Cambridge IGCSE Mathematics (with coursework) 0581 — 2002 Oct/Nov Paper 3 · Variant 1

This question paper consists of 12 printed pages. SJF2284/CG S14615/4 © CIE 2002 [Turn over CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/3, 0581/3 OCTOBER/NOVEMBER SESSION 2002 PAPER 3 2 hours Candidates answer on the question paper. Additional materials: Electronic calculator Geometrical instruments Mathematical tables (optional) Tracing paper (optional) TIME 2 hours INSTRUCTIONS TO CANDIDATES Write your name, Centre number and candidate number in the spaces at the top of this page. Answer all questions. Write your answers in the spaces provided on the question paper. If working is needed for any question it must be shown below that question. INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 104. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, the answer should be given to three significant figures. Answers in degrees should be given to one decimal place. For π, use either your calculator value or 3.142. Candidate Centre Number Number Candidate Name FOR EXAMINER’S USE www.XtremePapers.com

2 0580/3/O/N02 1 (a) A bottle of mass 480 grams contains 75 centilitres of water. (i) Write 75 centilitres in millilitres. Answer (a)(i) ……………..……… ml [1] (ii) Write 75 centilitres in litres. Answer (a)(ii) ……………………… l [1] (iii) The mass of 480 grams is correct to the nearest 10 grams. Complete the statement on the answer line. Answer (a)(iii) ………… g
mass < ………… g [2] (iv) Write 480 grams in kilograms. Answer (a)(iv) …………………… kg [1] (b) The diagrams below are accurate scale drawings of containers with water in them. (i) The capacity of this cylindrical jar is 600ml of water. By measuring the height of the jar and the height of the water, find the amount of water in the jar. Answer (b)(i) ……………….….… ml [2] (ii) The capacity of this bucket is 7 litres. Estimate the amount of water in the bucket. Answer (b)(ii) ……………………… l [2] For Examiner’s Use

3 0580/3/O/N02 [Turn over 2 (a) The results of the school’s senior football team during a year are recorded, using W for a win, L for a loss and D for a draw. They are: L L W D L W L W L L D L L W W L W L L W D L L W (i) Complete the table below to show these results. Then display this information in the pie chart below. [6] (ii) The team play another match. Based on the results above, what is the probability that they will win? Answer (a)(ii) …………………… [1] (b) The probability that the school’s junior team wins is 0.45 and the probability that it loses is 0.35. What is the probability of a draw? Answer (b) ……………….……… [2] For Examiner’s Use W Frequency Pie chart angle L D TOTAL 360°

4 0580/3/O/N02 3 In triangle LMN, angle LNM = 90°, angle MLN = 28° and LM = 10cm. (a) Calculate (i) MN, Answer (a)(i) MN = …………………… cm [2] (ii) LN, Answer (a)(ii) LN = …………………… cm [2] (iii) the area of triangle LMN. Answer (a)(iii) ………...……………… cm2 [2] (b) A circle is drawn with LM as diameter. (i) Work out the area of the circle. Answer (b)(i) …………………………. cm2 [2] (ii) Showing all your working, find the area of triangle LMN as a percentage of the area of the circle. Answer (b)(ii) …………………………... % [2] (iii) Explain why the point N is on the circle. Answer (b)(iii) … [1] For Examiner’s Use 28° L 10cm N M NOT TO SCALE

5 0580/3/O/N02 [Turn over For Examiner’s Use 4 (a) Describe fully the transformation which maps (i) shape L onto shape M, Answer (a)(i) … [2] (ii) shape L onto shape N. Answer (a)(ii) … [2] (b) (i) Translate shape L using the vector . [2] (ii) Enlarge shape L with centre of enlargement 0, scale factor . [2] 1–2 –7 –4 N L M 0 -1 -2 -3 -4 -5 -6 -7 1 2 3 4 5 6 7 x 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 y

6 0580/3/O/N02 For Examiner’s Use 5 The cuboid shown in the diagram has EF = 4cm, FG = 6cm and AE = 3cm. (a) Calculate (i) the volume of the cuboid, Answer (a)(i) …………………… cm3 [2] (ii) the surface area of the cuboid. Answer (a)(ii) …………………… cm2 [3] (b) The cuboid is divided into two equal triangular prisms. One of them is shown in the diagram. (i) Write down the volume of the triangular prism. Answer (b)(i) …………………… cm3 [1] (ii) Work out the area of the rectangle AFGD. Answer (b)(ii) …………………… cm2 [3] A NOT TO SCALE H D G E F A B E F 4cm 6cm D C G H NOT TO SCALE 3cm

