Cambridge IGCSE Mathematics 0580 — 2004 May/June Paper 1 · Variant 1

Centre Number Candidate Number Name UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/01 0581/01 Paper 1 (Core) May/June 2004 Candidates answer on the Question Paper. 1 hour Additional Materials: Electronic calculator Geometrical instruments Mathematical tables (optional) Tracing paper (optional) 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. 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 of the 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. Give answers in degrees to one decimal place. For π , use either your calculator value or 3.142. For Examiner’s Use This document consists of 8 printed pages. IB04 06_0580_01/4RP
UCLES 2004 [Turn over If you have been given a label, look at the details. If any details are incorrect or missing, please fill in your correct details in the space given at the top of this page. Stick your personal label here, if provided. www.XtremePapers.com

2 0580/1, 0581/1 Jun/04 For Examiner's Use 1 Work out 43 – 52. Answer [1] 2 The Dead Sea shore is 395 metres below sea level. Hebron is 447 metres above sea level. Find the difference in height. Answer [1] 3 Write as a fraction in its lowest terms (a) 75%, Answer (a) [1] (b) 0.07. Answer (b) [1] 4 Look at the numbers 21, 35, 49, 31, 24. From this list write down (a) a square number, Answer (a) [1] (b) a prime number. Answer (b) [1] 5 NOT TO SCALE A model of a car has a scale of 1:25. The model is 18 cm long. Calculate, in metres, the actual length of the car. Answer m [2]

3 0580/1, 0581/1 Jun/04 [Turn over For Examiner's Use 6 Without using a calculator, work out 2 1 4 1 2
as a single fraction. Show all your working. Answer [2] 7 Sergio’s height is 142 cm, to the nearest centimetre. Complete the statement about the limits of his height. Answer cm height < cm [2] 8 Factorise completely xz xy 6 4
. Answer [2] 9 Alix changed a traveller’s cheque for 200 euros (€) into dollars ($) when she visited the USA. The exchange rate was 1 dollar = 1.05 euros. How many dollars did she receive? Answer $ [2] 10 For the shape shown, write down (a) the number of lines of symmetry, Answer (a) [1] (b) the order of rotational symmetry. Answer (b) [1]

4 0580/1, 0581/1 Jun/04 For Examiner's Use 11 O P Q 35o NOT TO SCALE PQ is a chord of a circle, centre O. Angle OPQ = 35o. Calculate angle POQ. Answer Angle POQ = [2] 12 (a) 8 1 2 1

    x Write down the value of x. Answer (a) x = [1] (b) 1 7
y Write down the value of y. Answer (b) y = [1] 13 39 218
(a) (i) Write both numbers in the calculation above correct to one significant figure.
Answer (a)(i) [1] (ii) Use your answer to part (i) to estimate the value of the calculation. Answer (a)(ii) [1] (b) Use your calculator to find the value of the calculation correct to two significant figures. Answer (b) [1]

5 0580/1, 0581/1 Jun/04 [Turn over For Examiner's Use 14 Shampoo is sold in two sizes, A and B. 1.5 litres $2.30 800 millilitres $1.30 1.5 litres 800 millilitres NOT TO SCALE A B A contains 800 ml and costs $ 1.30. B contains 1.5 litres and costs $ 2.30. Which is the better value for money? Show your working clearly. Answer [3] 15 A B C 32o 5 m NOT TO SCALE In the right-angled triangle ABC, AC = 5 metres and angle CAB = 32o. Calculate the length of BC. Answer BC = m [3]

6 0580/1, 0581/1 Jun/04 For Examiner's Use 16 bc a y
 (a) Find the value of y when a = 3
, b = 2 and c = 8. Answer (a) y = [2] (b) Make c the subject of the formula. Answer (b) c = [2] 17 In a school, the number of students taking part in various sports is shown in the table below. Sport Number of students Basketball 40 Soccer 55 Tennis 35 Volleyball 70 Draw a bar chart below to show this data. Show your scale on the vertical axis and label the bars. Answer Sport Number of students [4]

7 0580/1, 0581/1 Jun/04 [Turn over For Examiner's Use 18 Carlos buys a box of 50 oranges for $ 8. He sells all the oranges in the market for 25 cents each. (a) Calculate the profit he makes. Answer (a) $ [2] (b) Calculate the percentage profit he makes on the cost price. Answer (b) % [2] 19 30 cm 80 cm NOT TO SCALE The diagram shows a cylindrical tank. The radius is 30 cm and the height is 80 cm. (a) Calculate the area of the base of the tank. Answer (a) cm2 [2] (b) Calculate the volume of the tank in litres. Answer (b) litres [2]

8 0580/1, 0581/1 Jun/04 For Examiner's Use 20 Solve the equations (a) 31 5 4
 x , Answer (a) x = [2] (b) 36 ) 5 ( 4
 y . Answer (b) y = [2] 21 The time in Dubai is 3 hours ahead of Birmingham. (a) If it is 21 15 on Sunday in Birmingham, what time on Monday is it in Dubai? Answer (a) [1] (b) An aircraft leaves Birmingham at 21 15 on Sunday and arrives in Dubai on Monday at 07 45 local time. (i) How long did the journey take? h Answer (b)(i) min [1] (ii) The distance from Birmingham to Dubai is 5620 km. Calculate the average speed of the aircraft. Answer (b)(ii) km/h [3]