Cambridge IGCSE Mathematics 0580 — 2021 Feb/March Paper 2 · Variant 2

1 (a) Complete this statement. The diagram has rotational symmetry of order ................... [1] (b) On the diagram, draw all the lines of symmetry. [2]

Mark scheme: Question Answer Marks Partial Marks 1(a) 2 1 1(b) 2 correct lines 2 B1 for each

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2 Sahil and Anika share $78 in the ratio 5 : 8. Calculate the amount each receives. Sahil $ ................................................. Anika $ ................................................. [2]

Mark scheme: 2 30 2 78 M1 for × k oe where k = 1, 5 or 8 48 5 + 8

More questions on Ratio and proportion

3 The number of passengers on a bus is recorded each day for 14 days. 15 18 22 17 35 38 24 19 19 24 25 31 36 29 (a) Complete the stem-and-leaf diagram. 1 2 3 Key: 1| 5 represents 15 passengers [2] (b) Find the median. ................................................. [1]

Mark scheme: 3(a) 2 B1 for two rows correct or for a fully correct 1 5 7 8 9 9 unordered stem-and-leaf diagram or for a correct diagram with one leaf incorrect or 2 2 4 4 5 9 omitted 3 1 5 6 8 3(b) 24 1

More questions on Classifying statistical data

4 By writing each number correct to 1 significant figure, find an estimate for the value of 2.8 # 82 .6 . 27.8 - 13.9 ................................................. [2]

Mark scheme: 4 3, 80, 30 and 10 seen 2 M1 for 3 out of 4 correct elements and answer 12 or for all correct but with any trailing zeros If 0 scored SC1 for answer 12

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5 The number of bowls of hot soup sold decreases when the temperature rises. What type of correlation does this statement describe? ................................................. [1]

Mark scheme: 5 Negative 1

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56 Joseph spends of one week’s earnings to buy a jacket. 24 The cost of the jacket is $56.50 . Calculate the amount Joseph earns in a week. $ ................................................ [2]

Mark scheme: 6 271.2[0] 2 M1 for 56.50 ÷ 5 or 56.50 × 24 oe or better

More questions on Ratio and proportion

1 27 Without using a calculator, work out 2 # 3 . 4 3 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]

Mark scheme: 7 9 11 M1 and oe improper fractions 4 3 99 A1 oe improper fraction 12 1 A1 dep on 1st A1 8 cao final answer 4 9 11 If M0 scored SC1 for or oe 4 3 improper fraction

More questions on Fractions, decimals and percentages

8 Write .037o o as a fraction. ................................................. [1]

Mark scheme: 8 37 1 oe fraction 99

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9 Calculate 4.8 # 10 6 + 3.7 # 10 7 . Give your answer in standard form. ................................................. [1]

Mark scheme: 9 4.18 × 107 cao 1

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10 North L M NOT TO SCALE N On a map, the positions of the towns L, M and N form an equilateral triangle. The bearing of M from L is 103°. Work out the bearing of L from N. ................................................. [2]

Mark scheme: 10 343 2 B1 for 103 in correct position and 60 or 103 17 in correct position 60 17

More questions on Ratio and proportion

11 Find the highest common factor (HCF) of 36 and 84. ................................................. [2]

Mark scheme: 11 12 2 M1 for 22 × 32 and 22×3×7 or for 2 × 2 × 3 final answer or B1 for 2, 3, 4 or 6 as final answer

More questions on Types of number

12 C NOT TO 6 cm SCALE O B 5 cm A The diagram shows a shape made from a quarter-circle, OAB, and a right-angled triangle OBC. The radius of the circle is 5 cm and OC = 6 cm. Calculate the area of the shape. .......................................... cm2 [3]

Mark scheme: 12 34.6 or 34.63 to 34.64 3 1 2 1 M2 for × π × 5 + × 5 × 6 oe 4 2 1 2 1 or M1 for × π × 5 oe or × 5 × 6 oe 4 2

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13 The population of one variety of butterfly is decreasing exponentially at a rate of 34% per year. At the end of 2014, the population was 125.9 million. Calculate the population at the end of 2019. ..................................... million [2]

Mark scheme: 13 15.8 or 15.76 to 15.77 2 5  34  M1 for 125.9 ×  1 −  oe  100 

More questions on Exponential growth and decay

14 (a) These are the first four terms of a sequence. 29 22 15 8 Write down the next two terms. ....................... , ....................... [2] (b) These are the first five terms of another sequence. 4 7 12 19 28 Find the nth term. ................................................. [2]

Mark scheme: 14(a) 1 − 6 2 B1 for each If 0 scored, SC1 for two terms with a difference of –7 14(b) n 2 + 3 oe 2 M1 for any quadratic or second differences = 2

More questions on Sequences

15 H G K NOT TO SCALE F x° 25° 47° E T Points E, F, G and H lie on the circle and EG = EH . HF and EG intersect at K. ET is a tangent to the circle at E. Angle FET = 47° and angle FEG = 25°. Find the value of x. x = ................................................. [2]

