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

This question paper consists of 7 printed pages and 1 blank page. © CIE 2002 [Turn over Centre Number Candidate Number Candidate Name International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS MATHEMATICS PAPER 1 OCTOBER/NOVEMBER SESSION 2002 1 hour Candidates answer on the question paper. Additional materials: Electronic calculator Geometrical instruments Mathematical tables (optional) Tracing paper (optional) Time 1 hour 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 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
, use either your calculator value or 3.142. FOR EXAMINER’S USE www.XtremePapers.com

2 0580/1/O/N/02 For Examiner's Use 1 Work out $50 – $23.46. Answer $.……………….……… [1] 2 A train leaves Johannesburg at 0945 and arrives in Pretoria at 1032. How many minutes does the journey take? Answer.……………….………minutes [1] 3 Work out . 13 37 13 37 3 3

Answer.……………….……… [2] 4 Write 24% as a fraction in its lowest terms. Answer.……………….……… [2] 5 The integer n is such that –3  n < 3. List all the possible values of n. Answer.……………….……… [2] 6 NOT TO SCALE AB and AC are tangents to the circle, centre O. Angle BAC = 54. (a) Write down the size of angle ABO. Answer (a) Angle ABO =.……………….……… (b) Work out angle BOC. Answer (b) Angle BOC =.……………….……… [1] [1] 54 B A C O

3 0580/1/O/N/02 [Turn over For Examiner's Use 7 When Carla started work she was paid $80 each week. After 3 months her pay was increased by 15%. After the increase how much was she paid each week? Answer $.……………….……… [2] 8 The population of Argentina is 3.164  107. Its area is 2.8  106 square kilometres. Work out the average number of people per square kilometre in Argentina. Answer.……………….………people/km2 [2] 9 The diagram shows a flood-warning post in a river. (a) Write down the water level shown in the diagram. Answer (a).……………….………cm (b) The water level rises by 1 metre. What is the new level? Answer (b).……………….………cm [1] [1] +1m +50cm -50cm -1m 0

4 0580/1/O/N/02 For Examiner's Use 10 Complete this diagram accurately so that it has rotational symmetry of order 3 about the point O. [2] 11 An athlete’s time for a race was 43.78 seconds. (a) Write this time correct to (i) one decimal place, Answer (a) (i).……………….………seconds (ii) one significant figure. Answer (a) (ii).……………….………seconds (b) Write 43.78 and your answers to (a) parts (i) and (ii) in order, largest first. Answer (b) .……………….………>.……………….………>.……………….……… [1] [1] [1] 12 In triangle ABC, AB = AC. (a) What is the special name of this triangle? Answer (a).……………….……… (b) Angle BAC = 128. Work out angle ABC. Answer (b) Angle ABC =.……………….……… [1] [2] O 128
A C B NOT TO SCALE

5 0580/1/O/N/02 [Turn over For Examiner's Use 13 T = 2 . n (a) Find T when n = 25. Answer (a) T =.……………….……… (b) Make n the subject of the formula. Answer (b) n =.……………….……… [1] [2] 14 Brussels is 220 km North and 139 km East of Paris. Calculate the bearing of Brussels from Paris, to the nearest degree. Answer.……………….……… [3] 15 (a) Write down the values of 20 = ……. , 21 = ……. , 22 = ……. , 23 = ……. , 24 = ……. [2] (b) Change 49 5 to a decimal. Write down your full calculator display. Answer (b) 49 5 =.……………….……… (c) What do you notice about your answers to parts (a) and (b)? Answer (c) .……...……….……………………………………………………….………. ……………………………………………………………………………………………. [1] [1] Paris Brussels 139 km 220 km North NOT TO SCALE

