Cambridge IGCSE Mathematics (with coursework) 0581 — 2004 May/June Paper 3 · Variant 1

Centre Number Candidate Number Name UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/03 0581/03 Paper 3 (Core) May/June 2004 Candidates answer on the Question Paper. 2 hours 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 104. 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 15 printed pages and 1 blank page. IB04 06_0580_03/6RP
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 you personal label here, if provided. www.XtremePapers.com

2 © UCLES 2004 0580/3, 0581/3 Jun/04 For Examiner's Use 1 (a) The list shows marks in an examination taken by a class of 10 students. 65, 51, 35, 34, 12, 51, 50, 75, 48, 39 (i) Write down the mode. Answer(a)(i) [1] (ii) Work out the median. Answer(a)(ii) [2] (iii) Calculate the mean. Answer(a)(iii) [2] (b) Grades were awarded for the examination. The table below shows the number of students in the whole school getting each grade. Grade Number of students Angle on a pie chart A 5 B 15 C 40 D 20 E 10 Totals 90 (i) Complete the table above by calculating the angles required to draw a pie chart. [2] (ii) Using the circle at the top of the opposite page, draw an accurate pie chart to show the data in the table. Label the sectors A, B, C, D and E.

3 © UCLES 2004 0580/3, 0581/3 Jun/04 [Turn over For Examiner's Use [3] (iii) What is the probability that a student chosen at random from the group taking the examination was awarded (a) grade C, Answer(b)(iii)(a) [1] (b) grade D or grade E? Answer(b)(iii)(b) [2]

4 © UCLES 2004 0580/3, 0581/3 Jun/04 For Examiner's Use 2 3 m 2 m 3 m NOT TO SCALE The diagram shows a shelter that Vudnella will build for her goats. The shelter will stand on level ground with four identical vertical posts at the corners. Three walls will be made by attaching thin rectangular pieces of wood to the posts. The front will be left open. The shelter will have a thin square roof, 3 metres by 3 metres. The shelter will be 2 metres high. (a) Calculate the area of the roof. Answer(a) m2 [1] (b) (i) Calculate the area of one wall. Answer(b)(i) m2 [1] (ii) Write down the total area of the three walls. Answer(b)(ii) m2 [1] (c) The three walls will be made up from thin rectangular pieces of wood. Each piece of wood is 3 metres long and 20 centimetres wide. You may ignore the thickness of the wood. (i) Calculate the area, in square metres, of one of the pieces of wood. Answer(c)(i) m2 [2] (ii) Calculate the total number of pieces of wood she will need to build the three walls of the shelter. Answer(c)(ii) [2]

5 © UCLES 2004 0580/3, 0581/3 Jun/04 [Turn over For Examiner's Use (d) The four corner posts are each 2 metres high and 10 centimetres by 10 centimetres in cross- section. Calculate the volume, in cubic metres, of one post. Answer(d) m3 [2] (e) To build the shelter, she will also need 1.5 kilograms of nails. Complete the table below. Item Total cost of item Posts at $1.20 each $…………………… Rectangular pieces of wood at $0.30 each $…………………… Roof material at $1.60 per m2 $…………………… Nails at $1.40 per kg $…………………… Total cost of shelter $…………………… [5]

6 © UCLES 2004 0580/3, 0581/3 Jun/04 For Examiner's Use 3 (a) Complete the table below for 2 8 x y
 . x -3.5 -3 -2.5 -2 -1.5 -1 0 1 1.5 2 2.5 3 3.5 y -4.25 -1 1.75 4 5.75 7 5.75 1.75 -4.25 [3] (b) On the grid below, draw the graph of 2 8 x y
 for 5.3
x 3.5. 11 10 9 8 7 6 5 4 3 2 1 _1 _2 _3 _4 _5 y x 0 _4 _3 _2 _1 1 2 3 4 [4]

7 © UCLES 2004 0580/3, 0581/3 Jun/04 [Turn over For Examiner's Use (c) Using the graph, write down the values of x for which 0 8 2
 x . and Answer(c) x = [2] (d) Complete the table below for 5 2
 x y . x 3
0 3 y 11 [2] (e) On the grid on the opposite page, draw the line 5 2
 x y for 3
x 3. [2] (f) Find the gradient of the line 5 2
 x y . Answer(f) [2] (g) Using your graphs, write down the x coordinates of the intersections of the graphs of 2 8 x y
 and 5 2
 x y . and Answer(g) x = [2]

8 © UCLES 2004 0580/3, 0581/3 Jun/04 For Examiner's Use 4 In this question the diagrams are not to scale. (a) Calculate the value of s. 80o 110o so 50o Answer(a) s = [1] (b) Calculate the value of t. 75o 75o t o 2t o Answer(b) t = [2] (c) (i) 50o 2yo xo x + 2y = Complete the equation [2]