7 0580/3/O/N02 [Turn over For Examiner’s Use 6 Ian and Joe start to dig a garden. They both dig at the same rate. (a) When they are half-way through the job, what fraction of the garden has Ian dug? Answer (a) …………….………… [2] (b) Keith then arrives to help. All three dig at the same rate until the job is finished. (i) What fraction of the garden did Ian dig after Keith arrived? Answer (b)(i) ….………………… [2] (ii) What fraction of the garden did Ian dig altogether? Answer (b)(ii) …………………… [2] (c) Ian and Joe started to dig at 0900. Keith started to dig at 1000. Each dug at the same rate throughout. At what time was the job finished? Answer (c) ….…………………… [2]

8 0580/3/O/N02 7 The graph of 3x + 2y = 12 is drawn on the grid above. (a) (i) Complete the table of values for y = 3x – 1. [2] (ii) On the grid above, draw the graph of y = 3x –1 for 0  x  2. [1] (b) Use the graphs to find the solution of the simultaneous equations 3x + 2y = 12, y = 3x – 1. Answer (b) x = ………… , y = ………… [2] (c) Use algebra to find the exact solution of the simultaneous equations 3x + 2y = 12, y = 3x – 1. Answer (c) x …………, y = ………… [4] For Examiner’s Use -2 0 -2 2 4 6 2 4 3x+2y=12 x y x 0 1 2 2 y

9 0580/3/O/N02 [Turn over 8 The diagram shows an island, drawn to a scale of 1cm to 30km. (a) Find the distance in kilometres between points A and B. Answer (a) AB = …………………… km [2] (b) On the diagram draw the locus of points on the island which are (i) 150km from A, [1] (ii) 150km from B. [1] Label the point T on the island where these two loci intersect. [1] (c) A tower is built at T, to send television signals to the western part of the island. The maximum range of its signals is 150km. Draw the locus of points 150km from T. [1] (d) A second tower is built, which can send television signals up to 120km, to reach the rest of the island. Use the points C, D and E to help you to find a suitable position for the second tower. Label the position X. Leave in any construction lines or arcs that you draw. [3] For Examiner’s Use A North Scale: 1cm to 30km B C E D

10 0580/3/O/N02 For Examiner’s Use 9 Students try to find the best price at which to sell their school newspaper. When the price was 10 cents, they sold 200 newspapers. When the price was 60 cents, they sold only 75 newspapers. They drew the graph below using this information. (a) Use the graph to answer these questions. (i) At what price will no-one buy the newspaper? Answer (a)(i) …………………… cents [1] (ii) 150 newspapers are sold. What was the price? Answer (a)(ii) …………………… cents [1] (iii) Complete the table below. [6] 200 150 100 Number of newspapers sold Price (cents) 50 0 0 10 20 30 40 50 60 70 80 90 Price (cents) 10 20 30 40 50 60 70 80 90 Number of newspapers sold 200 175 75 Money received (cents) 2000 3500 4500

11 0580/3/O/N02 [Turn over (b) Use the table in part (a)(iii) to answer these questions. The total printing cost is $20. (i) When the newspapers are sold at 20 cents each, calculate the profit in dollars. Answer (b)(i) $ …………….…………… [2] (ii) Estimate the price that will give the greatest profit. Answer (b)(ii) ………………...………… [1] 10 A number that has only two different prime factors is called semi-prime. For example, 77 is semi-prime since it has only two prime factors, 7 and 11. [Remember that 1 is not prime.] (a) Show that each of the three consecutive numbers 33, 34 and 35 is semi-prime. Answer (a) … … … [3] (b) Find the smallest semi-prime number. Answer (b) ……………………………… [2] (c) Find two consecutive numbers between 10 and 20 which are semi-prime. Answer (c) …………… and …………… [1] (d) Find three consecutive numbers between 80 and 90 which are semi-prime. Answer (d) …………… , …………… and …………… [3] For Examiner’s Use

12 0580/3/O/N02 For Examiner’s Use 11 The diagram shows wooden beams which support the roof of a house. (a) Complete the table below. [4] (b) When L = 10, find the values of x, y and T. Answer (b) x = …………………………… y = …………………………… T = …………………………… [3] (c) Write down a formula for (i) x in terms of L, Answer (c)(i)x = ………………………[1] (ii) y in terms of L, Answer (c)(ii) y = …..………………… [1] (iii) T in terms of L. Answer (c)(iii) T = …………………… [2] (d) When T = 83, find the value of L. Answer (d) L = ……..………………… [1] L metres 1m 1m 1m 1m 1m 2m 2m 2m 2m 2m 2m 2m Length of roof (L metres) 1 2 1 5 2 4 3 11 3 4 5 10 9 29 6 Number of 2 metre beams (x) Number of 1 metre beams (y) Total length of wood (T metres)

