Cambridge IGCSE Mathematics 0580 — 2020 May/June Paper 1 · Variant 1

1 Write down the value of the 7 in the number 570 296. ................................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1 70 000 1

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2 The table shows the temperature, in °C, at midday on the first day of each month during one year in a city. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 9 11 15 19 23.5 27.5 29 28 25 19.5 14.5 10 Calculate the mean of these temperatures. ............................................. °C [2]

Mark scheme: 2 19.25 2 M1 for sum of 12 numbers ÷ 12

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3 Write these numbers in order, starting with the smallest. 13 5 5.6% 0.065 201 89 .................... < .................... < .................... < .................... [2] smallest

Mark scheme: 3 5 13 2 B1 for 3 in correct order 5.6% 0.065 or M1 for 0.0647 0.056 0.0562 seen oe 89 201

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4 (a) On each shape draw all the lines of symmetry. [3] (b) Write down the order of rotational symmetry of this shape. ................................................. [1]

Mark scheme: 4(a) Three correct lines B2 B1 for one or more correct lines and no wrong lines One correct line B1 4(b) 2 1

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5 A NOT TO 38° SCALE B C D In the triangle ABC, AB = AC and angle BAC = 38°. BCD is a straight line. Work out angle ACD. Angle ACD = .................................................. [3]

Mark scheme: 5 109 3 M1 for (180 – 38) ÷ 2 oe M1 for 180 – their ACB

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6 (a) Diego flies from Madrid to Buenos Aires. His flight leaves at 20 55 and arrives at 03 50 local time. The local time in Buenos Aires is 5 hours behind the local time in Madrid. Work out, in hours and minutes, the time the flight takes. ................... h ................... min [2] (b) Diego changes 200 euros into Argentine Peso. The exchange rate is 1 euro = 24.8 pesos. Work out how many pesos he receives. ....................................... pesos [1] (c) The distance between Madrid and Buenos Aires is 10 050 km. Diego’s return flight takes 12 hours 30 minutes. Calculate the average speed, in km/h, for the return flight. ........................................ km/h [1]

Mark scheme: 6(a) 11[h] 55[min] 2 B1 for 08 50 or 15 55 or 6[h] 55[min] seen 6(b) 4960 1 6(c) 804 1

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7 Rectangle A measures 3 cm by 8 cm. 8 cm NOT TO 3 cm A SCALE Five rectangles congruent to A are joined to make a shape. NOT TO SCALE Work out the perimeter of this shape. ........................................... cm [2]

Mark scheme: 7 86 2 M1 for correct method to find the perimeter e.g. (8 + 3) × 2 × 5 – 3 × 8 If 0 scored, SC1 for answer 98

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8 Find the highest odd number that is a factor of 60 and a factor of 90. ................................................. [1]

Mark scheme: 8 15 1

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9 y 4 3 2 Q 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 1 P – 2 – 3 – 4 (a) Write PQ as a column vector. [1] f p (b) Write 3PQ as a single vector. [1] f p

Mark scheme: 9(a)  −5  1    3  9(b)  −15  1 FT their (a)    9 

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10 Work out the size of one interior angle of a regular 9-sided polygon. ................................................. [2]

Mark scheme: 10 140 2 M1 for 360 ÷ 9

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11 A cone has radius 4.5 cm and height 10.4 cm. Calculate, in terms of r, the volume of the cone. 1 2 [The volume, V, of a cone with radius r and height h is V = rr h .] 3 .......................................... cm3 [2]

Mark scheme: 11 70.2π 2 1 M1 for [π] × 4.52 × 10.4 3

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12 (a) The nth term of a sequence is 60 - 8n . Find the largest number in this sequence. ................................................. [1] (b) Here are the first five terms of a different sequence. 12 19 26 33 40 Find an expression for the nth term of this sequence. ................................................. [2]

Mark scheme: 12(a) 52 1 12(b) 7n + 5 oe final answer 2 B1 for 7n + a or bn + 5 b ≠ 0

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13 Factorise completely. 21a 2 + 28ab ................................................. [2]

Mark scheme: 13 7a(3a + 4b) final answer 2 B1 for partial factorisation 7(3a2 + 4ab) or a(21a + 28b)

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14 The diagram shows a trapezium. ( 97 - 3x)° NOT TO SCALE ( 69 + 5x)° Work out the value of x. x = .................................................. [3]

Mark scheme: 14 7 3 M2 for 166 + 2x = 180 or better or M1 for 97 – 3x + 69 + 5x = 180 oe

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15 Simplify. 4p 5 q 3 # p 2 q -4 ................................................. [2]

Mark scheme: 15 4p7q−1 2 4 pb B1 for 4p7qa or 4pbq−1 or q

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16 (a) Write the number 0.0605 in standard form. ................................................. [1] (b) Calculate ( 1. 63 # 10 12 ) # ( 2.47 # 10 -1 ) . Give your answer in standard form. ................................................. [1]

Mark scheme: 16(a) 6.05 × 10−2 1 16(b) 4.0261 × 1011 1

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17 Expand and simplify. ( x - 5)( x - 7) ................................................. [2]

Mark scheme: 17 x2 – 12x + 35 2 B1 for any three of x2, –5x, –7x, +35

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18 Mrs Salaman gives her class two mathematics tests. The scatter diagram shows information about the marks each student scored. 70 60 50 40 Test 2 30 20 10 0 0 10 20 30 40 50 60 70 Test 1 (a) Write down the highest mark scored on test 1. ................................................. [1] (b) Write down the type of correlation shown in the scatter diagram. ................................................. [1] (c) Draw a line of best fit on the scatter diagram. [1] (d) Hamish scored a mark of 40 on test 1. He was absent for test 2. Use your line of best fit to find an estimate for his mark on test 2.

Mark scheme: 18(a) 66 1 18(b) Positive 1 18(c) Ruled line of best fit 1 18(d) 46 to 50 1 FT their line of best fit if a positive gradient 2 B1 for each 19 29.65 29.75 If 0 scored, SC1 for both correct but reversed

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1 7 620 Without using a calculator, work out 2 - # . e 3 8 o 25 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [4]

Mark scheme: 20 M2 M2 for correct method for common denominator 56 21 − 7 24 24 or B1 for 3 35 6 M1 their × 24 25 7 A1 20

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21 Lucia invests $5000 at a rate of 4.5% per year compound interest. Calculate the value of her investment at the end of 7 years. $ .................................................. [2]

Mark scheme: 21 2 7 6800 or 6804 or M1 for 5000+ 1 5.4  6803.3 to 6803.31  100 

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22 y 6 L 5 4 3 2 1 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 – 6 (a) Find the equation of line L in the form y = mx + c. y = .................................................. [2] (b) On the grid, draw a line that is perpendicular to line L. [1]

Mark scheme: 22(a) 2x − 3 2 B1 for kx – 3 or 2x + k k ≠ −3 22(b) Ruled line perpendicular to L 1

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23 R 65° B NOT TO SCALE 78° Q 78° 37° A C P Explain why triangle ABC is similar to triangle PQR. ............................................................................................................................................................. ............................................................................................................................................................. [2] BLANK PAGE

Mark scheme: 23 Angle ACB = 65˚ or M1 Angle RPQ = 37˚ 2 pairs of equal angles oe A1

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