Cambridge IGCSE Mathematics 0580 — 2023 Oct/Nov Paper 2 · Variant 1

1 The diagram shows an isosceles triangle. 41° NOT TO SCALE x° Find the value of x. x = ................................................. [2]

Mark scheme: Question Answer Marks Partial Marks 1 98 2 M1 for x + 41 + 41 = 180 oe or better

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2 The stem‑and‑leaf diagram shows the time, in minutes, it takes each of 15 people to complete a race. 1 6 6 7 2 1 3 3 4 5 6 7 7 7 3 0 1 1 Key: 1 6 represents 16 minutes Find (a) the mode .......................................... min [1] (b) the range .......................................... min [1] (c) the median. .......................................... min [1]

Mark scheme: 2(a) 27 1 2(b) 15 1 2(c) 25 1

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3 Complete these statements. (a) When x = ..................... , x + 3 = 8 . [1] (b) When 7y = 63, 10 y = ..................... [1]

Mark scheme: 3(a) 5 1 3(b) 90 1

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4 The table shows some information about Amir’s shopping. Fruit Cost per kilogram Number of kilograms Amir buys Cost Oranges $2.35 3.2 $................... Bananas 2.8 $................... $................... Total $13.54 Complete the table. [3]

Mark scheme: 4 3 B1 for 7.52 B1 for 6.02 or B1FT for 13.54 – their 7.52 correctly evaluated provided their 7.52 < 13.54 B1FT for their 6.02 ÷ 2.8 correctly evaluated

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5 Factorise completely. (a) 42mk - 35m ................................................. [2] (b) h 2 - 144 ................................................. [1]

Mark scheme: 5(a) 7m(6k – 5) final answer 2 B1 for 7(6mk – 5m) or m(42k – 35) as final answer or 7m(6k – 5) seen and then spoiled 5(b) (h + 12)(h – 12) final answer 1

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6 For each of 10 people working in an office, the scatter diagram shows their salary and the value of their car. 10 000 9000 8000 7000 6000 Value of 5000 car ($) 4000 3000 2000 1000 0 0 10 000 20 000 30 000 40 000 50 000 60 000 70 000 80 000 Salary ($) (a) One of these people has a salary of $28 000. Find the value of their car. $ ................................................. [1] (b) Another person starts to work in the office. Their salary is $54 000 and the value of their car is $6100. Plot this information on the scatter diagram. [1] (c) What type of correlation is shown in the scatter diagram? ................................................. [1]

Mark scheme: 6(a) 4800 1 6(b) Point plotted at (54 000, 6100) 1 6(c) Positive 1

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7 The exchange rate between Singapore dollars and euros is 1 Singapore dollar = 0.62 euros. Find the value of 161.20 euros in Singapore dollars. ...................................... Singapore dollars [1]

Mark scheme: 7 260 1

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8 Calculate. 3 3 7 # 3 11 10 ................................................. [1]

Mark scheme: 8 24 cao 1

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9 Find the highest common factor (HCF) of 140 and 126. ................................................. [2]

Mark scheme: 9 14 2 B1 for answer 2 or 7 or M1 for 2 × 7 as final answer or [140 =] 2 × 2 × 5 × 7 and [126 =] 2 × 3 × 3 × 7 or 2 correct factor trees or tables

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10 Simplify. (a) n 5 # n ................................................. [1] (b) 8x 6 ' 2x 2 ................................................. [2] 2 (c) ( 243y 20 ) 5

Mark scheme: 10(a) n6 final answer 1 10(b) 4x4 final answer 2 B1 for kx4 or 4xk as final answer or correct answer seen and then spoiled 10(c) 9y8 final answer 2 B1 for ky8 or 9yk final answer or correct answer seen and spoiled

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11 Solve. 4 ( 2x - 3) H 43 + 3 x ................................................. [3]

Mark scheme: 11 x ⩾ 11 final answer 3 M1 for 8x – 12 ⩾ 43 + 3x or better M1 for e.g. 8x – 3x ⩾ 43 + 12 oe OR 43 3 x M1 for 2x – 3 ⩾ + 4 4 3 x 43 M1 for 2x – ⩾ +3 4 4

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12 Write .042o as a fraction in its simplest form. You must show all your working. ................................................. [3]

Mark scheme: 12 42.22… – 4.22… oe M1 M1 for correct working shown 19 A2 38 cao A1 for oe seen 45 90 k 19 If M0 scored SC1 for or for answer 90 45 with insufficient working.

