of cost in Baked Beans Cornflakes Eggs, 12 medium free range Milk, semiskimmed, 6 pints Pure corn oil White loaf (800 grams) (a) Column D B1 Condone 1 error (b) Question 7 Any correct in column E M1 A1 Only M1 for only 50% All E correct A1 Not ft eg Allow 3-5 for E3 To nearest integer B1 All correct D2 B2 B1 Or TOTAL 6 Total 4 parts B1 Mike has M1 C2 B2 B2 100 = 18 A1 SC2 for 6 or 6 &18 TOTAL 3 5

41 Money Management 9981/W (Pilot) - AQA FSMQ Mark Scheme 2010 June series Question 8 Pack Number of cans Cost of the pack (pence) Cost per can (pence) Single can or 52.0 Small Standard Large Special offer or 25.0 (a) Third column B1 Any correct in fourth column M1 A1 M1 only for 52p eg Allow for standard cost All column 4 correct A1 One decimal place B1 SC2 All costs in pounds (eg 0.52, 0.52; 2.53, 0.42 etc) (whether or not to 1dp) (b) Special offer B1 (c) Too many cans B1 Question 9 TOTAL 7 Starting value ( ) Interest ( ) Final value ( ) First 3 months Second 3 months Third 3 months Second 3 months M1 Accept Final value is Third 3 months M1 Accept Final value is A1 SC3 for TOTAL 4 A1 TOTAL MARK FOR PAPER 40 SC2 for 2p out. 6

42 Version : klm Free-Standing Mathematics Qualification Money Management (Pilot) 9981 Foundation level Report on the Examination 2010 examination June series

43 Further copies of this Report are available to download from the AQA Website: Copyright 2010 AQA and its licensors. All rights reserved. COPYRIGHT AQA retains the copyright on all its publications. However, registered centres for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within the centre. Set and published by the Assessment and Qualifications Alliance. The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number ) and a registered charity (registered charity number ).

44 Money Management (Pilot) - AQA Report on the Examination 2010 June series Money Management (Pilot) 9981 Examination General The candidates entered for this paper were of a variety of standard. Some were well prepared and achieved creditable marks, whereas there were also some who struggled with the paper and achieved very low totals. Some candidates showed enough working for method marks to be given where appropriate; however a significant proportion penalised themselves by failing to show their working when their answers were incorrect, for example in question 5 (a). Unless working was shown, method marks could not be given for any answer other than The topics which candidates found most difficult included: exchange rates, question 3; fractions, question 4, part (a); finding a percentage, question 6 (a). Relatively few candidates attempted trial and improvement or build up techniques. These are rarely given credit unless the answer is completely correct. Often candidates who do try such methods truncate their working which leads to errors and does not produce accurate answers. Question 1 Many candidates just wrote the line from the bank statement which was not accepted. Candidates were required to state that an item had been bought or that the money, 21.97, was paid to Bargain Books. Parts (b) and (c)(i) of this question were completed well although in part (c)(ii) a number of addition errors were seen. Question 2 Although many candidates were successful in this question, a significant proportion in part (a) did not attempt to divide 24 by 3. To divide by 3, they used approximate percentages to 1. 3 In part (b), a minority who found 45% of 31 did not subtract this reduction from 31, the original price. Question 3 This question was answered quite badly. A relatively small number of candidates divided 530 by 10.07, with only a small minority of these not rounding to Many candidates did not attempt this question. Question 4 Most candidates answered this question, on fractions, badly. Few showed any fraction in their 360 working. The creation of the fraction 800 caused major problems and even fewer could simplify 9 it to 20. Those who did obtain either of these fractions converted their answer in part (b) to 45% with no problem. 3

45 Money Management (Pilot) - AQA Report on the Examination 2010 June series Question 5 This question was answered well by most candidates; a few gave two 5 notes instead of one 10 note. Question 6 The increase in cost, column D, was usually completed correctly but a number of candidates made an error in one of their subtractions. For the few who attempted to complete column E of this spreadsheet the percentages were rarely given to the nearest integer. Only the better candidates attempted part (b) and it was rare for their solutions to be correct. Question 7 This question was answered well. The weaker candidates did not find the number of parts to be 4. Question 8 In part (a), most candidates completed the column of the Cost of the pack correctly but a significant number gave the costs in pounds as 2.53, 3.49, 7.41 and 5 rather than 253 pence, 349 pence, 741 pence and 500 pence. The cost per can was often not found correctly; many candidates did not give any of these costs per can correctly. Even when the cost of one can was given in their table as 52p, candidates did not give 52p as the Cost per can. Many candidates answered part (b) correctly with most giving a sensible reason why someone would not buy such a large number of cans. Question 9 A significant proportion of candidates completed this question correctly but the truncation of the first interest to be found to 21.75, rather than rounding its value to often gave a final answer of , rather than as required. Only a few candidates used each of the interest amounts to be 21.60; some even used and The lack of working being shown prevented some candidates being awarded method marks when their answer was incorrect. 4

