Cambridge IGCSE Mathematics 0580 — 2013 May/June Paper 3 · Variant 3

1 (a) Kasem earns $900 each month. For Examiner′s 14% of this amount is deducted for tax and insurance. Use Show that he receives $774 each month. Answer(a) [2] 2 (b) He pays of the $774 in rent. 9 Calculate the amount of rent he pays. Answer(b) $ ............................................... [1] (c) Kasem spends $480 each month on food, entertainment and clothes. He shares this in the ratio food : entertainment : clothes = 9 : 3 : 4. Calculate how much he spends on food each month. Answer(c) $ ............................................... [2] (d) Kasem saves the rest of his money. Work out the amount he saves as a percentage of $774. Answer(d) ........................................... % [2] _____________________________________________________________________________________

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 900 × 86 ÷ 100 = 74 2 M1 for 900 × 14 ÷ 100 A1 for 900 – 126 = 774 (b) [$] 172 1 (c) [$] 270 2 M1 for 480 ÷ (9 + 3 + 4) (d) 15.8 or 15.76(...) 2ft B1 for 774 – their (b) – 480 B1 Or 294 – their (b) SC1 for 38 or 37.9

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2 (a) For Examiner′s 2 12 144 40 .625 110 11 4 80 0.25 Use From this list of numbers, write down (i) a two-digit odd number, Answer(a)(i) ............................................... [1] (ii) a square number, Answer(a)(ii) ............................................... [1] (iii) the value of 2–2, Answer(a)(iii) ............................................... [1] (iv) an irrational number, Answer(a)(iv) ............................................... [1] (v) the lowest common multiple of 8 and 10, Answer(a)(v) ............................................... [2] (vi) the cube root of 8. Answer(a)(vi) ............................................... [1] (b) (i) Find the smallest factor, apart from 1, of 2013. Answer(b)(i) ............................................... [1] (ii) Write 2013 as the product of its prime factors. Answer(b)(ii) ................. × ................. × ................. [2] _____________________________________________________________________________________

Mark scheme: 2 (a) (i) 11 1 (ii) 144 or 4 or 0.25 1 (iii) 0.25 1 (iv) 12 1 (v) 40 cao 2 B1 for 80 or any common multiple of 40 (vi) 2 1 (b) (i) 3 1 (ii) 3 [×] 11 [×] 61 2 B1 for two of 3, 11 and 61 seen IGCSE – May/June 2013 0580 33

More questions on Types of number

3 For Examiner′s y Use 9 8 7 6 5 B A 4 3 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8 –9 (a) Write down the order of rotational symmetry of shape A. Answer(a) ............................................... [1] (b) Describe fully the single transformation which maps shape A onto shape B. Answer(b) ................................................................................................................................. [2] - 7 (c) (i) Translate shape A by the vector . -5 e o Label the image C. [2] (ii) Rotate shape A through 90° clockwise about the origin. Label the image D. [2] (d) Triangle LMN is drawn on the 1 cm2 grid below. For Examiner′s Use (i) Enlarge triangle LMN by scale factor 3 from the centre P. N L M P [2] (ii) Write down the length of the base, LM, and the height of triangle LMN. Answer(d)(ii) LM = ......................................... cm Height = ......................................... cm [2] (iii) Calculate the area of triangle LMN. Answer(d)(iii) ........................................ cm2 [2] (iv) Find the area of the enlarged triangle. Answer(d)(iv) ........................................ cm2 [2] _____________________________________________________________________________________

Mark scheme: 3 (a) 2 1 (b) Reflection 1 x = –1 1  − 7  B1 for 7 left or 5 down 2 (c) (i) Translation    − 5  SC1 for translation  − 5      − 7 (ii) Rotation 90° clockwise about 2 B1 for any other rotation of 90° about other the origin shown. point (d) (i) Correct enlargement shown 2 B1 for an enlargement with any correct scale factor and/or correct shape incorrect position (ii) 3, 2 1, 1 SC1 for 2, 3 (iii) 3 2ft M1 their LM × their height ÷ 2 (iv) 27 2ft M1 their base × their height ÷ 2 from their enlarged triangle.

