Cambridge IGCSE Mathematics 0580 — 2006 May/June Paper 2 · Variant 1

This document consists of 11 printed pages and 1 blank page. IB06 06_0580_02/5RP  UCLES 2006 [Turn over UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS Paper 2 (Extended) 0580/02 0581/02 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments May/June 2006 Mathematical tables (optional) Tracing paper (optional) 1hour 30 minutes 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 70. 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 *058002* For Examiner's Use www.XtremePapers.com

2 © UCLES 2006 0580/02, 0581/02 Jun 06 For Examiner's Use 1 The planet Neptune is 4 496 000 000 kilometres from the Sun. Write this distance in standard form. Answer km [1] 2 Write down the next prime number after 89. Answer [1] 3 The table gives the average surface temperature (°C) on the following planets. Planet Earth Mercury Neptune Pluto Saturn Uranus Average temperature 15 350 −220 −240 −180 −200 (a) Calculate the range of these temperatures. Answer(a) oC [1] (b) Which planet has a temperature 20 °C lower than that of Uranus? Answer(b) [1] 4 Work out ( )2 o o tan30 1 2tan30 − . Answer [2] 5 In triangle ABC, AB = 6 cm, AC = 8 cm and BC = 12 cm. Angle ACB = 26.4°. Calculate the area of the triangle ABC. A B C 6 cm 8 cm 12 cm 26.4o NOT TO SCALE Answer cm2 [2]

3 © UCLES 2006 0580/02, 0581/02 Jun 06 [Turn over For Examiner's Use 6 Write as a single fraction in its simplest form 1 4 5 + − x x . Answer [2] 7 Sima drinks 2.5 litres of water each day. A full glass holds 125 millilitres of water. How many full glasses of water does Sima drink each day? Answer [2] 8 Write the following in order of size, smallest first. 4 π 2 1 4 3 sin 47° < < < Answer [2] 9 The distance between Singapore and Sydney is 6300 km correct to the nearest 100 km. A businessman travelled from Singapore to Sydney and then back to Singapore. He did this six times in a year. Between what limits is the total distance he travelled? km total distance travelled < Answer km [2]

4 © UCLES 2006 0580/02, 0581/02 Jun 06 For Examiner's Use 10 For the sequence 5 2 1 , 7, 8 2 1 , 10, 11 2 1 , … (a) find an expression for the nth term, Answer(a) [2] (b) work out the 100th term. Answer(b) [1] 11 f(x) = x x 3 + , x ≠ 0. (a) Calculate f ( 4 1 ). Answer(a) [1] (b) Solve f(x) = 4 1 . Answer(b) x = [2] 12 Solve the simultaneous equations 0.4x + 2y = 10, 0.3x + 5y = 18. Answer x = y = [3]

5 © UCLES 2006 0580/02, 0581/02 Jun 06 [Turn over For Examiner's Use 13 Solve the equation 3 5 2 4 2 + = − x x . Answer x = [3] 14 A company makes two models of television. Model A has a rectangular screen that measures 44 cm by 32 cm. Model B has a larger screen with these measurements increased in the ratio 5:4. (a) Work out the measurements of the larger screen. cm by Answer(a) cm [2] (b) Find the fraction area screen model area screen model B A in its simplest form. Answer(b) [1] 15 Angharad had an operation costing $500. She was in hospital for x days. The cost of nursing care was $170 for each day she was in hospital. (a) Write down, in terms of x, an expression for the total cost of her operation and nursing care. Answer(a)$ [1] (b) The total cost of her operation and nursing care was $2370. Work out how many days Angharad was in hospital. Answer(b) [2]

6 © UCLES 2006 0580/02, 0581/02 Jun 06 For Examiner's Use 16 In 2004 Colin had a salary of $7200. (a) This was an increase of 20% on his salary in 2002. Calculate his salary in 2002. Answer(a)$ [2] (b) In 2006 his salary increased to $8100. Calculate the percentage increase from 2004 to 2006. Answer(b) % [2] 17 n(A) = 18, n(B) = 11 and n(A ∪ B)′ = 0. (a) Label the Venn diagram to show the sets A and B where n(A ∪ B) = 18. Write down the number of elements in each region. [2] (b) Draw another Venn diagram to show the sets A and B where n(A ∪ B) = 29. Write down the number of elements in each region. [2]

7 © UCLES 2006 0580/02, 0581/02 Jun 06 [Turn over For Examiner's Use 18 A B C D E 22o 60o wo xo yo zo NOT TO SCALE AD is a diameter of the circle ABCDE. Angle BAC = 22° and angle ADC = 60°. AB and ED are parallel lines. Find the values of w, x, y and z. Answer w= x= y= z= [4] 19 Factorise (a) 4x2 – 9, Answer(a) [1] (b) 4x2 – 9x, Answer(b) [1] (c) 4x2 – 9x + 2. Answer(c) [2]

8 © UCLES 2006 0580/02, 0581/02 Jun 06 For Examiner's Use 20 x y 2 3 4 5 6 7 8 0 1 4 3 2 1 8 7 6 5 y = mx + c (a) One of the lines in the diagram is labelled y = mx + c. Find the values of m and c. Answer(a) m= [1] c= [1] (b) Show, by shading all the unwanted regions on the diagram, the region defined by the inequalities x 1, y mx + c, y x+2 and y 4. Write the letter R in the region required. [2]