6 0580/1/O/N/02 For Examiner's Use 16 The diagram shows part of the graph of y = 6 – x2 for –3  x  0. Complete the graph for – 4  x  4. [4] 17 The frequency of radio waves (F) is connected to the wavelength (l) by the formula l 000 300
F . (a) Calculate the value of F when l = 1500. Answer (a) F = .……………….……… (b) Calculate the value of l when F = 433, giving your answer to the nearest whole number. Answer (b) l = .……………….……… [1] [3] 18 Seven people were asked to guess the number of beans in a jar. Their guesses were 194, 173, 170, 144, 182, 259, 159. (a) Find the median. Answer (a) ……………….……… (b) Work out the mean. Answer (b) .……………….……… [2] [2] 6 4 2 y=6 −x2 -2 -2 2 4 -4 -4 -6 -8 -10 0 x y

7 0580/1/O/N/02 For Examiner's Use 19 (a) Factorise 40a – 8b + 32c. Answer (a) .……………….……… (b) Solve the equations (i) x – 7 = 9, Answer (b) (i) x = .……………….……… (ii) 2 (y + 1) = 3y – 5. Answer (b) (ii) y = .……………….……… [2] [1] [2] 20 y x 3 2 1 -1 -2 -3 -1 1 2 3 4 -2 -3 0 (a) On the grid above, plot the points A (0,2), B (2,2), C (4,1) and D (–2, –1). (b) Find the area of the quadrilateral ABCD. Answer (b) .……………….………cm2 (c) The vector BC =
    y x . Find the value of x and the value of y. Answer (c) x =.……………….……… y =.……………….……… [1] [2] [2]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME FOR the November 2002 question papers 0580; 0581 Mathematics 0580/1; 0581/1 Paper 1 (Short Answer Questions, Core), maximum raw mark 56 0580/2; 0581/2 Paper 2 (Short Answer Questions, Extended), maximum raw mark 70 0580/3; 0581/3 Paper 3 (Structured Questions, Core), maximum raw mark 104 0580/4; 0581/4 Paper 4 (Structured Questions, Extended), maximum raw mark 130 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. . CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the November 2002 question papers for most IGCSE, Advanced Subsidiary (AS) Level and Advanced Level syllabuses.

Mark Scheme - Syllabus : IGCSE Examinations — November 2002 0580; 0581 Notes TYPES OF MARK. @ Marks are for correct method applied to appropriate numbers. Giy A marks are for accuracy, and depend on M marks.[MOA1 is IMPOSSIBLE] (ii) B marks are independent accuracy marks. Gv) S, P, C, Q marks are on graphs for scale, plotting, curve and quality. (v) Sc marks are for special cases, when full marks have not been scored. (vi) The symbol‘ or “double tick” means correct work following an error. Several places on the mark scheme have * in the L. H. margin where “wrong” answers will score because they follow through “correctly” from a previous wrong answer. [means a further error.] Where the mark scheme indicates ¥‘, the candidate may score from their correct follow through, or may score from the correct answer, as he may have started again and got it right, or left the correct answer on a calculator earlier. MISREADS. These happen the first time a candidate copies a number from the question paper, and must be consistent. The penalty is -1 A or B marks. As M marks are available for misreads, it should not often apply. Useful ABBREVIATIONS. ¢.a.0 => correct answer only C.S.0 => correct solution only ‘w.w.=> without working ‘w.w.w => without wrong working 0.e.=> or equivalent s.0.1=> seen or implied b.o.d => benefit of doubt. SCALE DRAWING. Any correct method carries full marks except scale drawings in a calculation. ACCURACY. The new IGCSE guidelines for questions where there is no specific accuracy demand in the question itself are as follows: (i) More than 3 sig.figs. in the answer but correct - no penalty. (ii) Less than 3 sig. figs. in the answer but 3 or more correct s.f. seen in working - allow the marks. (iii) Lack of final zeros in 3 sig. fig. answers - OK e.g. 26 is acceptable for 26.0 provided w.w.w. METHOD MARKS. (@ Method marks are given for complete correct method, where arithmetic error or lack of completion has lost the final mark. In cases where the correct method is seen, but then followed by another method step to produce a wrong answer, the method mark is forfeited. (i) In cases where two different methods have been attempted, the final answer indicates the candidate’s choice of which method we mark.

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

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