Cambridge IGCSE Mathematics (with coursework) 0581 — 2003 May/June Paper 3 · Variant 1

Centre Number Candidate Number Name CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/03 0581/03 Paper 3 May/June 2003 2 hours Candidates answer on the Question Paper. 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 soft 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 13 printed pages and 3 blank pages.
CIE 2003 [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 0580/3, 0581/3 Jun 03 For Examiner's Use 1 Fifty students take part in a quiz. The table shows the results. (a) How many students had 6 correct answers? Answer(a)……………….……… (b) How many students had less than 11 correct answers? Answer(b)……………………… (c) Find (i) the modal number of correct answers, Answer(c)(i)……………………. (ii) the median number of correct answers, Answer(c)(ii)……………...……. (iii) the mean number of correct answers. Answer(c)(iii)……….………….. (d) A bar chart is drawn to show the results. The height of the bar for the number of students who had 5 correct answers is 2cm. What is the height of the bar for the number of students who had 9 correct answers? Answer(d)……….………...…cm [1] [1] [1] [2] [3] [2] Number of correct answers 5 6 7 8 9 10 11 12 Number of students 4 7 8 7 10 6 5 3

3 0580/3, 0581/3 Jun 03 [Turn over For Examiner's Use (e) A pie chart is drawn to show the results. What is the angle for the number of students who had 11 correct answers? Answer(e)………………………. (f) The students who had the most correct answers shared a top prize of $22.50. How much did each of these students receive? Answer(f) $…………………….. (g) Work out the percentage of students who had less than 7 correct answers. Answer(g)………………….…% (h) A student is chosen at random from the fifty students. What is the probability that this student had (i) exactly 10 correct answers, Answer(h)(i)……………………. (ii) at least 10 correct answers, Answer(h)(ii)…………………… (iii) more than 1 correct answer? Answer(h)(iii)………………….. [2] [2] [2] [1] [1] [1]

4 0580/3, 0581/3 Jun 03 For Examiner's Use 2 (a) Complete the table for the equation x y 120
. (b) On the grid below, draw the curve x y 120
for 1 x 6. 1 2 3 4 5 6 0 20 40 60 80 100 120 x y (c) Use your graph to find x when y = 70. Answer(c) x = …………………. (d) Complete the table for the equation x y 20 120
 . (e) On the same grid above, draw the graph of x y 20 120
 for 0 x 6. [3] [4] [1] [2] [2] x 1 1.5 2 3 4 5 6 y 80 60 40 30 x 0 2 4 6 y 80 40

5 0580/3, 0581/3 Jun 03 [Turn over For Examiner's Use (f) The graphs of x y 120
and x y 20 120
 intersect at two points. Write down the coordinates of these two points. Answer(f) ( ….… , ….…) and (….… , ….…) (g) Write down the gradient of the line x y 20 120
 . Answer(g)……………………… [2] [2]

6 0580/3, 0581/3 Jun 03 For Examiner's Use 3 (a) Bottles of water cost 25 cents each. (i) Find the cost of 7 bottles in cents. Answer(a)(i)……………...cents (ii) Write down an expression in b for the cost of b bottles in cents. Answer(a)(ii)……………...cents (iii) Change your answer to part (i) into dollars. Answer(a)(iii) $…...…………… (iv) Write down an expression in b for the cost of b bottles in dollars. Answer(a)(iv) $………………… (b) The total cost, T, of n bars of chocolate is given by nc T
. (i) Write c in terms of T and n. Answer(b)(i) c = ………………… (ii) What does c represent? Answer(b)(ii) .…………………………………………………………………………… (c) The average cost of a book is $A. (i) The total cost of 8 books is $36. Find the value of A. Answer(c)(i) A = .……………… (ii) One of the 8 books is removed. The cost of this book is $6.60. Find the new value of A. Answer(c)(ii) A = ……………… [1] [1] [1] [1] [1] [1] [1] [2]

7 0580/3, 0581/3 Jun 03 [Turn over For Examiner's Use (iii) The total cost of x books is $y. Write an expression for A in terms of x and y. Answer(c)(iii) A = ……………… (iv) One of the x books is removed. The cost of this book is $7. Write a new expression for A in terms of x and y. Answer(c)(iv) A = ……………… [1] [2]

8 0580/3, 0581/3 Jun 03 For Examiner's Use 4 1 3 5 7 9 11 2 4 6 8 10 12 0 1 3 5 7 9 11 2 4 6 8 10 12 x y E D N M F G L K T A (a) Draw accurately the image of triangle T under the following transformations. (i) Translate triangle T by the vector
   