46 Surname Centre Number Other Names Candidate Number For Examiner s Use Candidate Signature Free-Standing Mathematics Qualification June 2008 Foundation Level USING SPATIAL TECHNIQUES (PILOT) 9982/W Unit 2 Wednesday 14 May pm to 2.30 pm For this paper you must have: * a clean copy of the Data Sheet (enclosed) * a protractor * a pair of compasses * a ruler * a calculator. Time allowed: 1 hour Instructions * Use black ink or black ball-point pen. Pencil should only be used for drawing. * Fill in the boxes at the top of this page. * Answer all questions. * You must answer the questions in the spaces provided. Answers written in margins or on blank pages will not be marked. * Do all rough work in this book. Cross through any work you do not want to be marked. * You may not refer to the copy of the Data Sheet that was available prior to this examination. A clean copy is enclosed for your use. For Examiner s Use Question Mark Question Mark Total (Column 1) œ Û Total (Column 2) Û TOTAL Examiner s Initials Information * The maximum mark for this paper is 40. * The marks for questions are shown in brackets. * You are expected to use a calculator where appropriate. Advice * In all calculations, show clearly how you work out your answer. (JUN089982W01) P9168/Jun08/9982/W 6/6/6/ 9982/W

47 2 Areas outside the box will not be scanned for marking SECTION A Answer all questions in the spaces provided. Use Screen blocks on page 2 of the Data Sheet. 1 (a) The diagrams below show two screen block designs. 1 (a) (i) Write the order of rotational symmetry under each diagram. Screen block A Screen block B Answers (2 marks) 1 (a) (ii) Draw all the lines of symmetry on each diagram above. (3 marks) 1 (b) One of the holes in Screen block B is in the shape of the polygon shown below. What is the mathematical name of this polygon? Answer... (1 mark) 6 (02) P9168/Jun08/9982/W

48 3 Areas outside the box will not be scanned for marking 2 A wall has a row of screen blocks with sides of length 30 cm. The height of the base of the wall is 90 cm and the coping stones on the top are 5 cm thick. The mortar between the screen blocks and the other parts of the wall is 1 cm thick. coping stones 30 cm 1cm 5cm 30 cm 1cm mortar Not to scale Height 90 cm base 2 (a) Calculate the total height of the wall, giving your answer in centimetres Answer... (3 marks) 2 (b) Write your answer to part (a) in metres correct to 1 decimal place Answer... (2 marks) 5 Turn over s (03) P9168/Jun08/9982/W

49 4 Areas outside the box will not be scanned for marking SECTION B Answer all questions in the spaces provided. Use The London Eye on page 3 of the Data Sheet. 3 The diameter of the London Eye wheel is 135 metres. 3 (a) (i) Calculate the circumference of the wheel. 135 m Answer... (2 marks) 3 (a) (ii) The wheel has 32 capsules spaced equally around its circumference. Find the distance around the circumference between one capsule and the next. Give your answer to the nearest metre Answer... (3 marks) (04) P9168/Jun08/9982/W

50 5 Areas outside the box will not be scanned for marking 3 (b) A scaled elevation of the wheel has been started below. diameter 3 (b) (i) Measure the diameter of this circle in centimetres. 3 (b) (ii) The diameter of the actual wheel is 135 metres. What is the scale used on the diagram above? Give your answer in the form 1 : n. Answer... (1 mark)... Answer... (2 marks) 8 Turn over s (05) P9168/Jun08/9982/W

51 6 Areas outside the box will not be scanned for marking SECTION C Answer all questions in the spaces provided. Use Tea caddies on page 3 of the Data Sheet. 4 (a) The diagram shows the shape of one tea caddy. What is the mathematical name of this shape? Answer... (1 mark) 4 (b) The cross section of another tea caddy is in the shape of the octagon shown below. x 4 (b) (i) Measure the angle marked x. Answer... (1 mark) 4 (b) (ii) The angles of the octagon are equal, but the octagon is not regular. How can you tell that the octagon is not regular? (1 mark) 3 (06) P9168/Jun08/9982/W