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4 (a) The table shows some values of y = x2 – 2x – 1. For Examiner′s Use x –3 –2 –1 0 1 2 3 4 y 14 2 –1 –2 7 (i) Complete the table. [2] (ii) On the grid, draw the graph of y = x2 – 2x – 1 for –3 Y x Y 4. y 16 14 12 10 8 6 4 2 x –3 –2 –1 0 1 2 3 4 –2 –4 [4] (b) Write down the equation of the line of symmetry of the graph. For Examiner′s Use Answer(b) ............................................... [1] (c) The point with co-ordinates (–3, 7) lies on the line y = –x + 4 . (i) Write down the co-ordinates of two other points on this line. Use x co-ordinates so that –3 < x Y 4 . Answer(c)(i) (............... , ...............) and (............... , ...............) [2] (ii) On the grid, draw the line y = –x + 4 for –3 Y x Y 4 . [1] (iii) Use both graphs to fi nd the solutions of the equation x2 – 2x – 1 = –x + 4 . Answer(c)(iii) x = ................. or x = ................. [2] _____________________________________________________________________________________

Mark scheme: 4 (a) (i) 7, –1, 2 2 B1 for any 2 correct (ii) 8 points plotted 3ft P2ft for 6 or 7 correct P1ft for 4 or 5 correct Correct smooth curve 1 (b) x = 1 1 (c) (i) Two correct points 1,1 x –2 –1 –0 –1 –2 –3– 4 y –6 –5 –4– 3– 2 –1 –0 (ii) Correct line drawn 1 Must be ruled and continuous (iii) –1.9 to –1.7, 2.7 to 2.9 2ft 1 for each correct

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5 (a) For Examiner′s North Use C B D North A Scale: 1 cm to 12 km The diagram shows four towns, A, B, C and D, joined by straight roads AB, BC and BD. The scale is 1 centimetre represents 12 kilometres. (i) Measure the bearing of B from A. Answer(a)(i) ............................................... [1] (ii) Work out the distance in kilometres from A to B. Answer(a)(ii) ......................................... km [2] (iii) Saraswati takes 1 hour 30 minutes to drive from A to B. Calculate her average speed, in kilometres per hour, for this journey. Answer(a)(iii) ...................................... km/h [1] (b) At B, Saraswati follows another straight road which is equidistant from BC and BD. For Examiner′s Use Using a straight edge and compasses only and leaving in all your construction lines, construct the line of this road on the diagram. [2] (c) Another motorist, Leah, leaves C and drives on a bearing of 165° to meet Saraswati at town E. Town E is on the road in part (b). Show Leah’s journey on the diagram and mark the town E. [1] (d) Saraswati travelled from B to E at an average speed of 55 km/h. Calculate the time, in hours and minutes, that she took. Answer(d) ......................... h ......................... min [4] (e) There is a speed limit of 50 km/h on all roads within 30 km of town D. On the diagram, show the boundary of the region where this speed limit applies. [2] _____________________________________________________________________________________

Mark scheme: 5 (a) (i) (0)35 to (0)39 1 (ii) 117.6 to 122.4 [km] 2 B1 for (10 ± 0.2) cm seen (iii) 80 or 78.4 to 81.6 1ft ft their (a)(ii) ÷ 1.5 (b) Bisector of angle CBD with 2 2 B1 correct line (±2°), some or all arcs absent correct pairs of arcs. (c) Ruled line from C to BD on a 1 bearing of 165° (d) 1 [h] 18 [min] to 1 [h] 26 [min] 4 B1ft measure BE www M1 change to kilometres. M1 for their distance ÷ 55 (e) Circle, centre D, with radius 2 M1 for 2.5 ± 0.2 soi. 2.5 ± 0.2 cm SC1 for circle, centre D, incorrect radius or freehand ‘correct’ circle IGCSE – May/June 2013 0580 33

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6 For Examiner′s Use Felix rolls two fair dice, each numbered from 1 to 6, and adds the numbers shown. He repeats the experiment 70 times and records the results in a frequency table. The fi rst 60 results are shown in the tally column of the table. The last 10 results are 6, 8, 9, 2, 6, 4, 7, 9, 6, 10 . Total Tally Frequency 2 3 4 5 6 7 8 9 10 11 12 (a) (i) Complete the frequency table to show all his results. [2] (ii) Write down the relative frequency of a total of 5. Answer(a)(ii) ............................................... [1] (b) (i) Write down the mode. For Examiner′s Use Answer(b)(i) ............................................... [1] (ii) Write down the range. Answer(b)(ii) ............................................... [1] (iii) Work out the median. Answer(b)(iii) ............................................... [2] (iv) Calculate the mean. Answer(b)(iv) ............................................... [3] (c) (i) Complete this table showing how different totals can be made when rolling two dice. Dice 1 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 3 Dice 2 4 7 5 7 9 6 12 [1] (ii) Explain why 7 is the most likely total. Answer(c)(ii) ..................................................................................................................... [1] _____________________________________________________________________________________

Mark scheme: 6 (a) (i) Frequency table completed 2 M1 for 8 correct frequencies SC1 for all correct tallies if no frequencies. OR SC1 for all correct frequencies in tally column (ii) 3 1 ft ft their table oe 70 (b) (i) 6 1 (ii) 10 1 (iii) 6 2 M1 for clear recognition of mid values used (iv) 6.43 to 3sf 3 M1 for total of freq × their result M1 dep for division by their 70 (c) (i) All totals filled in 1 Allow 1 error or omission (ii) More ways of getting 7 1 Any equivalent explanation

