Cambridge IGCSE Mathematics 0580 — 2013 Oct/Nov Paper 3 · Variant 1

1 Pedro is on a cruise ship. For Examiner′s Use (a) The ship has a climbing wall. These are the number of attempts that each of 30 people made at climbing the wall. 29 27 11 3 12 4 29 9 16 17 30 29 38 36 18 2 15 24 36 3 33 26 21 9 38 4 28 23 19 27 (i) Find the range. Answer(a)(i) ............................................... [1] (ii) Complete the frequency table. You may use the tally column to help you. Number of attempts Tally Frequency 1 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 31 – 35 36 – 40 [2] (iii) Draw a bar chart to show this information. Complete the scale on the frequency axis. Frequency 1 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 31 – 35 36 – 40 Number of attempts [3] (iv) Write down the modal group. For Examiner′s Use Answer(a)(iv) ............................................... [1] (b) Pedro left the ship in Cadiz at 08 45. He returned to the ship at 16 10. Find how long Pedro was in Cadiz. Answer(b) ....................... hours ....................... minutes [1] (c) Exchange Rate $1 = €1.428 (i) Pedro changed $167 into euros (€). Calculate how many euros Pedro received. Give your answer correct to 2 decimal places. Answer(c)(i) € ............................................... [2] (ii) Later, Pedro changed €107.10 back into dollars ($) using the same exchange rate. Calculate how many dollars Pedro received. Answer(c)(ii) $ ............................................... [2] _____________________________________________________________________________________

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) 36 cao 1 (ii) 5, 2, 3, 4, 3, 8, 1, 4 2 B1 for 6 or 7 frequencies correct or 8 correct tallies if frequency column blank or 8 correct frequencies in tally column (iii) fully correct bar chart 3FT B1 for a correct linear scaled frequency axis B2FT for correct height and equal width of bars or B1FT for correct height of at least 5 bars or all bars correct height but unequal widths or gaps SC2 for a fully correct bar chart but linear scale not marked (iv) 26 – 30 cao 1 (b) 7 (hours) 25 ( minutes) cao 1 (c) (i) 238.48 2 M1 for 167 × 1.428 soi by 238.47(6) or 238.5 or 238 (ii) 75 2 M1 for 107.1 ÷ 1.428

More questions on Averages and range

2 (a) (i) 1 and 120 are factors of 120. For Examiner′s Use Write down another factor of 120. Answer(a)(i) ............................................... [1] (ii) Find the highest common factor of 120 and 900. Answer(a)(ii) ............................................... [2] (b) 2 5 15 24 49 60 258 512 From the list, write down (i) a multiple of 30, Answer(b)(i) ............................................... [1] (ii) a square number, Answer(b)(ii) ............................................... [1] (iii) the cube root of 8. Answer(b)(iii) ............................................... [1] (c) Give an example to show that the following statements are not true. (i) An odd number multiplied by an even number gives an odd number. Answer(c)(i) ..................................................................... [1] (ii) The cube of a negative number is positive. Answer(c)(ii) ..................................................................... [1] (d) Use < , > , or = to complete the following statements. Each symbol may be used more than once. 3 (i) 0.5 ................................ [1] 8 (ii) 1.5 ................................ 105% [1] 11 (iii) 0.78 .............................. [1] 14 _____________________________________________________________________________________

Mark scheme: 2 (a) (i) 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 1 Award mark for any one from list. 40, 60. (ii) 60 2 B1 for any common factor on answer line, 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 (b) (i) 60 1 (ii) 49 1 (iii) 2 1 (c) (i) Any correct example 1 Calculation and correct answer must be seen IGCSE – October/November 2013 0580 31 (ii) Any correct example 1 Calculation and correct answer must be seen (d) (i) > 1 (ii) > 1 (iii) < 1

More questions on Types of number

3 (a) The diagram shows the position of town A and town B, on a map. For Examiner′s Use North A B (i) Measure the length, in millimetres, of the line AB. Answer(a)(i) ........................................ mm [1] (ii) Measure the bearing of town B from town A. Answer(a)(ii) ............................................... [1] (b) A triangular fi eld has sides of length 550 m, 300 m and 400 m. (i) Construct the triangle, using a ruler and compasses only. Use a scale of 1 cm to represent 50 m. The side of length 550 m has been drawn for you. 550 m [3] (ii) By making a suitable measurement on your diagram, calculate the area of the fi eld. Give your answer in square metres. Answer(b)(ii) .......................................... m2 [3] _____________________________________________________________________________________

Mark scheme: 3 (a) (i) 44 – 46 1 (ii) 231 – 235 1 (b) (i) Fully correct drawing with arcs 3 B2 for correct triangle without arcs B1 for 1 correct length side Or arc of 6cm or 8cm 1 52250 to 60500 nfww 3FT M2 for × 550 × 2 (their correct height × 50) 1 Or × 11 × their correct height in cm 2 or B1 for their correct height in cm or their correct height × 50 seen 1 If 0 scored then SC1 for × 550 × 2 (50 × k)

