Cambridge IGCSE Mathematics 0580 — 2011 Oct/Nov Paper 1 · Variant 1

1 For Examiner's Use A S The diagram shows the map of part of an orienteering course. Sanji runs from the start, S, to the point A. Write as a column vector.     Answer   [1]    

Mark scheme: Qu. Answers Mark Part Marks 1 −3  1    4  4

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4 2 When Ali takes a penalty, the probability that he will score a goal is . 5 Ali takes 30 penalties. Find how many times he is expected to score a goal. Answer [2]

Mark scheme: 4 2 24 or 24 out of 30 2 M1 for × 30 5

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3 The ratio of Anne’s height : Ben’s height is 7 : 9. Anne’s height is 1.4 m. Find Ben’s height. Answer m [2]

Mark scheme: 3 1.8 2 M1 for 1.4 ÷ 7 or SC1 for answer 180

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4 The distance between the centres of two villages is 8 km. For A map on which they are shown has a scale of 1 : 50 000. Examiner's Use Calculate the distance between the centres of the two villages on the map. Give your answer in centimetres. Answer cm [2]

Mark scheme: 4 16 2 B1 for 1cm to 0.5km oe or 800 000 (cm) or figs 16

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5 10 8 6 Frequency 4 2 0 Black Silver Red Green Blue Favourite colour The bar chart shows the favourite colours of students in a class. (a) How many students are in the class? Answer(a) [1] (b) Write down the modal colour. Answer(b) [1]

Mark scheme: 5 (a) 25 1 (b) Green cao 1 258 75

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45 × 5.75 For 6 Use your calculator to find . Examiner's 3.1 + 1.5 Use Answer [2]

Mark scheme: 258.75 6 7.5(0) cao 2 M1 for 6.4

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7 (a) Calculate 60% of 200. Answer(a) [1] (b) Write 0.36 as a fraction. Give your answer in its lowest terms. Answer(b) [2]

Mark scheme: 7 (a) 120 1 9 36 18 (b) cao 2 B1 or 25 for100 50 2

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8 A circle has a radius of 50 cm. (a) Calculate the area of the circle in cm2. Answer(a) cm2 [2] (b) Write your answer to part (a) in m2. Answer(b) m2 [1]

Mark scheme: 8 (a) 7853 to 7855 2 M1 for π × 502 or 7850 or 7860 www (b) 0.7853 to 0.7855 or 0.785 or 0.786 1ft Their (a) ÷ 10 000 evaluated

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9 For Examiner's 30 Use 25 20 Temperature 15 (°C) 10 5 0 6 am 9 am Noon 3 pm 6 pm Time The graph shows the temperature in Paris from 6 am to 6 pm one day. (a) What was the temperature at 9 am? Answer(a) °C [1] (b) Between which two times was the temperature decreasing? Answer(b) and [1] (c) Work out the difference between the maximum and minimum temperatures shown. Answer(c) °C [1]

Mark scheme: 9 (a) 15 1 (b) 2 (pm), 6 (pm) 1 (c) 15 1 Allow −15

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10 (a) Write down the mathematical name of a quadrilateral that has exactly two lines of symmetry. Answer(a) [1] (b) Write down the mathematical name of a triangle with exactly one line of symmetry. Answer(b) [1] (c) Write down the order of rotational symmetry of a regular pentagon. Answer(c) [1]

Mark scheme: 10 (a) Rectangle or rhombus 1 Either one or both given (b) Isosceles (triangle) 1 (c) 5 cao 1 IGCSE – October/November 2011 0580 11 11k

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1  2 1  For 11 Without using your calculator, work out  +  . Examiner's 2  3 4  Use Show all your working clearly and give your answer as a fraction. Answer [3]

Mark scheme: 11k 11 final answer www Method 1 (Addition first) 24 k 8 3 8 + 3 B1 or oe 12 +12 12 1 × their 11 M1 2 × their 12 A1 Method 2 (Multiplication first) 2 1 1 1 B1 + or + oe 6 8 3 8 ad + bc a c M1 for their + bd b d A1 11 11 If M0, SC1 if is only followed by 12 24 or if zero, SC1 if work is entirely in decimals & with answer of .0 458 3 to .0 45835

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12 y 9 8 7 6 5 4 3 2 1 x – 4 – 3 – 2 – 1 0 1 2 The diagram shows the graph of y = (x + 1)2 for −4 Y x Y 2. (a) On the same grid, draw the line y = 3. [1] (b) Use your graph to find the solutions of (x + 1)2 = 3. Give each solution correct to 1 decimal place. Answer(b) x = or x = [2]

