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Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), May/June 2024. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_s24_qp_210580_s24_ms_210580/21/M/J/24
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
y 8 7 6 A 5 4 3 C 2 1 B –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 x 3 4 5 –1 –2 The diagram shows two sides of a parallelogram ABCD. Find the coordinates of point D. ( …… , …… ) [2]
Mark scheme
1 (–3, 7) 2 B1 for correct diagram or correct coordinates for their point D or for ( −3, k ) or ( k , 7 )
Question
Geetha has a box of toys. She picks a toy at random from the box. The probability that she picks a wooden toy is 0.6 . (a) Work out the probability that she does not pick a wooden toy. …… [1] (b) The box contains three types of toys, wooden, plastic or metal. Type of toy Wooden Plastic Metal Number of toys 14 14 Probability 0.6 Complete the table. [2]
Mark scheme
2(a) 0.4 oe 1 2(b) 42 2 B1 for 42 0.2 0.2 B1 for 0.2 and 0.2 If B0 scored SC1 for their two probabilities being half their (a)
Question
The table shows some information about two sequences. nth term 5th term Sequence A 60 – 4n Sequence B n2 – 300 (a) Complete the table. [2] (b) Find the smallest positive number in sequence B. …… [2]
Mark scheme
3(a) 40 2 B1 for each –275 3(b) 24 2 B1 for 324 or 289 or 300 or 17.3…
Question
Find the greatest odd number that is a factor of 140 and a factor of 210. …… [2]
Mark scheme
4 35 2 B1 for answer 5, 7 or 70 or M1 for 2 × 2 × 5 × 7 and 2 × 3 × 5 × 7 or two correct factor trees or tables or 5 × 7 × k seen
Question
Calculate. 3 (a) 343 - 40.96 …… [1] (b) (192 + 4 # 16) 1.25 …… [1]
Mark scheme
5(a) 3 1 0.6 or 5 5(b) 1024 1
Question
D A 40° C E B NOT TO SCALE x° The diagram shows 5 kites that are congruent to kite ABCD. Each kite is joined to the next kite along one edge. Angle DAB = 40° and DCE is a straight line. Find the value of x. x = …… [3]
Mark scheme
6 145 3 M1 for 180 ÷ 6 or any angle congruent to BCD = 30 M1 for (360 – 40 – their 30) ÷ 2 oe
Question
12.8 cm J L NOT TO SCALE 12.8 cm K The diagram shows a shape made from a triangle JKL and a semicircle with diameter JL. JKL is an isosceles right-angled triangle with JK = JL = 12.8 cm. (a) Calculate the area of this shape. …… cm2 [3] (b) Calculate the perimeter of this shape. …… cm [4]
Mark scheme
7(a) 146 or 146.2 to 146.3 3 1 M1 for × 12.8 × 12.8 2 2 1 12.8 M1 for × π × 2 2 7(b) 51[.0] or 51.00 to 51.01… 4 1 M1 for × π ×12.8 2 12.8 M2 for 12.82 + 12.82 or oe sin 45 or M1 for 12.82 + 12.82 oe 12.8 or sin 45 = oe KL
Question
These are the first five terms of a sequence. 11 18 25 32 39 Find an expression for the nth term of the sequence. …… [2]
Mark scheme
8 7n + 4 oe final answer 2 B1 for 7n + j or kn + 4 k ≠ 0 , or 7n + 4 seen then spoilt
Question
The value of a car is $8000. Each year the value of the car decreases exponentially by 25%. Calculate the value of this car after 3 years. $ …… [2]
Mark scheme
9 3375 2 25 3 M1 for 8000 × 1 − oe 100
Question
Amir invests $1500 in an account. The account pays compound interest at a rate of r % per year. At the end of 8 years the value of his investment is $1656.73 . Find the value of r. r = …… [3]
Mark scheme
10 1.25 or 1.250… 3 1656.73 M2 for 8 oe 1500 or M1 for 1656.73 = 1500 ( k ) oe for any k 8
Question
y 7 6 5 4 3 R 2 1 –1 0 x 1 2 3 4 5 6 7 –1 Find the inequalities that define the unshaded region, R. …… [4]
Mark scheme
11 y<x 4 B1 for y < x x<6 B1 for x < 6 1 ⩽ y ⩽ 5 oe B2 for 1 ⩽ y ⩽ 5 or B1 for y ⩾ 1 or y ⩽ 5 If B0 scored, SC2 for y ⩽ x, x ⩽ 6 and 1 < y < 5 oe or SC1 for three correct from y = x, x = 6, y = 1 and y = 5
Question
Solve the simultaneous equations. You must show all your working. 3x + 5y = 5 2 4x - 3y = 46 x = …… y = …… [4]
Mark scheme
12 Correctly equating one set of M1 coefficients Correct method to eliminate one M1 variable x = 10, y = –2 A2 A1 for x = 10 A1 for y = –2 If M0 scored SC1 for 2 values satisfying one of the original equations.
