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Mathematics 0580/21 May/June 2022: question paper and mark scheme

Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), May/June 2022. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.

0580_s22_qp_210580_s22_ms_210580/21/M/J/22

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Paper
Paper 2 (Extended)
Total marks
70
Time
1 hour 30 minutes
Code on the paper
0580/21/M/J/22
0580_s22_ms_21.pdf

0580/21 mark scheme, question by question

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 11 mark

Question

Write down a prime number between 30 and 40. …… [1]

Mark scheme

1 31 or 37 1

Question 21 mark

Question

Calculate 4 5 - 5 4 . …… [1]

Mark scheme

2 399 1

Question 31 mark

Question

Jason starts a run at 10.05 am and finishes at 1.02 pm. Work out the time Jason takes to complete the run. …… h …… min [1] 1 - 0.7

Mark scheme

3 2h 57 min 1

Question 42 marks

Question

Calculate , giving your answer correct to 4 significant figures. 0.45 - 0.38 …… [2]

Mark scheme

4 4.286 cao 2 30 B1 for 4.285[7...] or 4.29 or or 4 72 7 or for correctly rounding their more accurate decimal to 4sf

Question 52 marks

Question

Kirsty changes $380.80 into pounds (£) when £1 = $1.19 . Calculate the amount Kirsty receives. £ …… [2]

Mark scheme

5 320 2 M1 for 380.8 ÷ 1.19 oe

Question 62 marks

Question

Write 180 as a product of its prime factors. …… [2] 3 2

Mark scheme

6 2 × 2 × 3 × 3 × 5 oe 2 B1 for 2, 2, 3, 3, 5 or M1 for correct factor tree/diagram/table.

Question 72 marks

Question

Without using a calculator, work out - . 7 21 You must show all your working and give your answer as a fraction in its simplest form. …… [2] 1

Mark scheme

7 9 21 2 and 21 oe M1 Allow any correct denominator 21k 1 A1 cao and correct working 3

Question 83 marks

Question

s = at 2 2 (a) Work out the value of s when a = 0.9 and t = 4. s = …… [1] (b) Rearrange the formula to find t in terms of s and a. t = …… [2]

Mark scheme

8(a) 7.2 oe 1 8(b) 2s 2 s 1 2 [±] final answer M1 for = t or 2s = at2 or better a a 2

Question 92 marks

Question

Factorise completely. 14xy - 7y 2 …… [2]

Mark scheme

9 7 y ( 2 x − y ) final answer ( ) 2 B1 for 7 2 xy − y 2 or y (14 x − 7 y ) or 7 y ( 2 x − y ) seen then spoilt

Question 103 marks

Question

22, 17, 12, 7, 2, … (a) Find the next term of the sequence. …… [1] (b) Find the nth term of the sequence. …… [2]

Mark scheme

10(a) –3 1 10(b) 27 – 5n oe final answer 2 B1 for j – 5n or 27 – kn, k ≠0 or for 27 – 5n seen then spoilt

Question 114 marks

Question

C R NOT TO 6 cm SCALE A B P Q 8 cm 6 cm Triangle ABC is mathematically similar to triangle PQR. (a) Calculate QR. QR = …… cm [2] (b) The two triangles are the cross-sections of two mathematically similar prisms. The volume of the larger prism is 320 cm 3 . Calculate the volume of the smaller prism. …… cm 3 [2]

Mark scheme

11(a) 4.5 oe 2 8 6 M1 for = oe or better 6 QR 11(b) 135 2 6 3 8 3 their 4.5 3 M1 for or or oe 8 6 6

Question 123 marks

Question

The interior angles of a pentagon are in the ratio 4 | 5 | 5 | 7 | 9. Find the size of the largest angle. …… [3]

Mark scheme

12 162 3 (5 − 2) × 180 M2 for × k where k = 1, 4, 5, 4+5+5+7+9 7, 9 or M1 for 180n ÷ (4 + 5 + 5 + 7 + 9) where n⩾2 or for (5 – 2) × 180 oe

Question 132 marks

Question

Work out 2 # 10 100 - 2 # 10 98 , giving your answer in standard form. …… [2]

Mark scheme

13 1.98 × 10100 2 B1 for 200 × 1098 or 0.02 × 10100 or answer with figs 198

Question 143 marks

Question

A train passes through a station at a speed of 108 km/h. The length of the station is 120 m. The train takes 7 seconds to completely pass through the station. Work out the length of the train. …… m [3] 1

Mark scheme

14 90 3 B2 for 210 or 0.09 km OR M1 for speed × time seen M1 for correct conversion of both km to m and between h and s

Question 151 mark

Question

4x = 64 Find the value of x. x = …… [1]

Mark scheme

15 –3 1

Question 163 marks

Question

y 9 8 T 7 6 5 4 3 P 2 1 0 1 2 3 4 5 6 7 8 9 10 11 x Describe fully the single transformation that maps triangle T onto triangle P. …… [3]

Mark scheme

16 Enlargement 3 B1 for each 1 [sf] − 2 [centre] (4, 4)

Question 173 marks

Question

Find the radius of a hemisphere of volume 80 cm 3 . 4 [The volume, V, of a sphere with radius r is V = rr 3 .] 3 …… cm [3]

Mark scheme

17 3.37 or 3.367 to 3.368 3 120 M2 for isolating r 3 , e.g. r 3 = π 1 4 or M1 for × × π r 3 = 80 oe 2 3 If 0 scored SC1 for answer 2.67 or 2.672 to 2.673...