Mark scheme: 12 (a) Correct ruled line 1 (b) −2.7, 0.7 1, 1ft B2ft their ruled line through (0, 3) for two intersections given to 1 decimal place or B1 for –2.70 to –2.75 and 0.70 to 0.75 or B1ft their ruled line through (0, 3) for two intersections not given to 1 decimal place

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13 For Examiner's Use NOT TO SCALE The front of a house is in the shape of a hexagon with two right angles. The other four angles are all the same size. Calculate the size of one of these angles. Answer [3]

Mark scheme: 13 135 cao 3 M1 for 720 or (6 – 2) × 180 oe seen in working and M1 for equation 180 + 4x = their 720 or M1 for (360 − 180) ÷ 4 (= 45) oe seen in working and M1 dep for 180 − their 45

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14 (a) Expand and simplify. 2(3x – 2) + 3(x – 2) Answer(a) [2] (b) Expand. x(2x2 – 3) Answer(b) [2]

Mark scheme: 14 (a) 9x − 10 final answer 2 B1 for 6x − 4 or 3x − 6 or for answer of 9x + j, or kx − 10 (b) 2x3 – 3x final answer 2 B1 for answer in form 2x3 + m or n – 3x

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15 For Examiner's 50 Use 40 30mark test 20English 10 0 10 20 30 40 50 60 70 80 Mathematics test mark The scatter diagram shows the marks obtained in a Mathematics test and the marks obtained in an English test by 15 students. (a) Describe the correlation. Answer(a) [1] (b) The mean for the Mathematics test is 47.3 . The mean for the English test is 30.3 . Plot the mean point (47.3, 30.3) on the scatter diagram above. [1] (c) (i) Draw the line of best fit on the diagram above. [1] (ii) One student missed the English test. She received 45 marks in the Mathematics test. Use your line to estimate the mark she might have gained in the English test. Answer(c)(ii) [1]

Mark scheme: 15 (a) Negative 1 Ignore embellishments (b) Correct point 1 (c) (i) Accurate ruled line 1 (ii) English mark 1ft Follow through their (c)(i)

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16 (a) For C Examiner's Use 110° A B NOT TO SCALE D E In the diagram, AB is parallel to DE. Angle ABC = 110°. Find angle BDE. Answer(a) Angle BDE = [2] (b) NOT TO SCALE O y° B 50° z° t ° A T TA is a tangent at A to the circle, centre O. Angle OAB = 50°. Find the value of (i) y, Answer(b)(i) y = [1] (ii) z, Answer(b)(ii) z = [1] (iii) t. Answer(b)(iii) t = [1]

Mark scheme: 16 (a) 70 2 B1 for angle ABD = 70° stated or seen on the diagram (b) (i) (y =) 80 1 (ii) (z =) 40 1 (iii) (t =) 10 1ft Follow through 90 − their y or 50 − their z IGCSE – October/November 2011 0580 11 2 2 ( )

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17 For Examiner's Use NOT TO SCALE 8 m y° 3 m The diagram shows a ladder, of length 8 m, leaning against a vertical wall. The bottom of the ladder stands on horizontal ground, 3 m from the wall. (a) Find the height of the top of the ladder above the ground. Answer(a) m [3] (b) Use trigonometry to calculate the value of y. Answer(b) y = [2]

Mark scheme: 17 (a) 7.42 or 7.416... cao 3 M2 for (8 2 − 3 2 ) or complete alternate method or M1 for x2 + 32 = 82 or better 3 (b) 67.97 to 68(.0) cao 2 M1 for cos (y) = oe 8 500 × 5 × 3

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18 (a) Lucinda invests $500 at a rate of 5% per year simple interest. For Examiner's Calculate the interest Lucinda has after 3 years. Use Answer(a) $ [2] (b) Andy invests $500 at a rate of 5% per year compound interest. Calculate how much more interest Andy has than Lucinda after 3 years. Answer(b) $ [4]

Mark scheme: 500 × 5 × 3 18 (a) 75 2 M1 for oe 100 or SC1 for answer of 575 (b) 3.81(25) 4 M2 for 500 × 1.05 × 1.05 × 1.05 or M1 for 500 × 1.05 × 1.05 A1 for 578.81(25) or 78.81(25) seen and A1ft for value of 500(1.05)3 – 500 – their (a)

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