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13 At the end of 2021 there were 27 000 rhinos living in the wild. The number of rhinos is expected to decrease exponentially by 3% each year. Work out the number of rhinos expected to be living in the wild 4 years later, at the end of 2025. Give your answer correct to the nearest whole number. ................................................. [3]

Mark scheme: 13 23 903 cao 3 B2 for answer 23900, 23902, 23902.9… or 23 903 seen then rounded OR  3  4 M1 for 27 000 × 1 − oe    100  B1 for their more accurate value seen and correctly rounded to the nearest whole number

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14 (a) A B 15 5x x + 5 12 – x The Venn diagram shows information about the number of elements in sets A, B and . n() = 52. Find n(A + B ). ................................................. [3] (b) In this Venn diagram, shade the region C + D + E . C D E [1]

Mark scheme: 14(a) 9 3 B2 for x = 4 or B1 for answer 4 (without x = 4 in working) OR M1 for 5x + x + 5 + 12 – x + 15 = 52 oe or better B1FT for identifying the correct region A  B 14(b) 1

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15 y 8 7 6 5 4 3 2 1 x 0 - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 6 7 - 1 - 2 - 3 By shading the unwanted regions of the grid, draw and label the region R which satisfies these inequalities. y 2 1 x G 2 y H x + 2 [5]

Mark scheme: 15 5 B1 for y = 1 dashed line B1 for x = 2 solid line B1 B1 for y = x + 2 solid line R B2 for region identified satisfying all 3 inequalities B1 or B1 for region identified satisfying only 2 of these inequalities with y = 1, x = 2 and y = x + B1 2 all drawn

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16 P = 2 w + 2h w = 11 and h = 9.5 , both correct to 2 significant figures. Find the lower bound and the upper bound for P. Lower bound = ................................................. Upper bound = ................................................. [3]

Mark scheme: 16 [Lower bound =] 39.9 nfww 3 B2 for one correct [Upper bound =] 42.1 nfww or M1 for 11 + 0.5 or 9.5 + 0.05 or 11 – 0.5 or 9.5 – 0.05

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17 D C 53° NOT TO SCALE 20° E O A x° B A, B and C are points on the circumference of a circle, centre O. Tangent DE touches the circle at C. Angle BCE = 53° and angle ACO = 20°. Find the value of x. x = ................................................. [3]

Mark scheme: 17 33 3 B2 for 254 + 20 + x + 53 = 360 oe or better or 53 + 20 + x + 37 + 37 = 180 oe or better or OAB = 33 or AOB = 114 or 70 and 37 correctly identified or 53 and 20 correctly identified or B1 for any correct relevant angle identified

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18 105° 8.3 cm NOT TO SCALE y° 16.2 cm Calculate the value of y. y = ................................................. [3]

Mark scheme: 18 29.7 or 29.66[...] 3 8.3sin105 M2 for [sin y = ] 16.2 16.2 8.3 or M1 for = oe sin105 sin y

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19 (a) y 1 x 0 360° – 1 Sketch the graph of y = cos x for 0° G x G 360 ° . [2] (b) When cosx = 0 .21 , find the reflex angle x. ................................................. [2]

Mark scheme: 19(a) 2 B1 for correct cosine curve shape through (0,1) Correct sketch to go through (0, 1), close to (360, 1) and reasonably close to (180, –1) 19(b) 282.1 or 282.12… 2 B1 implied by 77.9 or 77.87 to 77.88 or 282.13 or M1 for 360 – their acute angle

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20 Write as a single fraction in its simplest form. 10x 2 - 60x (a) 2 x - x - 30 ................................................. [3] 7 5 (b) + x + 3 8x - 1 ................................................. [3]

Mark scheme: 20(a) 10 x 3 B1 for 10x(x – 6) final answer B1 for (x – 6)(x + 5) x + 5 20(b) 61x + 8 3 B1 for common denominator of (x + 3)(8x – 1) final answer ( x + 3 )( 8 x − 1) isw B1 for 7(8x – 1) + 5(x + 3) or better isw

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21 H G E F 9.2 cm NOT TO SCALE D C 4.5 cm A B 15.1 cm The diagram shows a cuboid ABCDEFGH. AB = 15.1 cm, BC = 4.5 cm and CG = 9.2 cm. Calculate the angle that the diagonal BH makes with the face ADHE. ................................................. [4] Question 22 is printed on the next page.

Mark scheme: 21 55.9 or 55.85… 4 15.1 M3 for tan[…] = oe 4.5 2 + 9.2 2 or M2 for [AH2 =] 4.52 + 9.22 or [BH2 =] 4.52 + 9.22 + 15.12 or M1 for recognising angle BHA if 0 scored SC1 for [angle BHD =] 59.7[1…] or 59.72

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22 B 41° 13.6 cm A C NOT TO SCALE D ABCD is a rhombus with side length 13.6 cm. Angle ABC = 41°. BAC is a sector of a circle with centre B. DAC is a sector of a circle with centre D. Calculate the shaded area. .......................................... cm2 [4]

Mark scheme: 22 110 or 110.3… 4 1 41 M3 for [2 ×] (2( × 13.62 × sin 41) – ( × 2 360 π × 13.62)) oe OR  1  M1 for  13.62 × sin 41 oe    2  41 M1 for [2×] × π × 13.62 oe 360

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