More questions on Angles

4 For Examiner′s y Use 8 7 6 5 B 4 3 C 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 A –4 –5 –6 (a) (i) Describe fully the single transformation which maps shape B onto shape A. Answer(a)(i) ...................................................................................................................... ........................................................................................................................................... [2] (ii) Describe fully the single transformation which maps shape B onto shape C. Answer(a)(ii) ..................................................................................................................... ........................................................................................................................................... [3] (b) (i) Refl ect shape B in the y-axis. Label the image D. [1] (ii) Rotate shape B through 90° anticlockwise about the origin. Label the image E. [2] _____________________________________________________________________________________

Mark scheme: 4 (a) (i) Translation 1  − 7  8  − 1 Accept 7 left and 8 down  (ii) Enlargement 1 [Scale factor] 0.5 1 [Centre] (0, 0) 1 (b) (i) D at ( –2, 4) (–4 , 4) (–3 , 6) 1 (ii) E at ( –4, 2) ( –4 , 4) ( –6 ,3) 2 B1 for correct orientation, incorrect centre or 90° rotation clockwise about (0,0). IGCSE – October/November 2013 0580 31

More questions on Transformations

5 (a) The cost, $C, of a party for n people is calculated using the following formula. For Examiner′s Use C = 130 + 4n (i) Calculate C when n = 25. Answer(a)(i) ............................................... [2] (ii) Eurdley has a party which costs $1138. How many people is this party for? Answer(a)(ii) ............................................... [2] (b) Solve the following equations. (i) 3x = 27 Answer(b)(i) x = ............................................... [1] (ii) 8y – 4 = 24 Answer(b)(ii) y = ............................................... [2] (iii) 4(5q – 2) = 72 Answer(b)(iii) q = ............................................... [3] (c) Solve the simultaneous equations. 6x + 8y = –31 14x – 5y = 46 Answer(c) x = ............................................... y = ............................................... [4] _____________________________________________________________________________________

Mark scheme: 5 (a) (i) 230 2 M1 for 130 + 4 × 25 or better (ii) 252 2 M1 for 4n = 1138 – 130 or better Or (1138 – 130) / 4 or better (b) (i) 9 1 (ii) 3.5 2 M1 for 8y = 24 + 4 or better Or y – 4/8 = 24/8 or better (iii) 4 3 M1 for first correct step M1FT for second correct step (c) x = 1.5 or 3/2 4 M1 for correctly equating one set of y = –5 coefficients. M1 for correct method to eliminate one variable. A1 for x = 1.5 A1 for y = –5

More questions on Percentages

6 For Examiner′s 30 m A B Use NOT TO SCALE HOUSE 17 m D C The rectangle ABCD shows Mr Liu’s garden. (a) Mr Liu puts a fence around three sides of his garden, AB, BC and CD. The fence costs $3.28 per metre. Calculate the cost of the fence. Answer(a) $ ............................................... [2] (b) (i) Calculate the area of Mr Liu’s garden. Answer(b)(i) .......................................... m2 [2] (ii) Mr Liu uses an area of 408 m2 in his garden for a lawn, fl owers and vegetables. He divides this area into three parts, in the ratio lawn : fl owers : vegetables = 5 : 3 : 4 . Calculate the area used for each part. Answer(b)(ii) Lawn ................................................. m2 Flowers ............................................. m2 Vegetables ........................................ m2 [3] (c) Mr Liu walks in a straight line across his garden from A to C. For Examiner′s Use Calculate the distance Mr Liu walks. Answer(c) ........................................... m [3] (d) Mr Liu has a circular pond, radius 4.5 m, in his garden. (i) Calculate the area of the pond. Answer(d)(i) .......................................... m2 [2] (ii) The pond is fi lled with water to a depth of 2 metres. Calculate the volume of water in the pond. Answer(d)(ii) .......................................... m3 [1] _____________________________________________________________________________________

Mark scheme: 6 (a) 252.56 2 M1 for (30 + 30 + 17) × 3.28 or better oe (b) (i) 510 2 M1 for 30 × 17 (ii) 170 3 M2 for 2 correct areas clearly identified 102 or M1 for 408 ÷ (5 + 3 + 4) soi by 34 or 136 one correct area clearly identified SC2 for three correct answers in incorrect places (c) 34.5 3 M2 for 30 2 + 17 2 soi by 1189 or M1 for 302 + 172 soi by 1189 (d) (i) 63.6 or 63.61 – 63.63 2 M1 for 4.52 × π or 20.25 π (ii) 127 or 127.2… 1FT FT for their (d)(i) × 2 IGCSE – October/November 2013 0580 31

More questions on Area and perimeter

7 (a) Complete the table of values for y = x2 – x + 2 . For Examiner′s Use x –3 –2 –1 0 1 2 3 4 y 8 2 4 [3] (b) On the grid, draw the graph of y = x2 – x + 2 for −3 Y x Ğ 4 . y 16 14 12 10 8 6 4 2 x –3 –2 –1 0 1 2 3 4 [4] (c) Write down the equation of the line of symmetry of the graph. For Examiner′s Use Answer(c) ............................................... [1] (d) (i) On the grid, draw the line y = 9 . [1] (ii) Solve the equation x2 – x + 2 = 9 . Answer(d)(ii) x = ....................... or x = ....................... [2] _____________________________________________________________________________________

