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Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), May/June 2021. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_s21_qp_210580_s21_ms_210580/21/M/J/21
Each question as it's printed, and the mark scheme's points for it, as text. Diagrams, tables and graphs are in the PDFs above.
Question
(a) Write down the order of rotational symmetry of this diagram. …… [1] (b) On the diagram, draw all the lines of symmetry. [2]
Mark scheme
1(a) 4 1 1(b) 2 B1 for 2 or 3 correct lines drawn or for 4 correct lines and one wrong extra line
Question
The probability that a train is late is 0.15 . Write down the probability that the train is not late. …… [1]
Mark scheme
2 0.85 oe 1
Question
The stem-and-leaf diagram shows the number of hours that each of 16 students studied last week. 1 2 5 6 8 2 0 1 1 7 9 3 2 3 4 5 4 4 5 7 Key: 1q2 represents 12 hours Find (a) the median, …… h [1] (b) the mode, …… h [1] (c) the range. …… h [1]
Mark scheme
3(a) 28 1 3(b) 21 1 3(c) 35 1
Question
NOT TO 59° 37° SCALE a° c° b° The diagram shows two parallel lines intersected by two straight lines. Find the values of a, b and c. a = …… b = …… c = …… [3]
Mark scheme
4 [a =] 59 3 B1 for each [b =] 37 [c =] 84 If 0 scored SC1 for their (a + b + c) = 180 if a, b, c > 0
Question
Work out. 6 8 (a) e o + e o -5 -1 f p [1] -4 (b) 3 e o 7 f p [1]
Mark scheme
5(a) 14 1 −6 5(b) −12 1 21
Question
(a) The nth term of a sequence is n 2 + 3n . Find the first three terms of this sequence. ……, ……, …… [2] (b) These are the first five terms of a different sequence. 25 18 11 4 -3 Find the nth term of this sequence. …… [2]
Mark scheme
6(a) 4 10 18 2 B1 for 2 correct 32 − 7n oe final answer 2 B1 for 32 – kn oe k ≠ 0 or j – 7n oe 6(b) or 32 − 7n seen then spoilt
Question
Solve the simultaneous equations. You must show all your working. 2x + y = 3 x - 5y = 40 x = …… y = …… [3] 3 5
Mark scheme
7 correctly eliminating 1 variable M1 x=5 A1 y=−7 A1 If M0 scored SC1 for two values satisfying one of the original equations
Question
Without using a calculator, work out 1 - . 8 6 You must show all your working and give your answer as a fraction in its simplest form. …… [3]
Mark scheme
8 11 5 3 1 B1 Correct step for dealing with mixed [– ] + number 8 6 8 6 11k Allow 8k 33 20 9 4 M1 Correct method to find common and and denominator 24 24 24 24 9 20 e.g. 1 and 24 24 13 A1 cao 24
Question
A is the point (5, - 5) and B is the point (9, 3). (a) Find the coordinates of the midpoint of AB. ( ……, …… ) [2] (b) Find the length of AB. …… [3]
Mark scheme
9(a) (7, − 1) 2 B1 for each 9(b) 8.94 or 8.944… 3 M2 for ( 9 − 5 )2 + ( 3 − −5)2 oe or M1 for ( 9 − 5 ) + ( 3 − −5 ) oe 2 2
Question
y 10 8 6 4 2 C –8 –6 –4 –2 0 2 4 6 8 10 x –2 –4 –6 A B –8 – 10 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, …… [3] (ii) triangle A onto triangle C. …… [3] 2 (b) Draw the image of triangle A after a translation by the vector e o. [2] 10
Mark scheme
10(a)(i) Rotation 3 B1 for each 90° anticlockwise oe (0, − 1) 10(a)(ii) enlargement 3 B1 for each 1 [s.f.] 3 (6, 6) 10(b) triangle at (− 4, 7) (− 4, 1) (− 1, 1) 2 k 2 B1 for translation by or 10 k
Question
(a) Simplify fully. (4ab 5) 4 …… [2] 1 (b) 2p 3 = 6 Find the value of p. p = …… [1] (c) 812 ' 3 t = 9 Find the value of t. t = …… [2]
Mark scheme
11(a) 256a 4b 20 final answer 2 B1 for two correct elements in final answer 11(b) 27 1 11(c) 6 2 M1 for 3k ÷ 3t = 32 or 38 ÷ 3t = 3 k oe or better or 3t = 729 oe
Question
The profit a company makes decreases exponentially at a rate of 0.9% per year. In 2014, the profit was $9500. Calculate the profit in 2019. $ …… [2]
Mark scheme
12 9080 or 9080.13 2 0.9 5 M1 for 9500 × 1 − 100
Question
On a map, a lake has an area of 32 cm 2 . The scale of the map is 1 : 24 000. Calculate the actual area of the lake. Give your answer in km 2 . …… km 2 [2] 14 y is directly proportional to the square root of (x - 3) . When x = 28 , y = 20 . Find y when x = 39 . y = …… [3]
Mark scheme
13 1.8432 2 32 × 24000 × 24000 M1 for oe 100000 × 100000 If 0 scored, SC1 for figs 184[32]... as answer
Question
In the question paper above.
