Cambridge IGCSE Mathematics (with coursework) 0581 — 2004 Oct/Nov Paper 1 · Variant 1

This document consists of 9 printed pages and 3 blank pages. IB04 11_0580_01/3RP © UCLES 2004 [Turn over UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS Paper 1 (Core) 0580/01 0581/01 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments October/November 2004 Mathematical tables (optional) Tracing paper (optional) 1hour READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen in the spaces provided on the Question Paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN THE BARCODE. DO NOT WRITE IN THE GREY AREAS BETWEEN THE PAGES. Answer all questions. If working is needed for any question it must be shown below that question. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 56. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Given answers in degrees to one decimal place. For π , use either your calculator value or 3.142. Candidate Name Centre Number Candidate Number *051001* For Examiner's Use www.XtremePapers.com

2 © UCLES 2004 0580/01/O/N/04 For Examiner's Use 1 At a weather centre the temperature at midnight was −21 oC. By noon the next day it had risen to −4 oC. By how many degrees had the temperature risen? Answer oC [1] 2 Place brackets in the following calculation to make it a correct statement. 60 3 9 5 10 = + × − [1] 3 Write 9 5 as a decimal, correct to two decimal places. Answer [2] 4 When x = 5 find the value of (a) 4x2, Answer(a) [1] (b) (4x)2. Answer(b) [1] 5 Antonia is making a cake. She uses currants, raisins and sultanas in the ratio currants : raisins : sultanas = 4 : 3 : 5. The total mass of the three ingredients is 3.6 kilograms. Calculate the mass of sultanas. Answer kg [2]

3 © UCLES 2004 0580/01/O/N/04 [Turn over For Examiner's Use 6 Write as a 3-figure bearing the direction (a) West, Answer(a) [1] (b) North-East. Answer(b) [1] 7 Reflex Right Acute Obtuse Use one of the above terms to describe each of the angles given. (a) 100o Answer(a) [1] (b) 200o Answer(b) [1] 8 a =       4 3 and b =       2 1 – Work out a – 2b.       Answer [2] 9 5 3 ÷ 10 7 = 7 6 Show how this calculation is done without using a calculator. Write down the working. Answer [2]

4 © UCLES 2004 0580/01/O/N/04 For Examiner's Use 10 Simplify the following expressions. (a) a2 × a5 Answer(a) [1] (b) b4 ÷ b3 Answer(b) [1] 11 = < > Use one of the above symbols to complete each of the statements in the answer spaces. 23 Answer(a) 32 [1] 9 % Answer(b) 0.09 [1] 12 Write down the order of rotational symmetry of each of the following shapes. (a) Equilateral Triangle Answer(a) [1] (b) Rhombus Answer(b) [1]

5 © UCLES 2004 0580/01/O/N/04 [Turn over For Examiner's Use 13 The diagram shows a pyramid with a square base. All the sloping edges are the same length. In the space below sketch a net of the pyramid. [2] 14 Bernard is buying a radio priced at $19.60. The shopkeeper gives him a 15% discount. Calculate how much Bernard pays. Answer $ [3]

6 © UCLES 2004 0580/01/O/N/04 For Examiner's Use 15 350 cm 350 cm 200 cm NOT TO SCALE A large tank, in the shape of a cuboid, has a square base of side 350 cm and height 200 cm. The tank is filled with water. Find, in litres, the volume of water it holds when full. Answer litres [3] 16 NOT TO SCALE 8 cm 6 cm The measurements shown are correct to the nearest centimetre. (a) Write down the least possible measurement of (i) the base of the right-angled triangle, base = Answer(a)(i) cm [1] (ii) the height of the right-angled triangle. height = Answer(a)(ii) cm [1] (b) Use your answers to part (a) to calculate the least possible area of the triangle. area = Answer(b) cm2 [1]