Mark scheme: 7 (a) 14, 4, 2, 8, 14 3 B2 for 4 correct B1 for 2 or 3 correct (b) 8 points correctly plotted P3FT P2FT for 6 or 7 points correctly plotted P1FT for 4 or 5 points correctly plotted Smooth and correct curve through all C1 correct points 1 (c) x = 0.5 or x = 1 2 (d) (i) y = 9 ruled 1 (ii) –2.15 to –2.25 1FT 3.15 to 3.25 1FT

More questions on Graphs of functions

8 For Examiner′s Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Use Average temperature in °C –4.4 –4.2 –2.7 0.3 4.8 9.1 11.8 10.8 6.7 2.7 –1.1 –3.3 The table shows the average temperature for Tromso, Norway each month. (a) (i) Write down the month which had the highest average temperature. Answer(a)(i) ............................................... [1] (ii) How much warmer was it in September than in February? Answer(a)(ii) .......................................... °C [1] (iii) The lowest temperature in October was 12.3°C below the average temperature for that month. Work out the lowest temperature in October. Answer(a)(iii) .......................................... °C [1] (b) In a survey, some tourists were asked how they had travelled to Norway. The pie chart shows the results. Road Boat Train Plane (i) 150 of these tourists travelled by boat. For Examiner′s Use Show that 600 tourists took part in the survey. Answer(b)(i) [1] (ii) Calculate the number of these tourists who travelled by plane. Answer (b)(ii) ............................................... [3] (c) A train ticket from Oslo to Stavanger costs 885 krone. There is a discount of 12% on the total cost of the tickets for a group of 10 or more people. Calculate the cost of tickets for a group of 15 people. Answer(c) ..................................... krone [3] (d) On 1 January 2000, the population of Norway was 4 480 000, correct to 3 signifi cant fi gures. (i) Write this number in standard form. Answer(d)(i) ............................................... [1] (ii) On 1 January 2011, the population of Norway was 4 920 000, correct to 3 signifi cant fi gures. Calculate the percentage increase in the population. Answer(d)(ii) ........................................... % [3] _____________________________________________________________________________________

Mark scheme: 8 (a) (i) July or Jul 1 (ii) 10.9 1 (iii) – 9.6 1 90 360 (b) (i) 150 ÷ oe 1 Accept 150 × , 150 × 4 360 90 (ii) 250 3 M1 for their 150/360 × 600 or their 150 × 150/90 and B1 for 150 seen as angle (c) 11682 3 M2 for 885 × 15 × 0.88 oe M1 for 885 × 0.88 oe or 885 × 15 × 0.12 oe (d) (i) 4.48 × 106 cao 1 4920000− 4480000 (ii) 9.82 3 M2 for × 100 oe 4480000  4920000  or  −1 × 100 oe  4480000  or B1 for 440000 or 0.44 or 1.098(….) or 109.8(…..) IGCSE – October/November 2013 0580 31

More questions on The four operations

9 For Examiner′s G Use E B C 24° NOT TO SCALE x° O 78° A y° D H F A, B, C and D are points on the circumference of a circle, centre O. EF is a tangent to the circle at A. GH is a straight line through the point A. Angle CBD = 24° and angle OAG = 78°. (a) (i) Write down the mathematical names of lines BC and OA. Answer(a)(i) BC is a ............................................................. OA is a ............................................................. [2] (ii) Find the value of x, giving a reason for your answer. Answer(a)(ii) x = ............................ because ................................................................... ........................................................................................................................................... [2] (iii) Find the value of y, giving a reason for your answer. Answer(a)(iii) y = ............................ because .................................................................. ........................................................................................................................................... [3] (b) The diagram shows a regular polygon, centre O. For Examiner′s Use NOT TO SCALE O w° (i) Write down the name of this polygon. Answer(b)(i) ............................................... [1] (ii) Find the value of w. Show all your working. Answer(b)(ii) w = ............................................... [3] (c) The exterior angle of another regular polygon is 24°. Calculate the number of sides this polygon has. Answer(c) ............................................... [2] _____________________________________________________________________________________

Mark scheme: 9 (a) (i) Chord 1 Radius 1 (ii) 12 1 Tangent [meets] radius [at] 90 [°] 1 (iii) 66 2 M1 for BCD identified as 90 or 180–24–90 Angles [in] triangle 180 or 1 Angle [in a] semi–circle [= 90] (b) (i) Octagon 1 alternative method (ii) 360 ÷ 8 [= 45] M1 M1 for (8–2) × 180 [=1080] or 6 × 180 [=1080] (180 – their 45) ÷ 2 M1FT M1FT for (their 1080 ÷ 8) ÷ 2 or their 1080 ÷ 16 67.5 A1 A1 for 67.5 (c) 15 2 M1 for 360 / 24

More questions on Geometrical terms