Cambridge IGCSE Mathematics 0580 — 2023 Oct/Nov Paper 2 · Variant 3

1 Tara goes on a journey by train. The train leaves at 06 48. The journey takes 12 hours and 35 minutes. Find the time when Tara arrives. ................................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1 19 23 or 7 23 pm 1

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2 61 63 64 66 68 69 From this list, write down (a) a cube number ................................................. [1] (b) a prime number. ................................................. [1]

Mark scheme: 2(a) 64 1 2(b) 61 1

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3 The stem-and-leaf diagram shows the heights, in centimetres, of some plants. 10 4 8 11 1 3 4 6 12 2 3 6 9 13 2 6 9 Key: 10 4 represents 10.4 cm (a) Find the median height. ............................................ cm [1] (b) Work out the mean height. ............................................ cm [2]

Mark scheme: 3(a) 12.2 1 3(b) 12.1 2 B1 for 157.3 oe or M1 for their total ÷ 13

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4 Shubhu invests $750 in a savings account for 5 years. The account pays simple interest at a rate of 1.8% per year. Calculate the total interest she earns during the 5 years. $ ................................................ [2]

Mark scheme: 4 67.5[0] 2 750  1.8 5  M1 for oe 100

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5 B NOT TO 112° SCALE 44° C M A The diagram shows triangle ABC. M is the midpoint of AC. Triangle ABC is rotated 180° about centre M. The image and the original triangle together form a quadrilateral ABCD. (a) Write down the mathematical name of the quadrilateral ABCD. ................................................. [1] (b) Find angle BAD. Angle BAD = ................................................ [2]

Mark scheme: 5(a) Parallelogram 1 5(b) 68 2 M1 for 180 – 112 oe or for 180 − 112 − 44

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6 Rama asks a group of students how they travel to school. The table shows the probability of how a student, chosen at random, travels to school. Bus Walk Car Other Probability 0.4 0.32 0.17 (a) Complete the table. [2] (b) There are 1800 students at the school. Find the expected number of students that walk to school. ................................................. [1]

Mark scheme: 6(a) 0.11 oe 2 M1 for 1 – (0.4 + 0.32 + 0.17) oe 6(b) 576 1

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5 117 Without using a calculator, work out 1 ' . 6 15 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]

Mark scheme: 7 11 15 M2 11  or B1 for oe 6 11 6 55k 22 k their 11 15  oe with common or M1 for their  30 k 30 k 6 11 denominator 1 A1 2 cao 2

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8 Find the highest common factor (HCF) of 48 and 80. ................................................. [2]

Mark scheme: 8 16 2 B1 for answer 2 or 4 or 8 or M1 for 2  2  2  2 oe as final answer or [48 =] 2  2  2  2  3 and [80 =] 2  2  2  2  5 or for 2 correct factor trees or tables

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2wy 2 9 P = 3 Find the positive value of y when P = 108 and w = 8 . y = ................................................ [3]

Mark scheme: 9 1 9 3 3 P 3 108 4.5, 4 or M2 for y2 = or y2 = or better 2 2 2 w 2  8 2 y8 2 or M1 for 108 = or better 3

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7 10 AB = e- 3o (a) Find 3AB . [1] f p (b) Find AB . AB = ................................................ [2]

Mark scheme: 10(a)  21  1    −9  10(b) 7.62 or 7.615 to 7.616 2 M1 for (7)2 + ( – 3)2 oe If 0 scored SC1 for 22.8 or 22.84 to 22.85

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11 A bronze sphere has radius 3.6 cm. The density of bronze is 8.05 g/cm3. Find the mass of the sphere. Give your answer in kilograms, correct to the nearest gram. 4 3 [The volume, V, of a sphere with radius r is V = rr .] 3 [Density = mass ' volume .] ............................................. kg [4]

Mark scheme: 11 1.573 cao 4 B3 for answer figs 157[0] or 1573… OR 4 3 M2 for π 3.6  8.05 oe or better 3 4 3 or M1 for   3.6 oe 3 M1 for division by 1000 of their mass in g and correct rounding to 3 dp

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12 Oliver sent 22% more messages in June than in May. He sent 305 messages in June. Find how many more messages he sent in June than in May. ................................................. [3]

Mark scheme: 12 55 3 B2 for 250 or M2 for (305 ÷ 122)  22 oe or better  22  or M1 for  1 +  m = 305 oe or better  100 

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13 The graph of y = 2x + 1 is drawn on the grid. y 5 4 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 x -1 -2 -3 -4 By shading the unwanted regions of the grid, find and label the region R which satisfies these inequalities. y H 2x + 1 y H 1 4x + 3y 1 12 [4]

