Cambridge IGCSE Mathematics 0580 — 2025 May/June Paper 1 · Variant 3

1 (a) Write the number 70 000 000 in words. ..................................................................................................................................................... [1] (b) (i) Write down the value of the 5 in the number 0.25 . Give your answer as a fraction. ................................................. [1] (ii) Find the value of the reciprocal of 0.25 . ................................................. [2]

Mark scheme: Question Answer Marks Partial Marks 1(a) Seventy million(s) cao 1 1(b)(i) 5 1 1 or 100 20 1(b)(ii) 4 2 1 4 M1 for oe or 0.25 1

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2 (a) Write down the mathematical name for an angle between 90° and 180°. ................................................. [1] (b) Write down the mathematical term that describes two polygons that are the same shape and size. ................................................. [1]

Mark scheme: 2(a) Obtuse 1 2(b) Congruent 1

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3 (a) Write down 169 . ................................................. [1] (b) Work out the value of 24. ................................................. [1] (c) Work out the value of 10 -2 . ................................................. [1] (d) Work out -18 ' -4 . ................................................. [1] (e) Work out 1.6 # 0. 02 . ................................................. [1]

Mark scheme: 3(a) 13 1 3(b) 16 1 3(c) 1 1 or 0.01 100 3(d) 9 1 1 or 4.5 or 4 2 2 3(e) 0.032 1

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4 The diagram shows a quadrilateral with sides of equal length. NOT TO SCALE a° 2a° (a) Write down the mathematical name for this quadrilateral. ................................................. [1] (b) Work out the value of a. a = ................................................. [2]

Mark scheme: 4(a) Rhombus 1 4(b) 60 2 M1 for a + 2a = 180 oe or better

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5 Find the next term in each sequence. (a) 1, 5, 10, 16, 23, … ................................................. [1] (b) 1, 2, 4, 8, 16, … ................................................. [1]

Mark scheme: 5(a) 31 1 5(b) 32 1

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6 These are the lengths of time, in minutes, of seven phone calls. 10 22 5 7 35 8 75 (a) (i) Find the median. ........................................... min [2] (ii) Find the range. ........................................... min [1] (b) The longest phone call is 75 minutes. Write 75 minutes in hours. ............................................... h [1]

Mark scheme: 6(a)(i) 10 2 M1 for at least the first four or last four correctly ordered 6(a)(ii) 70 1 6(b) 1 1 1.25 or 14

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7 70 students study one of French, Spanish and German. The ratio number who study French : number who study Spanish = 3 : 7. 15 students study French. Find the number of students who study German. ................................................. [3]

Mark scheme: 7 20 3  15  7  M2 for 70 −  15 +  oe  3  15 or M1 for k , k = 1, 7 or 10 3

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8 The diagram shows two faces of a net of a cuboid on a 1 cm 2 grid. (a) Complete the statement. The dimensions of the cuboid are .......... cm by .......... cm by .......... cm. [1] (b) On the grid, complete a net of the cuboid. [3] (c) Work out the volume of the cuboid. .......................................... cm3 [2]

Mark scheme: 8(a) 3, 3, 5 1 8(b) Fully correct net 3 B2 for 2 correct extra faces in correct places or B1 for 1 correct extra face in correct place 8(c) 45 2 FT their dimensions from (a) M1 for 3 × 3 × 5 oe

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9 The diagram shows the net of a square-based pyramid. 4 cm NOT TO SCALE 5 cm The perpendicular height of each triangle is 4 cm. The base has side length 5 cm. (a) Calculate the surface area of the pyramid. .......................................... cm2 [2] (b) Write down the number of edges of the square-based pyramid. ................................................. [1]

Mark scheme: 9(a) 65 2 1 M1 for 4  5 4 + 5  5 oe 2 9(b) 8 1

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10 (a) Line A has equation y = 3x + 1. Line B has equation y = 3x - 1. Draw a ring around the description that is correct. Line A intersects Line A has a Line A is line B steeper gradient perpendicular to than line B line B Line A is parallel Line A and Line B to line B intersect the y-axis at the same point [1] (b) y 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 On the grid, draw the graph of y = 2x - 1. [2]

Mark scheme: 10(a) Circle around the statement 1 Line A is parallel to line B 10(b) Correct graph of y = 2x – 1 2 B1 for short or unruled line or for two correct coordinates plotted or for line with positive gradient passing through (0, –1) or for line with gradient 2

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11 Jo asks 90 people whether they prefer pop, rock, classical, jazz or folk music. The pie chart shows some of the results. Pop 120° 100° Rock (a) Work out the number of people who prefer pop. ................................................. [2] (b) The sector angle for classical is 80°. Draw this sector on the pie chart. [1] (c) 9 people prefer jazz and the rest prefer folk. (i) Work out the size of the sector angle for jazz. ................................................. [2] (ii) Complete the pie chart. [1]

Mark scheme: 11(a) 30 nfww 2 120 M1 for 36090 oe 11(b) Sector 80 drawn on pie chart 1 11(c)(i) 36 2 9 M1 for  360 oe 90 11(c)(ii) Completed pie chart 1 FT their (c)(i) dependent on their (c)(i)  60

