Cambridge IGCSE Mathematics 0580 — 2024 Oct/Nov Paper 2 · Variant 2

1 These are the first eight terms of a sequence. c -3 -9 -15 -21 -27 -33 k Find the value of c and the value of k. c = ................................................ k = ................................................ [2]

Mark scheme: Question Answer Marks Partial Marks 1 [c =] 3 2 B1 for each [k =] –39 or SC1 for c = –39 and k = 3

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2 The diagram shows an isosceles triangle. x° NOT TO SCALE 43° Find the value of x. x = ................................................. [2]

Mark scheme: 2 94 2 M1 for x + 2 × 43 = 180 oe

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3 1 0.25 3.142 3 - 3 24 - .04 1.2 - 4 Complete each statement with a number from the list. .................................................. is a natural number. .................................................. is an irrational number. .................................................. is the reciprocal of 4. [3]

Mark scheme: 3 24 3 B1 for each 3 0.25

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4 The scatter diagram shows the number of rooms and the number of people in each of eight buildings. 70 60 50 40 Number of rooms 30 20 10 0 0 10 20 30 40 50 60 70 80 Number of people (a) One of the buildings has 67 rooms. Write down the number of people in this building. ................................................. [1] (b) In another building there are 42 people and 33 rooms. On the scatter diagram, plot this point. [1] (c) (i) On the scatter diagram, draw a line of best fit. [1] (ii) There are 45 people in a different building. Find an estimate for the number of rooms in this building. ................................................. [1] (d) What type of correlation is shown in the scatter diagram? ................................................. [1]

Mark scheme: 4(a) 76 1 4(b) Point correctly plotted at 1 (42, 33) 4(c)(i) Correct ruled line of best fit 1 4(c)(ii) An integer in the range 1 27 to 33 FT their line of best fit provided line shows positive correlation and answer is an integer 4(d) Positive 1

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5 Convert 7.51 m 2 into cm2. .......................................... cm2 [1]

Mark scheme: 5 75 100 1

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6 The diagram shows a trapezium. NOT TO 9.5 cm SCALE x cm 6 cm The area of the trapezium is 42 cm 2. Calculate the value of x. x = ................................................. [2]

Mark scheme: 6 4.5 oe 2 1 M1 for 6 ( x + 9.5 ) = 42 oe 2 2 or 42  −9.5 oe 6

More questions on Area and perimeter

2 6 7 Without using a calculator, work out ' . 7 11 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [2]

Mark scheme: 7 2 11 M1  or 7 6 22 42  oe with common 77 77 denominator 11 A1 cao 21

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8 The diagram shows a parallelogram. (132 – 2x)° NOT TO SCALE (15 + 5x)° Work out the size of the smallest interior angle of the parallelogram. ................................................. [4]

Mark scheme: 8 70 4 B3 for x = 11 OR M1 for 132 – 2x + 15 + 5x = 180 oe M1 for collecting x terms on one side and number terms on the other for their equation. M1 for 15 + 5 × their x oe where –3 < their x < 15 or for 132 – 2 × their x oe where 21 < their x < 66

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9 A B NOT TO SCALE D C Points A, B, C and D lie on a circle. ABCD is a square with area 72 cm 2. Calculate the area of the circle. Give your answer as a multiple of r. .......................................... cm2 [3]

Mark scheme: 9 36π cao 3 B2 for answer 113 or 113.0 to 113.1… or an answer in terms of π which rounds to 113 or M1 for correct first step for finding d or r e.g. 72 + 72 = d 2 oe  72  2  72  2 72 = r2 + r2 oe or   +   = r2 oe      2   2  r 72 = oe sin 45 1 72 × r × r = oe 2 4

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310 Calculate 1 + 10 .9 # 0 .42 . ................................................. [1]

Mark scheme: 10 1.4 oe 1

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11 Factorise fully. (a) 24x 2 - 9 xy ................................................. [2] (b) 63x 2 - 28y 2 ................................................. [3]

Mark scheme: 11(a) 3x(8x – 3y) final answer 2 B1 for 3(8x2 – 3xy) or x(24x – 9y) or 3x(8x – 3y) seen then spoilt 11(b) 7(3x + 2y)(3x – 2y) final answer 3 B2 for (21x + 14y)(3x – 2y) or (3x + 2y)(21x – 14y) or 7(3x + 2y)(3x – 2y) seen then spoilt or M1 for 7(9x2 – 4y2) or [...](3x + 2y)(3x – 2y)

More questions on Algebraic manipulation

12 y is directly proportional to the square root of x + 1. y = 10 .5 when x = 8 . Find y when x = 1.56 . y = ................................................ [3]

Mark scheme: 12 5.6 oe 3 M1 for y = k x + 1 oe M1 for y = their k 1.56 + 1 oe

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13 y 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 The region R satisfies these inequalities. - 3 1 y G 2 y G x - 1 By drawing suitable straight lines and shading unwanted regions, find and label the region R. [4]