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7 (a) For Examiner′s 8.4 cm B C Use NOT TO SCALE 5.5 cm h 70° A 12.5 cm D In the quadrilateral ABCD, BC is parallel to AD. AB = 5.5 cm, BC = 8.4 cm, AD = 12.5 cm and angle BAD = 70°. The height of the quadrilateral is h. (i) Write down the mathematical name of the quadrilateral ABCD. Answer(a)(i) ............................................... [1] (ii) Use trigonometry to show that h = 5.2 cm, correct to 1 decimal place. Answer(a)(ii) [2] (iii) Calculate the area of the quadrilateral ABCD. Answer(a)(iii) ........................................ cm2 [2] (iv) The quadrilateral forms the cross section of a prism with length 6.8 cm. For Examiner′s Use Calculate the volume of the prism. Give your answer correct to 2 signifi cant fi gures. Answer(a)(iv) ........................................ cm3 [2] (b) B 95° NOT TO SCALE w° x° C 64° A z° y° E D The diagram shows a pentagon, ABCDE. AB is parallel to DC. A straight line, parallel to ED, passes through the vertex C. (i) Find the values of w, x and y. Answer(b)(i) w = ............................................... x = ............................................... y = ............................................... [3] (ii) The sum of the angles of a pentagon is 540°. Find the value of z. Answer(b)(ii) z = ............................................... [2] _____________________________________________________________________________________

Mark scheme: 7 (a) (i) Trapezium 1 (ii) h M1 = sin 70 or better 5.5 5.17 or 5.16(8...) seen A1 (iii) 54.3 or 54.34 or 54.(0...) 2 M1 for 0.5 (8.4 + 12.5) × 5.2 oe (iv) 370 2ft B1ft Their (a)(iii) × 6.8 not correctly rounded to 2sf (b) (i) 64 1 21 1ft ft 85 – their (b)(i) 116 1 (ii) 154 2ft M1 for 540 – (90 + 95 + 64 + their x + their y)

More questions on Types of number

8 (a) Simplify the following expressions. For Examiner′s Use (i) 3m – 5m + 6m Answer(a)(i) ............................................... [1] (ii) 5e – 4f – 3e – 6f Answer(a)(ii) ............................................... [2] (b) s = u + at (i) Calculate the value of s when u = 27, a = –2 and t = 15. Answer(b)(i) s = ............................................... [2] (ii) Make t the subject of the formula s = u + at. Answer(b)(ii) t = ............................................... [2] (c) Solve the simultaneous equations. 5x + 2y = 4 4x – y = 11 Answer(c) x = ................................................ y = ................................................ [3] _____________________________________________________________________________________

Mark scheme: 8 (a) (i) 4m 1 (ii) 2e – 10f 2 B1 for ae – 10f or 2e ± bf (a,b ≠ 0) (b) (i) –3 2 M1 for 27 + (–2) × 15 or better (ii) s − u s u 2 M1 first step correct [t=] or − a a a SC1 for s – u ÷ a www (c) [x =] 2, [y =] –3 3 M1 for correct method to eliminate one variable. A1 for x or y correct IGCSE – May/June 2013 0580 33

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9 (a) Write down the next term and the rule for fi nding the next term for the following sequences. For Examiner′s Use (i) 3, 9, 27, 81, ... Answer(a)(i) Next term .................. rule ......................................................................... [2] (ii) 2, 3, 6, 11, 18, ... Answer(a)(ii) Next term .................. rule ....................................................................... [2] 1 (iii) 4, 2, 1, , ... 2 Answer(a)(iii) Next term .................. rule ...................................................................... [2] (iv) 5, –10, 20, –40, ... Answer(a)(iv) Next term .................. rule ....................................................................... [2] (b) (i) Write down the next two terms of this sequence. 5, 13, 21, 29, ............. , ............. [2] (ii) Write down the nth term of this sequence. Answer(b)(ii) ............................................... [2] (iii) Find the 100th term. Answer(b)(iii) ............................................... [1] _____________________________________________________________________________________

Mark scheme: 9 (a) (i) 243 1 Multiply by 3 oe 1 (ii) 27 1 Add next odd number oe 1 Add 1 first and keep adding 2 more each time (iii) 1 or 0.25 1 4 Halve or divide by 2 1 (iv) 80 1 Multiply by –2 oe 1 (b) (i) 37, 45 1, 1ft ft is (ans) + 8 (ii) 8n – 3 oe final answer 2 B1 for 8n + a or B1 for bn – 3 (b ≠ 0) (iii) 797 1ft Only follow through a linear expression

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