7 © UCLES 2004 0580/01/O/N/04 [Turn over For Examiner's Use 17 Ferdinand’s electricity meter is read every three months. The reading on 1st April was 70683 units and on 1st July it was 71701 units. (a) How many units of electricity did he use in those three months? Answer(a) units [1] (b) Electricity costs 8.78 cents per unit. Calculate his bill for those three months. Give your answer in dollars, correct to the nearest cent. Answer(b) $ [2] 18 (a) List all the factors of 30. Answer(a) [2] (b) Write down the prime factors of 30. (1 is not a prime number.) Answer(b) [1]

8 © UCLES 2004 0580/01/O/N/04 For Examiner's Use 19 In New Zealand, a bus leaves New Plymouth at 8.10 am and arrives in Wellington at 2.55 pm. (a) How long, in hours and minutes, does the journey take? h Answer(a) min [1] (b) The distance from New Plymouth to Wellington is 355 kilometres. Calculate, in kilometres per hour, the average speed for the journey. Answer(b) km/h [3] 20 Aminata has a bag containing 35 beads. The beads are either blue, yellow or red. One bead is chosen at random. The probability of choosing a blue bead is 7 2 and the probability of choosing a yellow bead is 5 3 . Calculate (a) the number of blue beads in the bag, Answer(a) [2] (b) the probability of choosing a red bead. Answer(b) [2]

9 © UCLES 2004 0580/01/O/N/04 For Examiner's Use 21 Calculate, giving your answer in standard form, (a) (1.5 × 103) + (8.4 × 102), Answer(a) [2] (b) (1.5 × 103) × (8.4 × 102). Answer(b) [2] 22 O A B NOT TO SCALE The diagram shows half of a circle, centre O. (a) What is the special name of the line AB? Answer(a) [1] (b) AB = 12 cm. (i) Calculate the perimeter of the shape. Answer(b)(i) cm [2] (ii) Calculate the area of the shape. Answer(b)(ii) cm2 [2]

12 Every reasonable effort has been made to trace all copyright holders where the publishers (i.e. UCLES) are aware that third-party material has been reproduced. The publishers would be pleased to hear from anyone whose rights they have unwittingly infringed. University of Cambridge International Examinations is part of the University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. 0580/01/O/N/04 BLANK PAGE

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the November 2004 question papers 0580/0581 MATHEMATICS 0580/01, 0581/01 Paper 1 (Core), maximum raw mark 56 This mark scheme is published as an aid to teachers and students, to indicate the requirements of the examination. It shows the basis on which Examiners were initialy instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began. Any substantial changes to the mark scheme that arose from these discussions will be recorded in the published Report on the Examination. All Examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes must be read in conjunction with the question papers and the Report on the Examination. • CIE will not enter into discussion or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the November 2004 question papers for most IGCSE and GCE Advanced Level syllabuses. www.XtremePapers.com

Grade thresholds taken for Syllabus 0580/0581 (Mathematics) in the November 2004 examination. minimum mark required for grade: maximum mark available A C E F Component 1 56 N/A 40 28 23 The threshold (minimum mark) for B is set halfway between those for Grades A and C. The threshold (minimum mark) for D is set halfway between those for Grades C and E. The threshold (minimum mark) for G is set as many marks below the F threshold as the E threshold is above it. Grade A* does not exist at the level of an individual component.

TYPES OF MARK Most of the marks (those without prefixes, and ‘B’ marks) are given for accurate results, drawings or statements. • M marks are given for a correct method. • B marks are given for a correct statement or step. • A marks are given for an accurate answer following a correct method. ABBREVIATIONS a.r.t. Anything rounding to b.o.d. Benefit of the doubt has been given to the candidate c.a.o. Correct answer only (i.e. no ‘follow through’) e.e.o. Each error or omission f.t. Follow through o.e. Or equivalent SC Special case s.o.i. Seen or implied ww Without working www Without wrong working Work followed through after an error: no further error made

November 2004 INTERNATIONAL GCSE MARK SCHEME MAXIMUM MARK: 56 SYLLABUS/COMPONENT: 0580/01, 0581/01 MATHEMATICS Paper 1 (Core)