9 © UCLES 2006 0580/02, 0581/02 Jun 06 [Turn over For Examiner's Use 21 (a) Shade one square in each diagram so that there is (i) one line of symmetry, [1] (ii) rotational symmetry of order 2. [1] (b) On the diagram below, sketch one of the planes of symmetry of the cuboid. [1] (c) Write down the order of rotational symmetry of the equilateral triangular prism about the axis shown. axis Answer(c) [1]

10 © UCLES 2006 0580/02, 0581/02 Jun 06 For Examiner's Use 22 (a) A B C D E 8 cm p cm q cm 5 cm 4 cm NOT TO SCALE 4 cm In the diagram triangles ABE and ACD are similar. BE is parallel to CD. AB = 5 cm, BC = 4 cm, BE = 4 cm, AE = 8 cm, CD = p cm and DE = q cm. Work out the values of p and q. Answer(a) p = q = [4] (b) A spherical balloon of radius 3 metres has a volume of 36π cubic metres. It is further inflated until its radius is 12 m. Calculate its new volume, leaving your answer in terms of π. Answer(b) m3 [2]

11 © UCLES 2006 0580/02, 0581/02 Jun 06 For Examiner's Use 23 V W S R U P Q T O a b The origin O is the centre of the octagon PQRSTUVW. = a and = b. (a) Write down in terms of a and b (i) , Answer(a)(i) [1] (ii) , Answer(a)(ii) [1] (iii) , Answer(a)(iii) [2] (iv) the position vector of the point P. Answer(a)(iv) [1] (b) In the diagram, 1 centimetre represents 1 unit. Write down the value of a – b. Answer(b) [1]

12 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. 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. 0580/02, 0581/02 Jun 06 BLANK PAGE

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2006 question paper 0580 and 0581 MATHEMATICS 0580/02 and 0581/02 Paper 2, maximum raw mark 70 These mark schemes are published as an aid to teachers and students, to indicate the requirements of the examination. They show the basis on which Examiners were initially instructed to award marks. They do 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. The minimum marks in these components needed for various grades were previously published with these mark schemes, but are now instead included in the Report on the Examination for this session. • CIE will not enter into discussion or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the May/June 2006 question papers for most IGCSE and GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. www.XtremePapers.com

Page 1 Mark Scheme Syllabus Paper IGCSE – May/June 2006 0580 and 0581 02 © University of Cambridge International Examinations 2006 1 4.496 x 109 1 2 97 cao 1 3 (a) (–)590 1 (b) Neptune 1 4 1.73 2* Allow √3 M1 for 1.15… or 0.666… 5 21.3 2* M1 ½ x 8 x 12 x sin26.4 oe 6 )1 ( 5 + + x x x 2* M1 5(x + 1) – 4x or better 7 20 2* M1 2.5 Q 0.125 oe 8 1/√2, sin 47, ¾, π /4 2* M1 for correct conversion to decimals 0.78(53..) 0.70(71...) 0.75 0.73(13..) 9 75000 76200 2* B1 B1 or M1 6250, 6350 seen 10 (a) 4 + 1½n 2* B1 for 4 B1 for 1½n o.e (b) 154 1 f.t 11 (a) 13 cao 1 (b) –4 2* M1 3x/4 + 3 = 0 or x = x/4 – 3 or 4(x + 3) = x or 1 + 3/x =1/4 or better WWW 12 x=10 y=3 3* M1 Multiplying and subtracting consistently or M1 rearrange and substitute 13 x = –5.2 3* M1 any two steps completed correctly M1 any other two steps completed correctly 14 (a) 55, 40 2 B1 B1 (b) 25 16 1 15 (a) 500 + 170x 1 (b) 11 2* M1 their part (a) = 2370 16 (a) 6000 2* M1 7200 Q=1.2 oe (b) 12.5 2* M1 (8100 – 7200) Q=7200 oe

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2006 0580 and 0581 02 © University of Cambridge International Examinations 2006 17 (a) 2 B1 numbers B1 labels (b) 2 B1 numbers B1 labels Allow 0 in an intersection of A and B 18 w = 30 x = 22 y = 30 z = 52 1,1 1 f.t. 1 f.t. y = w w + 22 19 (a) (2x – 3)(2x + 3) 1 (b) x(4x – 9) 1 (c) (4x – 1)(x – 2) 2 20 (a) (b) m = –1 c = 8 1,1 2* 21 (a) 1 1 or (b) plane of symmetry 1 (c) 3 1

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2006 0580 and 0581 02 © University of Cambridge International Examinations 2006 22 (a) p = 7.2 q = 6.4 2,2* (b) 2304π 2* M1 for x by vsf 64 allow 7240 for 2 marks 23 (a) a + b, a – b, 3a + b 1½a + ½b 1,1,2* 1 f.t. M1 in (iii) for (i) + a + (ii) + b ½ TP (b) 4 1 TOTAL 70