52 7 Areas outside the box will not be scanned for marking 5 A different tea caddy is in the shape of a cuboid. The diagram gives its internal dimensions. Not to scale 14 cm 9cm 9cm 5 (a) Calculate the volume of tea when the caddy is full. State the units (b) It takes 20 cm 3 of tea to make a full pot of tea. Answer... (3 marks) How many full pots of tea can be made with the tea from this caddy? Answer... (3 marks) 6 Turn over for the next question Turn over s (07) P9168/Jun08/9982/W

53 8 Areas outside the box will not be scanned for marking SECTION D Answer all questions in the spaces provided. Use Skatepark on page 4 of the Data Sheet. 6 The diagram shows the side elevation of a launch ramp. C A B Another drawing of this side elevation has been started below. The angle at B is a right angle. Use a ruler and compasses only to construct a line through B perpendicular to AB. Leave all your construction lines on your drawing. A B (3 marks) 3 (08) P9168/Jun08/9982/W

54 9 Areas outside the box will not be scanned for marking 7 The diagram below shows the side elevation of a banked wedge ramp. Calculate the area of this side of the ramp. 1.3 m Not to scale 1.2 m 4.5 m Answer... (5 marks) 5 Turn over for the next question Turn over s (09) P9168/Jun08/9982/W

55 10 Areas outside the box will not be scanned for marking 8 The diagram below shows the dimensions of a wedge box ramp. The shaded skating surfaces are all rectangular. The front and back faces are vertical. Not to scale 120 cm 250 cm 320 cm 150 cm 180 cm In the space below, draw an accurate plan of the wedge box ramp looking vertically down from above in the direction of the arrow. Use a scale of 1 : 50. (4 marks) END OF QUESTIONS 4 (010) P9168/Jun08/9982/W

56 11 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED (011) P9168/Jun08/9982/W

57 12 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED ACKNOWLEDGEMENT OF COPYRIGHT-HOLDERS AND PUBLISHERS London Eye: London Eye Copyright Ó 2008 AQA and its licensors. All rights reserved. (012) P9168/Jun08/9982/W

58 Free-Standing Mathematics Qualification June 2008 Foundation Level USING SPATIAL TECHNIQUES (PILOT) Unit /PM PRELIMINARY MATERIAL DATA SHEET To be issued to candidates between Wednesday 30 April 2008 and Wednesday 7 May 2008 REMINDER TO CANDIDATES YOU MUST NOT BRING THIS DATA SHEET WITH YOU WHEN YOU SIT THE EXAMINATION. A CLEAN COPY WILL BE MADE AVAILABLE. P9170/Jun08/9982/PM 6/6/6/ 9982/PM

59 ~ 2 Screen blocks Screen blocks are sometimes used to decorate walls. There are a variety of different designs. screen block ~ The screen blocks can be built into the wall in groups. coping stones screen block ~ ~ They can also be put in a row on top of a base, with coping stones above. base ~ mortar mortar ~ Mortar is used between the bricks and the screen blocks. P9170/Jun08/9982/PM

60 3 The London Eye The London Eye is the world s tallest observation wheel. Passengers are carried in capsules attached to the wheel. Tea caddies Tea caddies are containers for tea. They come in various shapes and sizes. P9170/Jun08/9982/PM Turn over s

61 4 Skatepark Some of the ramps in a skatepark are shown below. Wedge Box Ramp Launch Ramps Banked Wedge Ramp Half-Pipe Ramp END OF DATA SHEET ACKNOWLEDGEMENT OF COPYRIGHT-HOLDERS AND PUBLISHERS London Eye: Tea caddies: Skatepark: London Eye Courtesy of Ahmad Tea Ltd Courtesy of Marks & Spencer Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders have been unsuccessful and AQA will be happy to rectify any omissions of acknowledgements in future papers if required. Copyright Ó 2008 AQA and its licensors. All rights reserved. P9170/Jun08/9982/PM

62 Version 1.0: 0608 abc Free-Standing Mathematics Qualification Using Spatial Techniques 9982/W Foundation Level Mark Scheme 2008 examination June series