Mark scheme: 13 Correct region indicated 4 B1 for 4x + 3y = 12 dashed line B1 for y = 1 solid line B2 for region identified satisfying all 3 inequalities 1 or B1 for region satisfying only 2 of these inequalities with 4x + 3y = 12 and y = 1 R 1 both drawn 1

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14 The box-and-whisker plot shows information about the mass, in kg, of some parcels. 1 1.5 2 2.5 3 3.5 Mass (kg) (a) Find the mass of the heaviest parcel. ............................................ kg [1] (b) Find the interquartile range. ............................................ kg [1]

Mark scheme: 14(a) 3.3 1 14(b) 0.55 1

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15 T = 3d - e Rearrange the formula to make d the subject. d = ................................................ [3]

Mark scheme: 15 T 2 + e 3 M1 for T 2 = 3d – e [d =] oe final answer M1 for isolating term in d 3 M1 for dividing by 3 Max 2 marks if answer incorrect

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16 A cylinder with height 12.5 cm has a curved surface area of 105r cm2 . Calculate the volume of the cylinder. ......................................... cm3 [4]

Mark scheme: 16 693 or 692.7 to 692.8… 4 105 M2 for oe 2 12.5 or M1 for 2    r  12.5 = 105 or better M1 for   (their r)2  12.5

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17 (a) Simplify. 2 64y 27 3 ` j ................................................. [2] (b) Simplify. x - 5 x 2 - 25 ................................................. [2]

Mark scheme: 17(a) 16y18 final answer 2 B1 for 16yk or ky18 as final answer or correct answer spoiled 17(b) 1 2 B1 for (x + 5)(x – 5) final answer x + 5

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18 F is proportional to the product of m and a. Calculate the percentage change in F when m is increased by 40% and a is decreased by 15%. ............................................. % [3]

Mark scheme: 18 19 3  40  15  M2 for  1 +  1 −  [ma] oe  100  100  or M1 for F = kma or better or  40   15   1 +  and  1 −  oe seen  100   100 

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19 R NOT TO 13.5 cm SCALE Q 42° 18 cm P Calculate the obtuse angle PRQ. Angle PRQ = ................................................. [4]

Mark scheme: 19 116.9 or 116.85… 4 −1 18sin 42  M3 for 180 – sin    13.5  or B3 for 63.1 or 63.14 to 63.15 18sin 42 or M2 for [sin PRQ = ] 13.5 18 13.5 or M1 for = oe sin PRQ sin 42

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20 ( x + a)( x + 2)( 2x + 3) is equivalent to 2x 3 + bx 2 + cx - 18 . Find the value of each of a, b and c. a = ................................................ b = ................................................ c = ................................................ [3]

Mark scheme: 20 [a =] – 3 3 B1 for a = – 3 [b =] 1 B1FT for b = 7 + 2  their a [c =] – 15 B1FT for c = 6 + 7  their a If B0 scored B1 for correct expansion of a pair of brackets or of three brackets x 2 + ax + 2 x + 2a 2 x + 3 or ( ) or 2 x 2 + 4 x + 3 x + 6  x + a ( ) 2 x3 + ( 2a + 7 ) x 2 + ( 7a + 6 ) x + 6a oe or for b = 7 + 2a or for c = 6 + 7a

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21 H M G NOT TO E F SCALE 8 cm D C 5 cm A B 14 cm The diagram shows a cuboid ABCDEFGH. AB = 14 cm, BC = 5 cm and CG = 8 cm. M is the midpoint of HG. (a) Calculate BM. ............................................ cm [3] (b) Calculate the angle that BM makes with the base ABCD. ................................................. [3] Question 22 is printed on the next page.

Mark scheme: 21(a) 11.7 or 11.74 to 11.75 3 2  14  M2 for   + 52 + 82 oe  2   14  2  14  2 or M1 for   + 52, 52 + 82 or   + 82  2   2  21(b) 42.9 to 43.14 3 8 M2 for sin [….] = oe their (a) or M1 for recognising angle MBX where X is the midpoint of DC

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22 Find the coordinates of the point where the line 4x + y = 9 intersects the curve y + x 2 = 5 . You must show all your working. ( ...................... , .......................) [5]

Mark scheme: 22 x2 – 4x + 4 [= 0] M2 M1 for 9 – 4x = 5 – x2 oe (x – 2)(x – 2) M1 Accept alt methods e.g. use of formula, complete the square for their 3 – term quadratic equation (2, 1) B2 B1 for x = 2

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