Mark scheme: 13 4 B1 for y = 2 solid line B1 for y = x – 1 solid line B1 for y = –3 dashed line B1 for correct region identified satisfying the given inequalities R

More questions on Inequalities

14 20 NOT TO SCALE Speed (m/s) 00 10 17 Time (seconds) The diagram shows the speed–time graph for 17 seconds of a car journey. (a) Find the acceleration of the car during the first 10 seconds. ......................................... m/s2 [1] (b) Calculate the total distance travelled by the car during the 17 seconds. .............................................. m [3]

Mark scheme: 14(a) 2 1 14(b) 240 3 M2 for correct complete area statement 1 e.g. × 20 × 10 + 7 × 20 oe 2 or M1 for one correct area

More questions on Area and perimeter

15 At the start of an experiment there are 40 000 bacteria. The number of bacteria increases at a rate of 15% per hour. Calculate the number of bacteria after 3 hours. ................................................. [2]

Mark scheme: 15 60835 2 3  15  M1 for 40 000  1 + oe    100 

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16 75 people are asked if they have a car, C, and if they have a job, J. The Venn diagram shows the results. % J C 9 51 13 2 A person is chosen at random from those who have a car. Find the probability that this person also has a job. ................................................. [1]

Mark scheme: 16 17 1 oe 20

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17 A B 64° D x° O NOT TO SCALE C A, B and C are points on the circumference of a circle with centre O. DA and DC are tangents to the circle. Angle ABC = 64°. Work out the value of x. x = ................................................ [2]

Mark scheme: 17 52 2 M1 for 360 – 90 – 90 – 128 oe or B1 for [obtuse angle] AOC = 128 or AOD or COD = 64 or DAO or DCO = 90

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18 (a) % = {8 # 10 -1 , .08o , 8%, .008} A = { a: 0.08 1 a G 0.8 } B = { b: b H 0.8 } % A B Complete the Venn diagram. [3] (b) Shade the region ( A , C ) + Bl in the Venn diagram. % A B C [1]

Mark scheme: 18(a) 3 B2 for three correctly placed A B or B1 for two correctly placed or correct conversion of 8 × 10–1, 8% and 0.08 ξ0.08 8 × 10–1 0. 8ሶ to 0.8, 0.08, 0.2[8…] or 0.3 8% 18(b) 1 A B C

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19 4.3 cm NOT TO SCALE 11.9 cm A solid is made from a cylinder and a hemisphere, both of radius 4.3 cm. The cylinder has length 11.9 cm. (a) Calculate the volume of the solid. 4 3 [The volume, V, of a sphere with radius r is V = r r .] 3 .......................................... cm3 [3] (b) Calculate the total surface area of the solid. [The surface area, A, of a sphere with radius r is A = 4 rr 2 .] .......................................... cm2 [4]

Mark scheme: 19(a) 858 or 857.7 to 857.9 3  1  4 3 M2 for   π  4.3 + π × 4.32 × 11.9 oe    2  3  1  4 3 or M1 for   π  4.3    2  3 or π × 4.32 × 11.9 19(b) 496 or 495.7 to 495.8… 4 M3 for 1 2 2 4  4.3 +  4.3 + 2  4.3 11.9 2 oe OR M1 for π × 4.32 × k where k is a whole number M1 for 2 × π × 4.3 × 11.9

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20 Find an expression for the nth term of this sequence. 1 , 1, 7, 49, 343, 2401, … 7 ................................................. [2]

Mark scheme: 20 7n – 2 oe final answer 2 M1 for recognition of terms being powers of 7

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21 Expand and simplify. ( x + 3)( x + 5)( 2x + 1) ................................................. [3]

Mark scheme: 21 2x3 + 17x2 + 38x + 15 3 B2 for correct expansion of the three brackets final answer unsimplified or for simplified four-term expression of correct form with three terms correct or B1 for correct expansion of two of the given brackets with at least three terms out of four correct

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22 A is the point (17, 9) and B is the point (23, 39). Find the equation of the perpendicular bisector of line AB. Give your answer in the form y = mx + c . y = ................................................ [5] Question 23 is printed on the next page.

Mark scheme: 22 1 5 [y =] – x + 28 final answer B1 for midpoint (20, 24) soi 5 39 − 9 M1 for [gradient = ] oe 23 − 17 − 1 M1 for their gradient M1 for substitution of their midpoint into their y = mx + c oe

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23 NOT TO SCALE x cm 3.5 cm Small box Large box The small box is mathematically similar to the large box. The volume of the large box is 72.8% greater than the volume of the small box. The small box has length 3.5 cm and the large box has length x cm. Calculate the value of x. x = ................................................ [3]

Mark scheme: 23 4.2 oe 3 72.8 M2 for 3 1 +  3.5 oe 100 3 172.8 or M1 for oe 3 100 3 100 or oe 3 172.8 x 3 172.8 or = oe 3.5 3 100

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