Question 183 marks

Question

U D 38° 60° NOT TO T SCALE C B x° y° A A, B, C and D are points on a circle. TU is a tangent to the circle at D. DA is parallel to CB. Find the value of x and the value of y. x = …… y = …… [3]

Mark scheme

18 [x = ] 38 3 B1 for [x = ] 38 and [y = ] 22 B2 for [y = ] 22 or M1 for angle ACB = their x or angle BAD = 60 or angle CBA = 120

Question 194 marks

Question

A B NOT TO SCALE X P Q In the diagram, AB is parallel to PQ. AQ and PB intersect at X with AX = XQ. Complete the following statements. In triangles ABX and QPX, AX = XQ is given information. Angle BAX = Angle …… because …… Angle AXB = Angle …… because …… Triangle ABX is congruent to triangle QPX because of the congruency criterion …… PX = …… because the triangles are congruent. [4]

Mark scheme

19 PQX and alternate 4 B2 for lines 1 and 2 correct PXQ and [vertically] opposite oe or B1 for line 1 or 2 correct, or both angles correct ASA XB B1 for line 3 correct B1 for line 4 correct

Question 203 marks

Question

12 NOT TO Speed (m/s) SCALE 0 0 16 24 Time (s) The diagram shows the speed–time graph for 24 seconds of a car journey. Calculate (a) the deceleration of the car in the final 8 seconds, …… m/s2 [1] (b) the total distance travelled during the 24 seconds. …… m [2]

Mark scheme

20(a) 1 1 1.5 or 1 2 20(b) 240 2 M1 for one correct area

Question 212 marks

Question

Factorise completely. 1 – q – a + aq …… [2] 2

Mark scheme

21 (1 – q)(1 – a) or (a – 1)( q – 1) 2 B1 for 1 – q – a(1 – q) or 1 – a – q(1 – a) or final answer better or correct answer seen and spoilt

Question 222 marks

Question

Simplify fully (216y 216) 3 . …… [2]

Mark scheme

22 36 y144 final answer 2 B1 for ky144 or 36 y k final answer k ≠ 0 or correct answer seen and spoilt

Question 234 marks

Question

x 2 + 8x + 10 = (x + p) 2 + q (a) Find the value of p and the value of q. p = …… q = …… [2] (b) Solve. x 2 + 8x + 10 = 30 x = …… or x = …… [2]

Mark scheme

23(a) [p = ] 4 2 B1 for one correct [q = ] –6 or ( x + 4 ) − 6 or x2 + px + px + p2 [+ q] 2 23(b) –10 and 2 2 M1 for ( x + 4 )2 = 36 or ( x + their 4 ) = 30 − their ( −6 ) 2 or for correct method to solve quadratic e.g. ( x + 10 )( x − 2 )

Question 246 marks

Question

A cuboid measures 24 cm by 12 cm by 8 cm. Calculate the length of a diagonal of the cuboid. …… cm [3] 25 w is proportional to the square root of y. y is inversely proportional to x. When x = 4, y = 16 and w = 8. Find w in terms of x. w = …… [3]

Mark scheme

24 28 3 M2 for 242 + 122 + 82 or M1 for 242 + 122 or 242 + 82 or 122 + 82

Question 25

Question

In the question paper above.

Mark scheme

25 16 3 k oe final answer M2 for w = oe x x OR M1 for w = j y c M1 for y = x

Question 264 marks

Question

B NOT TO SCALE b K L O a A The diagram shows a triangle OAB and a parallelogram OALK. The position vector of A is a and the position vector of B is b. K is a point on AB so that AK | KB = 1 | 2. Find the position vector of L, in terms of a and b. Give your answer in its simplest form. …… [4]

Mark scheme

26 5 1 4 ρ 1 1 ρ 2 2 a + b final answer M1 for AK = − a + b or BK = a − b 3 3 3 3 3 3 ρ ρ ρ M1 for AL (or OK ) = a + their AK oe soi ρ ρ or OK (or AL ) = b + their AK⃗ oe soi ρ or BL = a + their AK⃗ oe soi ρ ρ M1 for a correct route e.g. OL , a + AL , b + ρ BL

Question 274 marks

Question

The line y = x + 1 intersects the graph of y = x 2 - 3x - 11 at the points A and B. Find the coordinates of A and the coordinates of B. You must show all your working. A ( …… , …… ) B ( …… , …… ) [4]

Mark scheme

27 (–2, –1) and (6, 7) 4 B3 for x = – 2 and 6 OR M1 for x 2 − 3 x − 11 = x + 1 or better M1 for correct method to solve their quadratic e.g. ( x + 2 )( x − 6 ) If 0 scored, SC1 for one correct pair of coordinates

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How this paper is marked

Examiners 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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Where can I find the 0580/21 May/June 2022 mark scheme?

On this page, free: the mark scheme for IGCSE Mathematics 0580/21, May/June 2022 (0580_s22_ms_21), and the question paper (0580_s22_qp_21), to read or download, with each question's marking points written out underneath.

How many marks is 0580/21 out of?

Mathematics 0580/21 for May/June 2022 is out of 70 marks, with 1 hour 30 minutes to answer it.

Can I get my 0580/21 answers marked?

Yes. Upload your answers to 0580/21/M/J/22 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.