Question
p° NOT TO SCALE 4m° 5m° (4m + 38)° The diagram shows a cyclic quadrilateral. Find the value of p. p = …… [3]
Mark scheme
13 62 3 B2 for m = 20 or M1 for 5m + 4m = 180 soi or p + 4m + 38 = 180 soi
Question
48° NOT TO SCALE 9 cm The diagram shows a circle with radius 9 cm. Calculate the area of the shaded major sector. …… cm2 [3] o o as a fraction in its simplest form.
Mark scheme
14 221 or 220.5 to 220.6 3 360 − 48 M2 for × π × 92 360 k or M1 for × π × 92 where k < 360 360 or B1 for 312
Question
Write 0.146 You must show all your working. …… [3]
Mark scheme
15 − 1.46 146.46 oe M1 29 A2 145 cao Al for oe 198 990 k If M0 scored SC1 for with insufficient 990 working.
Question
(a) In the Venn diagram, shade the region M l + N l . M N [1] (b) Find n (B + (Al , C )) . A B 33 16 3 10 18 4 20 9 C …… [1]
Mark scheme
16(a) 1 M N 16(b) 17 1
Question
B 6.7 cm 81° A NOT TO 5.9 cm SCALE C Calculate the area of triangle ABC. …… cm2 [2]
Mark scheme
17 19.5 or 19.52… 2 1 M1 for × 6.7 × 5.9 × sin 81 oe 2
Question
y 8 7 6 5 4 3 2 1 – 3 – 2.5 – 2 – 1.5 – 1 – 0.5 0 0.5 1 1.5 x –1 –2 –3 The diagram shows the graph of y = x 3 + 4x 2 - 2 for - 3 G x G 1.5 . By drawing a suitable straight line, solve the equation x 3 + 4x 2 - 2 = 2x for - 3 G x G 1.5 . x = …… or x = …… [3]
Mark scheme
18 y = 2x ruled B1 x = –0.5 to –0.55 B2 B1 for –0.5 to –0.55 x = 0.85 to 0.9 B1 for 0.85 to 0.9
Question
Factorise completely. (a) 12m 2 - 75t 2 …… [3] (b) xy + 15 + 3y + 5x …… [2]
Mark scheme
19(a) 3(2m + 5t)(2m – 5t) final answer 3 B2 for (6m + 15t)(2m – 5t) or (2m + 5t)(6m – 15t) or B1 for 3(4m2 – 25t2) or (2m + 5t)(2m – 5t) 19(b) (x + 3)(y + 5) final answer 2 B1 for x(y + 5) + 3(y + 5) or y(x + 3) + 5(x + 3)
Question
Solve the equation 8 sin x + 6 = 1 for 0c G x G 360c. x = …… or x = …… [3]
Mark scheme
20 218.7, 321.3 3 B2 for one correct 5 or M1 for sin x = – oe 8 If M1 or 0 scored, SC1 for two reflex angles with a sum of 540 or two non-reflex angles with a sum of 180
Question
E 9.1 cm F 6.5 cm A B NOT TO SCALE H G 4 cm D C The diagram shows a cuboid. HD = 4 cm, EH = 6.5 cm and EF = 9.1 cm. Calculate the angle between CE and the base CDHG. …… [4]
Mark scheme
21 33.2 or 33.18… 4 6.5 M3 for tan = oe 42 + 9.12 or M2 for 42 + 9.12 oe or 42 + 9.12 + 6.52 oe or M1 for recognising the angle ECH
Question
Bag A and bag B each contain red counters and blue counters only. Stephan picks a counter at random from bag A and Jen picks a counter at random from bag B. The probability that Stephan picks a red counter is 0.4 . The probability that Stephan and Jen both pick a red counter is 0.25 . Find the probability that Stephan and Jen both pick a blue counter. …… [4]
Mark scheme
22 0.225 oe 4 0.25 M3 for 1 – × (1 – 0.4 ) oe 0.4 OR 0.25 M2 for 0.4 or M1 for 0.4 × p = 0.25 oe M1 for (1 –theirP(Jen red))×(1 – 0.4) oe
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Mark my 0580/21Examiners follow the generic marking principles at the front of the scheme, then each question's points: method (M), accuracy (A) and independent (B) marks, error carried forward where the scheme allows it, and positive marking, so you're credited for what you got right.
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On this page, free: the mark scheme for IGCSE Mathematics 0580/21, May/June 2024 (0580_s24_ms_21), and the question paper (0580_s24_qp_21), to read or download, with each question's marking points written out underneath.
Mathematics 0580/21 for May/June 2024 is out of 70 marks, with 1 hour 30 minutes to answer it.
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