Mark scheme
14 24 3 M1 for y = k x − 3 oe M1 for y = their k 39 − 3 oe
Question
Make h the subject of the formula 2mh = g (1 - h) . h = …… [4]
Mark scheme
15 g 4 M1 for expanding brackets or ÷g final answer M1 for isolating terms in h 2m + g M1 for factorising M1 for dividing by bracket to isolate h Incorrect/unsimplified final answer scores max 3 marks
Question
y 5 4 l 3 2 1 –3 –2 –1 0 1 2 3 4 5 6 x –1 –2 –3 (a) Find the gradient of line l. …… [2] (b) Find the equation of line l in the form y = mx + c . y = …… [2] (c) Find the equation of the line that is perpendicular to line l and passes through the point (12, - 7 ). Give your answer in the form y = mx + c . y = …… [3]
Mark scheme
16(a) 3 2 M1 for correct rise over run – or − 0.75 4 3 or B1 for answer oe 4 16(b) 3 2 FT [ y = ] their (a) x + 2 oe [ y =] − x + 2 oe 4 B1 for [ y =] their (a) x + c or [ y = ] mx + 2 . 16(c) 4 3 −1 [ y =] x − 23 oe M1 for gradient 3 their (a) M1 for (12, − 7) substituted into y = their mx + c
Question
A bag contains 3 blue buttons, 8 white buttons and 5 red buttons. Two buttons are picked at random from the bag, without replacement. Work out the probability that the two buttons are either both red or both white. …… [3]
Mark scheme
17 19 3 8 7 5 4 oe M2 for × + × 60 16 15 16 15 8 7 5 4 or M1 for × or × 16 15 16 15 89 If 0 scored SC1 for oe 256
Question
P NOT TO S SCALE a O b Q S is a point on PQ such that PS : SQ = 4 : 5. Find OS , in terms of a and b, in its simplest form. OS = …… [2]
Mark scheme
18 5 4 2 4 5 a+ b M1 for (b – a) or (a – b) or a correct 9 9 9 9 route
Question
(a) Sketch the graph of y = tan x for 0° G x G 360° . y 0 90° 180° 270° 360° x [2] (b) Solve the equation 5 tan x = 1 for 0° G x G 360° . x = …… or x = …… [2]
Mark scheme
19(a) Correct sketch 2 1 for one correct branch or correct sketch but with branches joined 19(b) 11.3 or 11.30 to 11.31 2 B1 for each and If 0 scored SC1 for two answers with a difference of 180° 191.3 or 191.30 to 191.31
Question
The distance between two towns is 600 km, correct to the nearest 10 km. A car takes 8 hours 40 minutes, correct to the nearest 10 minutes, to travel this distance. Calculate the lower bound for the average speed of the car in km/h. …… km/h [3]
Mark scheme
20 68 nfww 3 600 − 5 590 to 600 M2 for or oe 8h 40 to8h 50 8h 40 + 5 [ m ] or M1 for 600 – 5 oe or 8h 40 + 5[m] oe or 520 + 5 oe[m] seen
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On this page, free: the mark scheme for IGCSE Mathematics 0580/21, May/June 2021 (0580_s21_ms_21), and the question paper (0580_s21_qp_21), to read or download, with each question's marking points written out underneath.
Mathematics 0580/21 for May/June 2021 is out of 70 marks, with 1 hour 30 minutes to answer it.
Yes. Upload your answers to 0580/21/M/J/21 as a PDF or photos, and CIE Buddy marks every question against this paper's official mark scheme, using Cambridge's marking rules. You get your score, each lost mark explained on your own script, and the topics to revise. It's a guide, not an official Cambridge grade.