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12 A music group has 30 members. 7 members play a flute (F ) and play a clarinet (C ). 12 members play a flute. 1 member does not play a flute and does not play a clarinet. (a) Use this information to complete the Venn diagram. % F C [2] (b) Find n(C ). ................................................. [1]

Mark scheme: 12(a) 2 B1 for two correct values in the correct E C position F 5 7 17 1 12(b) 24 1 FT their diagram provided a value in both sections of C

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13 By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 62.5 . 9.7 # 0.52 ................................................. [2]

Mark scheme: 13 60 M1 10  0.5 12 A1 If 0 scored, SC1 for 2 correct roundings or for all correct but with any trailing zeros

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14 4 cm NOT TO SCALE h cm 10 cm The diagram shows a trapezium. The area of the trapezium is 42 cm 2. Work out the value of h. h = ................................................. [2]

Mark scheme: 14 6 nfww 2 1 M1 for (4 + 10) h = 42 oe or better 2

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15 (a) Write down the inequality represented on the number line. x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 ............................................................................ [2] 1 (b) Write down the smallest integer that satisfies the inequality d 2-3 . 4 ................................................. [1]

Mark scheme: 15(a) –4 ⩽ x < 3 2 B1 for –4 ⩽ x or x < 3 15(b) –3 cao 1

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16 On Monday the cost of a concert ticket is $x. On Tuesday the cost of a ticket for the same concert is 20% more than the cost on Monday. Jack buys 4 tickets on Monday and 5 tickets on Tuesday. Jack pays $270 in total. Work out the value of x. x = ................................................. [3]

Mark scheme: 16 27 3 B2 for 10 or 10x  20  or M1 for [5 ×]  x + x  oe  100 

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17 Simplify. (a) y 4 # y 6 ................................................. [1] p 5 (b) p 8 ................................................. [1] 3 (c) `w4j ................................................. [1]

Mark scheme: 17(a) y10 1 17(b) 1 1 p–3 or p 3 17(c) w12 1

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18 NOT TO SCALE P 25° O x° y° Q R S T The diagram shows a circle, centre O. P and S are points on the circle. POR is a straight line. QRST is a tangent to the circle at S. (a) Find the value of x. Give a geometrical reason for your answer. x = .................... because ............................................................................................................ [2] (b) Find the value of y. y = ................................................ [3]

Mark scheme: 18(a) 25 2 B1 for either base angles of an isosceles triangle are equal 18(b) 140 3 M2 for [ORS = ]180 – (90 + their 25 + 25) oe or B1 for OSR= 90 or ROS = 50

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19 60° NOT TO SCALE 3 cm The diagram shows a sector of a circle with radius 3 cm and sector angle 60°. Calculate the area of the sector. Give your answer in terms of r in its simplest form. ......................................... cm2 [2]

Mark scheme: 19 3 1 2 60 2 π , 1 π , or 1.5π M1 for π 3 oe 2 2 360

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20 Find the highest common factor (HCF) of 36 and 54. ................................................. [2]

Mark scheme: 20 18 2 B1 for answer 2 or 3 or 6 or 9 or M1 for 2  3  3 oe as final answer or 36 = 2  2  3  3 and 54 = 2  3  3  3 or 2 correct factor trees or tables

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21 In this question, all lengths are in centimetres. 2x − 1 2x + 1 9 NOT TO x SCALE x + 3 The perimeter of the triangle is equal to the perimeter of the rectangle. Form an equation and solve it to find the value of x. x = ................................................. [4]

Mark scheme: 21 3x = 15 M3 M2 for 2x + 1 + x + 3 + 9 = 2(x + 2x – 1) or better or M1 for rearranging their equation to give ax = b or B1 for 3x + 13 or 6x – 2 5 A1 dep on at least M2 If 0 scored, SC1 for answer 5 with no algebra

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h 22 g = - 8 3 Rearrange the formula to make h the subject. h = ................................................. [2]

Mark scheme: 22 3(g + 8) or 3g + 24 2 h M1 for g + 8 = or 3g = h – 24 3

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23 8 cm NOT TO SCALE 2 cm x cm 1.5 cm Rectangle A Rectangle B Rectangle A is mathematically similar to rectangle B. Work out the value of x. x = ................................................. [2]

Mark scheme: 23 6 nfww 2 1.5 2 M1 for = oe or better x 8

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1 4 24 Work out 3 - 1 . 2 7 Give your answer as a mixed number in its simplest form. ................................................. [3]

Mark scheme: 24 13 3 27 114 cao nfww B2 for 14 7 k 11k or B1 for or 2 k 7 k 49 22 M1 for and 14 14 7 8 or 3 and 1 14 14 their 7  7 their 11  2 or and 2  7 7  2 or211 and 8 14 14 35 8 or and 14 14 8 or 72 and 14 14

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25 Solve the simultaneous equations. 8x + 5y = 4 2x - y = 10 x = ................................................. y = ................................................. [3]

Mark scheme: 25 [x = ] 3 final answer nfww 3 M1 for correctly eliminating one variable [y = ] –4 OR M1 for correct substitution of x or y into the other equation A1 for x = 3 A1 for y = –4 If A0 scored, SC1 for 2 values satisfying one of the original equations.

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