63 Mark schemes are prepared by the Principal Examiner and considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the standardisation meeting attended by all examiners and is the scheme which was used by them in this examination. The standardisation meeting ensures that the mark scheme covers the candidates responses to questions and that every examiner understands and applies it in the same correct way. As preparation for the standardisation meeting each examiner analyses a number of candidates scripts: alternative answers not already covered by the mark scheme are discussed at the meeting and legislated for. If, after this meeting, examiners encounter unusual answers which have not been discussed at the meeting they are required to refer these to the Principal Examiner. It must be stressed that a mark scheme is a working document, in many cases further developed and expanded on the basis of candidates reactions to a particular paper. Assumptions about future mark schemes on the basis of one year s document should be avoided; whilst the guiding principles of assessment remain constant, details will change, depending on the content of a particular examination paper. Further copies of this Mark Scheme are available to download from the AQA Website: Copyright 2008 AQA and its licensors. All rights reserved. COPYRIGHT AQA retains the copyright on all its publications. However, registered centres for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within the centre. Set and published by the Assessment and Qualifications Alliance. The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number ) and a registered charity (registered charity number ). Registered address: AQA, Devas Street, Manchester M15 6EX Dr Michael Cresswell Director General

64 Version 1.0: 0608 Key to mark scheme and abbreviations used in marking M m or dm A B E mark is for method mark is dependent on one or more M marks and is for method mark is dependent on M or m marks and is for accuracy mark is independent of M or m marks and is for method and accuracy mark is for explanation or ft or F follow through from previous incorrect result MC mis-copy CAO correct answer only MR mis-read CSO correct solution only RA required accuracy AWFW anything which falls within FW further work AWRT anything which rounds to ISW ignore subsequent work ACF any correct form FIW from incorrect work AG answer given BOD given benefit of doubt SC special case WR work replaced by candidate OE or equivalent FB formulae book A2,1 2 or 1 (or 0) accuracy marks NOS not on scheme x EE deduct x marks for each error G graph NMS no method shown c candidate PI possibly implied sf significant figure(s) SCA substantially correct approach dp decimal place(s) No Method Shown Where the question specifically requires a particular method to be used, we must usually see evidence of use of this method for any marks to be awarded. However, there are situations in some units where part marks would be appropriate, particularly when similar techniques are involved. Your Principal Examiner will alert you to these and details will be provided on the mark scheme. Where the answer can be reasonably obtained without showing working and it is very unlikely that the correct answer can be obtained by using an incorrect method, we must award full marks. However, the obvious penalty to candidates showing no working is that incorrect answers, however close, earn no marks. Where a question asks the candidate to state or write down a result, no method need be shown for full marks. Where the permitted calculator has functions which reasonably allow the solution of the question directly, the correct answer without working earns full marks, unless it is given to less than the degree of accuracy accepted in the mark scheme, when it gains no marks. Otherwise we require evidence of a correct method for any marks to be awarded. 3

65 Free-Standing Mathematics Qualification (Pilot) Using Spatial Techniques (9982/W) Answers and Marking Scheme - June 2008 Question 1 (a)(i) Screen block A: 4 B1 Screen block B: 2 B1 (a)(ii) 1 correct line of symmetry B1 All lines of symmetry B1 Do not allow second B1 if there are extra incorrect lines Both lines of symmetry B1 Do not allow if there are extra incorrect lines (b) Pentagon B1 TOTAL 6 Question 2 (a) Total height = M1M1 = 127 (cm) A1 (b) Height = 1.27 (m) B1 = 1.3 (m) correct to 1 decimal place B1 First M1 for 2 (or 1+1) for mortar and second M1 for adding the other items Could be implied FT from answer to (a) TOTAL 5 4

66 Question 3 (a)(i) Circumference = π d = π 135 M1 = (m) A1 Allow omission of units. Accept values that round to 424 (from other values of π ) (a)(ii) M1 32 = A1 FT from answer to (a) = 13 (m) to the nearest metre B1 (b)(i) 13.5 (cm) B1 Accuracy ± 0.1 cm (b)(ii) 13.5 : M1 = 1 : 1000 A1 TOTAL 8 Any use of 1m = 100 cm or 1 m = 1000 mm (may be implied) Question 4 (a) Cylinder B1 (b)(i) 135 B1 Accuracy ± 2 (b)(ii) Sides are not equal B1 TOTAL 3 Question 5 (a) Volume = length width height = M1 =1134 A1 Accept 1130 cm 3 B1 (units) (b) M1 = 56.7 A1 FT from answer to (a) = 56 pots of tea B1 TOTAL 6 Must be rounded down 5