Mark scheme: 15 36 2 M1 for angle EHG = 72 or for angle EHF = 47 and GHF = 25

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

Mark scheme: 16 3 correct ruled lines 5 B1 for each line and R clearly indicated y = 1 dashed y = 2 x + 2 dashed x + y = 3 solid B2 for correct region R or B1 for region satisfying 2 inequalities 0 1 1 2 0 1 0 or SC1 for shading of the wanted region only

More questions on Graphs of functions

17 Some students were asked how many books they each had in their school bags. The table shows some of this information. Number of books 5 6 7 8 9 10 Frequency 4 5 x 11 7 5 The mean number of books is 7.6 . Calculate the value of x. x = ................................................. [3]

Mark scheme: 17 13 nfww 3 M2 for 251 + 7 x = 7.6 ( 32 + x ) or better or M1 for 5 × 4 + 6 × 5 + 7 x + 8 × 11 + 9 × 7 + 10 × 5 = 7.6 32 + x oe

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2 18 Simplify 343x 9 3 . ` j ................................................. [2]

Mark scheme: 18 49 x 6 final answer 2 B1 for 49 kx or nx 6 as final answer

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19 Solve the simultaneous equations. You must show all your working. x - y = 7 x 2 + y = 149 x = ................... y = ................... x = ................... y = ................... [5]

Mark scheme: 19 x2 + x – 156 [=0] M2 2 M1 for x + x = 7 + 149 or y2 + 15y – 100 [=0] or correct substitution ( x − 12 )( x + 13 ) [=0] M1 or for correct factors for their quadratic or ( y − 5 )( y + 20 ) [=0] equation or for correct use of quadratic formula or completing the square for their equation [x =] 12 [y =] 5 B2 B1 for x = 12, x = −13 or for y = 5, y = –20 [x =] −13 [y =] −20 or for a correct pair of x and y values If B0 scored and at least 2 method marks scored SC1 for correct substitution of both of their x values or their y values into x – y = 7 or x2 + y = 149

More questions on Equations

20 (a) P NOT TO A SCALE x cm 1.61 cm R 3.2 cm Q C 2.8 cm B Triangle ABC is mathematically similar to triangle PQR. Find the value of x. x = ................................................. [2] (b) NOT TO SCALE The diagram shows two mathematically similar bowls. The larger bowl has capacity 7.8 litres and height 11.5 cm. The smaller bowl has capacity 4 litres. Calculate the height of the smaller bowl. ............................................ cm [3]

Mark scheme: 20(a) 1.84 2 1.61 2.8 M1 for = oe x 3.2 20(b) 9.20 or 9.204 to 9.205 3 4 M2 for 11.5 × 3 oe 7.8 4 7.8 or M1 for 3 or 3 oe seen 7.8 4 11.53 7.8 or for = oe x 3 4

More questions on Similarity

21 On the axes, sketch the graph of each of these functions. 1 (a) y = x y x O [2] (b) y = 4x y x O [2]

Mark scheme: 21(a) Correct sketch 2 B1 for one correct branch or attempt at correct shape 21(b) Correct sketch 2 B1 for correct shape but crossing x-axis or correct shape but just in one quadrant

More questions on Graphs of functions

22 (a) A bag of rice has a mass of 25 kg, correct to the nearest kilogram. Calculate the lower bound of the total mass of 10 of these bags. ............................................. kg [1] (b) Virat has 200 metres of wire, correct to the nearest metre. He cuts the wire into n pieces of length 3 metres, correct to the nearest 20 centimetres. Calculate the largest possible value of n. n = ................................................. [3]

Mark scheme: 22(a) 245 1 22(b) 69 cao nfww 3 200 + 0.5 M2 for oe 3 − 0.1 or M1 for 200 ± 0.5 oe or 3 ± 0.1 oe seen

More questions on Limits of accuracy

23 V NOT TO SCALE 14 cm D C 10 cm M A 12 cm B The diagram shows a pyramid VABCD with a rectangular base. V is vertically above M, the intersection of the diagonals AC and BD. AB = 12 cm, BC = 10 cm and VC = 14 cm. Calculate the angle that VC makes with the base ABCD. ................................................... [4] Question 24 is printed on the next page.

Mark scheme: 23 56.1 or 56.09… 4 1 2 2 10 + 1 2 2 M3 for cos[…] = oe 14 1 2 2 or M2 for [MC =] 10 + 12 oe 2 or M1 for [AC 2 =] 10 2 + 122 oe or B1 for indicating required angle

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24 A curve has equation y = x 3 - 2x 2 + 5 . Find the coordinates of its two stationary points. (.............. , ..............) and (.............. , ..............) [5]

Mark scheme: 24 (0, 5) 5 2 B2 for 3x − 4 x or B1 for 3x 2 or − 4x  4 103   ,  oe dy  3 27  M1 for their derivative = 0 oe or = 0 dx 4 B1 for [x =] 0 and 3 or for 1 correct coordinate pair

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