CAMBRIDGE INTERNATIONAL EXAMINATIONS NOVEMBER 2002 INTERNATIONAL GCSE UNIVERSITY of CAMBRIDGE Local Examinations Syndicate

semicircle = 90° Page 1 Mark Scheme Syllabus [Paper IGCSE Examinations — November 2002 0580; 0581 [| 3 Question | Mark scheme Part Notes Question number mark total la) i) 750 ml 1 ii) 0.75 Loe 1 iii) 475 <M<485 14+1 [ iv) 0.48(0) kg 1 b) i) 400 ml (+20 ml) 2 M1 for 2600 ii) any valueinthe | 2 SC1 for 3.5 lor 2< V<2.5 range 2.5 < V<3.5 9 2a) i) W8 L13 D3 2 SC1 if one (compensating) error accurate pie chart, M1 for a correct calculation, with angles 3 such as 3 x360 120°,195°,45° (+ 2° Al for one correct angle Sectors labelled (dep) | 1 ii)Loe V 1 b) 0.2 oe 2 M1 for 1-(0.45+0.35) 9 3a) i) 4.69 cm 2 M1 for 10sin28° ii) 8.83cm 2 M1 for 10cos28° (SC2 for both answers, to at > least 2s.f.,reversed) iii) 20.7cm? (V) 2 MI for 4 their a) i)xtheir a)ii), _, oe complete method b) i) art. 78.5cm* 2 MI for xx5? seen their20.7 ii) 26.4% ) 2 M1 for Ther 785° oe, seen iii) Angle ina 1 i

Page 2 Mark Scheme [__ Syllabus Paper IGCSE Examinations — November 2002 [_ 0580; 0581 3 {4a) i) Reflection 1 in x-axis oe 1 ii) Rotation 1 through 90° anticlockwise,about O | 1 b) i) correct translation 2 SC for any translation involving movement in the x- and y- directions ii) correct enlargement }| 2 SC1 for any other enlargement of L, centre O or for correct enlargement with i one vertex wrong 5a) )Rem | 2 M1 for 3x4x6 ii) 108 cm 3 M2 for 2(3x4+3x6+4x6) | or M1 if one error in this i expression b) i) 36cm? a) 1 ii) 30 cm? 3 M2 for V3?+4? x6 | or MI for ¥3?+4? _ s.0.i. i} 6a) 4 2 MI for $x+ oe b) yt 72 MI for $x} oe ii) 5) 2 MI for their +their c) 1040 2 7a) i) -1,5 I+] ii) Correct straight line | 1 drawn b) x=1.4 to 1.7, y=3.5to | 1+1 dep on correct line in a) 3.8 c) x=, y= oe 4 M2 for correct method as far as ax=borcy=d Al for either correct answer 8 a) 23%km (+6 km) 2 MI for 8cm (+0.2) seen b) (part of ) circle centre | 1 A, radius 5cm (part of ) circle centre J 1 B, radius 5 cm T labelled at 1 | intersection c) circle centre T drawn, | 1 should pass through A and B radius 5 cm

Page 3 Mark Scheme Syllabus Paper IGCSE Examinations — November 2002 0580; 0581 3 +1mm) d) correctly placed point, B1 for correct point with no with method of evidence finding it clear or M1 for relevant construction | seen but point wrong 9 9 a) i) 90 cents \ ii) 30 cents iii) LH column SC1 for 3 or more correct 150,125,100,—,50,25,0 RH column M1 for attempt to multiply first 4500,5000,5000,-, column by second column at 3500,2000,0 least once Al+1+1 for each two correct b) i) $15 MI for 35-20 ii) 45eents 11 10 a) 33=3x11 34=2x17 35=5x7 b) 6 MI for some correct experimentation seen c) 14 and 15 d) 85,86 and87 SC1 for two of the three correct or M1 for correct factors of any of them seen 9 lla) First line 6,8,12 Alternatively 1 mark for each Second line 5,7,11 correct column. Award Third line 17,23,35 whichever total is greater b)_ 20,19,59 c) i) x=2L, i)y=2L1 (V) Must be in terms of / iii) T=6L-1_(V) d) 14 a) from their c)iii) 12 TOTAL 104