67 Question 6 B1 Arcs centred on B intersecting AB (extended) B1 Arcs centred on points of intersection of arcs and AB (extended) A B B1 Perpendicular drawn, passing through B Allow SC1 for any line drawn perpendicular to AB TOTAL 3 6

68 Question 7 Area of rectangle = = 1.56 (m 2 ) Base of triangle = =3.2 (m) Area of triangle = B1 B1 M1 Alternatively: Outer rectangle: = 5.4 (m 2 ) B1 = 1.92 (m 2 ) A1 FT from their base Total area = = 3.48 (or 3.5) (m 2 ) B1 Using their values TOTAL 5 Alternatively: = = 3.48 (m 2 ) B1 Alternative method: Area of trapezium = ( ) B1 formula, B1 correct values = M1, A1 (for 2.9) 2 =3.48 ( m ) A1 7

69 Question 8 See diagram below B1 Any evidence of correct use of the 1:50 scale TOTAL 4 TOTAL MARK FOR PAPER 40 B1 B1 B1 6.4 cm 3 cm 3.6 cm Rectangle 6.4cm by 5cm (or 13cm by 5cm) Rectangle 3cm by 5cm Rectangle 3.6cm by 5cm (Accuracy to ± 0.1cm) Do not allow last B1 if any other faces are shown Allow SC1 if rectangles all have correct lengths but incorrect height SC1 for correctly drawn plan to a consistent but different scale. 5 cm 8

70 Version : 1.0: 0708 Free-Standing Mathematics Qualification Using Spatial Techniques (Pilot) 9982 Foundation Level Report on the Examination 2008 examination - June series

71 Further copies of this Report are available to download from the AQA Website: Copyright 2008 AQA and its licensors. All rights reserved. COPYRIGHT AQA retains the copyright on all its publications. However, registered centres for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within the centre. Set and published by the Assessment and Qualifications Alliance. The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number ) and a registered charity (registered charity number ). Registered address: AQA, Divas Street, Manchester M15 6EX Dr Michael Cresswell Director General. 2

72 Using Spatial Techniques (Pilot) - AQA FSMQ Report on the Examination 2008 June series Using Spatial Techniques (Pilot) (9982) Examination General A small number of centres entered candidates for this examination and in each centre the marks achieved ranged from the low teens to over 35. Candidates seemed to have enough time and most of them attempted every question on the paper. Some questions were answered very well, but in others many of the candidates did not appear to know the formulae or techniques that they needed to use. The shapes to be used in most of the questions are shown on the Data Sheet and it is disappointing that the candidates did not know some of the relevant methods. For example, the information on the London Eye on the Data Sheet made it fairly obvious that the questions on this context could well include the circumference of a circle, yet a large proportion of the candidates did not calculate this correctly. Question 1 On the whole, candidates did well on part (a) of this question with the majority achieving both marks for giving the order of rotational symmetry correctly for each diagram. Most of the candidates also drew all of the lines of symmetry correctly. Those who did not get full marks for part (a) often said that the second diagram had rotational symmetry of order 1 or omitted some of the lines of symmetry. Some candidates recognised that the shape in part (b) was a pentagon, but a significant minority gave other answers such as trapezium, hexagon or octagon. Question 2 Part (a) of this question was generally answered confidently and well, with most of the candidates correctly giving the total height to be 127 cm. Just a few of the candidates omitted one or more of the items from the total. Only a small proportion of the candidates were able to complete all of part (b) correctly. A few of the candidates did not convert centimetres to metres correctly and many more lost the last mark by not rounding to one decimal place the height in metres. Question 3 The responses to this question were generally poor. Fewer than half of the candidates were able to calculate the circumference of the circle correctly in part (a)(i). Some candidates multiplied by the radius instead of the diameter, some calculated 2 d and some calculated the area instead of the circumference. Other candidates squared 135 or multiplied 135 by 360 or 90 and some omitted this part altogether. Candidates who found the correct circumference often went on in part (a)(ii) to calculate the distance between consecutive capsules correctly, but in some cases they lost the last mark by not rounding to the nearest metre. Follow through marks were allowed for this part of the question so those candidates who divided their incorrect answer to (a)(i) by 32 were able to pick up one or two marks here. 3