Page 1 Mark Scheme Syllabus Paper IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 1 © University of Cambridge International Examinations 2005 Number Answers Mark Notes 1 17 1 Not -17 2 (10 - 5) x (9 + 3) 1 Ignore omission of final bracket only 3 0.56 2 B1 for 5 ÷ 9 or digits 55 (….) or digits 56 Common answer for B1 is 0.55 4 (a) 100 (b) 400 1 1 5 1.5 (0...) 2 M1 for ) 5 3 4 ( 5 + + x 3.6 SC1 for 1.2 or 0.9 (ie. Wrong ingredient) 6 (a) 270 (b) (0)45 1 1 7 Obtuse Reflex 1 1 8       0 5 1 + 1 One mark each component. If only number 5 in bracket allow 1 mark. If 0 scored SC1 for      − 4 2 or       −4 2 seen, or       5 0 Ignore a line between Components 9 5 3 x 7 10 35 30 = 7 6 or 7 1 2 3 × × = 7 6 M1 E1 Only acceptable method.

Page 2 Mark Scheme Syllabus Paper IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 1 © University of Cambridge International Examinations 2005 10 (a) a7 (b) b 1 1 Allow b1 11 (a) < (b) = 1 1 12 (a) 3 (b) 2 1 1 Ignore any added words 13 Net of the pyramid. A square with 4 equal isosceles triangles correctly positioned. 2 1 for a square 1 for all 4 triangles, isosceles or equilateral. Reasonable accuracy by eye. Ignore any tabs shown. 14 16.66 cao 3 M1 for 0.15 x 19.60 (implied by 2.94 seen) M1 for 19.60 – his 2.94 (allow if 2.94 is rounded to 2.90, method only) or M2 for 0.85 x 19.60 [allow for (1 – 0.15) x 19.60] Answer 1666 2 marks, 1670 1 mark ww. 16.7(0) implies M2 15 24500 3 M1 for 350 x 350 x 200 or 3.5 x 3.5 x 2 soi A1 for 24500000 or 24.5 seen B1 for his ‘volume’ correctly converted to litres. 16 (a) (i) (base) = 7.5 (ii) (height) = 5.5 1 1 Allow 2 marks for correct answers reversed. Allow 1 mark for one of the answers seen in either (i) or (ii). (b) 20.6 (25) or 20.62 or 20.6 (3) f.t. 1 A correct calculation of the area using his values of base and height regardless of his values. 17 (a) 1018 (b) 89.38 final answer ft. 1 2 M1 for his (a) x 8.78 soi or SC1 for answer in cents.

Page 3 Mark Scheme Syllabus Paper IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 1 © University of Cambridge International Examinations 2005 18 (a) 1,2,3,5,6,10,15,30 cao or 1 x 30, 2 x 15, 3 x 10, 5 x 6 cao (b) 2,3,5 or 2 x 3 x 5 2 1f.t. B1 for 4 correct factors, none incorrect. All the correct primes from his part (a), and at least one prime and no non-primes. 19 (a) 6 (hours) 45 (minutes) (b) rounds to 52.6 or 52 27 16 1 3f.t. B1 for 6.75 or 6 4 3 oe used or his time correctly converted to hours. M1 for 355 ÷ his time. (any form) (55.0…or 0.87….ww implies M1) A1 f.t. provided his (a) correctly converted to hours. 20 (a) 10 (b) 35 4 oe or 0.114 (...) or 11.4% 2 2 M1 for 7 2 x 35 M1 for 1 -       + 5 3 7 2 soi or [35 - (his (a) + 5 3 x 35] ÷ 35 0.11 or 11% seen imply M1 21 (a) 2.34 x 103 (b) 1.26 x 106 2 2 SC1 for figs 234 seen or 2.3 x 103 SC1 for figs 126 seen or 1.3 x 106 22 (a) diameter (b)(i) rounds to 30.8 or 30.9 (ii) rounds to 56.5 or 56.6 1 2 2 M1 for 0.5 x π x 12 or 12 + π x 12 (implied by rounding to18.8 or 18.9 or 49.7 seen) M1 for using π x 62 (implied by 113 (. ) seen