9 © UCLES 2004 0580/3, 0581/3 Jun/04 [Turn over For Examiner's Use (ii) 160o xo yo 100o x + y = Complete the equation [2] (iii) Solve the simultaneous equations given by your answers to parts (c)(i) and (c)(ii) to find the values of x and y. , y = Answer(c)(iii) x = [3]

10 © UCLES 2004 0580/3, 0581/3 Jun/04 For Examiner's Use 5 (a) Change 200 metres to kilometres. Answer(a) km [1] (b) In the diagram, Q and S lie on a circle, radius 7.8 kilometres, centre C. CQ is extended by 200 metres to P. PS is a tangent to the circle at S. (i) Why is angle PSC a right angle? Answer(b)(i) [1] (ii) Write down the length of PC in kilometres. Answer(b)(ii) km [1] (iii) Calculate the length of PS in kilometres. Answer(b)(iii) km [3] (iv) Calculate the area of triangle PSC. Give your answer correct to 2 significant figures. Answer(b)(iv) km2 [3] C S Q P 200 m 7.8 km NOT TO SCALE

11 © UCLES 2004 0580/3, 0581/3 Jun/04 [Turn over For Examiner's Use 6 y x 0 8 7 6 5 4 3 2 1 _1 _2 _3 _4 _5 _6 8 7 6 5 4 3 2 1 _1 _3 _4 _5 _6 _7 _8 _2 A C D E F B (a) Describe fully the single transformation that maps (i) shape A onto shape B, Answer(a)(i) [3] (ii) shape C onto shape D. Answer(a)(ii) [3] (b) On the grid above, draw (i) the reflection of shape E in the y-axis, [2] (ii) the enlargement of shape F, with scale factor 2 and centre (0, 0). [2]

12 © UCLES 2004 0580/3, 0581/3 Jun/04 For Examiner's Use 7 (a) (i) What is the special name given to a five-sided polygon? Answer(a)(i) [1] (ii) Calculate the total sum of the interior angles of a regular five-sided polygon. Answer(a)(ii) [2] (iii) Calculate the size of one interior angle of a regular five-sided polygon. Answer(a)(iii) [1] (b) North North North A B C 70 o xo yo 160 o 100 km 120 km NOT TO SCALE A ship sails 100 kilometres from A on a bearing of 070o to B. It then sails 120 kilometres on a bearing of 160o to C. (i) Show that x + y = 90o. Answer(b)(i) [2] (ii) Use trigonometry to calculate the size of angle BAC. Answer(b)(ii) [2]

13 © UCLES 2004 0580/3, 0581/3 Jun/04 [Turn over For Examiner's Use (iii) Find the three-figure bearing of C from A. Answer(b)(iii) [1] (iv) Find the three-figure bearing of A from C. Answer(b)(iv) [1]

14 © UCLES 2004 0580/3, 0581/3 Jun/04 For Examiner's Use 8 A B C ROAD The map shows three towns, A, B and C and a road. (a) (i) Measure and write down the distance, in centimetres, from A to B. Answer(a)(i) cm [1] (ii) The towns A and B are 60 kilometres apart. The map is drawn to scale. Complete the statement in the answer space. Answer(a)(ii) 1 cm represents km [2] (iii) Find the actual distance, in kilometres, from town A to town C. Answer(a)(iii) km [1] (b) An airport is to be built 10 kilometres from the road. On the map, draw accurately the locus of the points that are 10 kilometres from the road. [2] (c) The airport must be the same distance from A as it is from B. Using compasses and a straight edge only, draw the locus of the points that are equidistant from A and B. [2] (d) The airport must be not more than 40 kilometres from C. Draw the locus of points that are 40 kilometres from C. [2] (e) Mark and label L, the position for the airport. [1]

15 © UCLES 2004 0580/3, 0581/3 Jun/04 For Examiner's Use 9 (a) Look at the sequence of dots and squares below. Number of dots Number of squares 4 1 6 2 8 3 10 4 Find the number of dots when there are (i) 5 squares, Answer(a)(i) [1] (ii) 9 squares, Answer(a)(ii) [1] (iii) n squares. Answer(a)(iii) [2] (b) Another sequence of dots and squares is shown below. Diagram Number of dots Number of squares 1 4 1 2 8 4 3 12 9 4 16 16 (i) For diagram 5, find (a) the number of dots, Answer(b)(i)(a) [1] (b) the number of squares. Answer(b)(i)(b) [1] (ii) Find the number of dots in the diagram that has 144 squares. Answer(b)(ii) [2] (iii) Find the number of squares in the diagram that has 40 dots. Answer(b)(iii) [2]

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