3 4 . Label it P. [2] (ii) Reflect triangle T in the line x = 8. Label it Q. [2] (iii) Rotate triangle T about the point A through 90° anti-clockwise. Label it R. [2] (iv) Enlarge triangle T with centre of enlargement A and scale factor 2. Label it S. [2]

9 0580/3, 0581/3 Jun 03 [Turn over For Examiner's Use (b) Describe fully the single transformation which maps (i) triangle P onto triangle T, Answer(b)(i)…………………………………………………………………………………. [2] (ii) triangle S onto triangle T. Answer(b)(ii)………………………………………………………………………………… [3] (c) The rectangle DEFG is rotated onto the rectangle KLMN, with D mapped onto K. Write down (i) the angle of the rotation, Answer(c)(i)…...…………………... [1] (ii) the coordinates of the centre of the rotation. Answer(c)(ii) (…..…….. , ……..….) [2]

10 0580/3, 0581/3 Jun 03 For Examiner's Use 5 B O A The quarter-circle above has centre O and radius 7 cm. (a) Using a straight edge and compasses only construct (i) the perpendicular bisector of AO, [2] (ii) the locus of points inside the quarter-circle which are 5 cm from O. [2] (b) Shade the region, inside the quarter-circle, containing the points which are more than 5 cm from O and nearer to A than O. [1] (c) (i) The line OX bisects angle AOB and is 12 cm long. Draw OX accurately. [2] (ii) Draw accurately the tangent to the quarter-circle at A. [1] (iii) This tangent meets the line OX at Y. Measure the length of AY. Answer(c)(iii) AY = …………..…….cm [1]

11 0580/3, 0581/3 Jun 03 [Turn over For Examiner's Use 6 1cm 2.5cm 9cm 1.5cm 1.5cm 1.5cm 1cm 1cm 3cm In the diagram above, all the angles are right angles. (a) Show that the area of the shape is 13.5cm2. Answer(a) (b) The shape is the cross-section of a metal prism of length 2.8 metres. Calculate the volume of the prism in cubic centimetres. Answer(b)………………….cm3 (c) A metal cuboid is melted down so that prisms as described in part (b) can be made. The cuboid measures 2 metres by 1.2 metres by 0.8 metres. (i) Calculate the volume of the cuboid in cubic metres, Answer(c)(i)……...…………..m3 (ii) Calculate the volume of the cuboid in cubic centimetres. Answer(c)(ii)……..…………cm3 (iii) Calculate the number of prisms which can be made. Answer(c)(iii)……...……………. (d) Draw any lines of symmetry of the shape on the diagram above. (e) Describe the rotational symmetry of the shape above. Answer(e)……………………………………………………………………………….. [2] [3] [2] [2] [2] [1] [1]

12 0580/3, 0581/3 Jun 03 For Examiner's Use 7 4 8 12 16 2 6 10 14 18 20 0 20 40 60 10 30 50 70 80 90 Time (minutes) Temperature ( OC) The graph shows the temperature of a cup of tea cooling down in a room. (a) What is the temperature of the tea after (i) 0 minutes, Answer(a)(i)……………………. [1] (ii) 20 minutes? Answer(a)(ii)...…………………. [1] (b) After how many minutes is its temperature 30 °C? Answer(b)……………………… [1] (c) By how much has its temperature gone down between 4 minutes and 8 minutes? Answer(c)……………………… [1] (d) (i) Complete the table which shows falls in temperature. [3] (ii) What pattern do you notice about these falls in temperature? Answer(d)(ii)…………………………………………………………………… [1] Between 0 and 4 minutes 4 and 8 minutes 8 and 12 minutes 12 and 16 minutes Fall in temperature

13 0580/3, 0581/3 Jun 03 For Examiner's Use (e) Estimate the room temperature. Answer(e)…………………. °C [1] 8 Diagram 4 Diagram 1 3 dots 1 triangle Diagram 2 4 dots 3 triangles Diagram 3 5 dots 6 triangles Look at the diagrams above. (a) Complete Diagram 4 to continue the pattern. [2] (b) Complete the table below. [3] (c) Complete the table below. [3] (d) A line is now drawn inside each of the diagrams as shown below. Diagram 1 2 triangles Diagram 2 6 triangles Diagram 3 How many triangles are there in Diagram 3? Answer(d)………………………[2] Diagram 1 2 3 4 5 n Number of dots 3 4 5 Diagram 1 2 3 4 5 6 10 Number of triangles 1 3 6 10