Question 11 mark
Question
At noon, the temperature is 4 °C. At midnight, the temperature is - 9 °C. Work out the difference in temperature between noon and midnight. …… °C [1]
Mark scheme
1 13 or – 13 1
Mathematics 0580/22 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_220580_s22_ms_220580/22/M/J/22
- Paper
- Paper 2 (Extended)
- Total marks
- 70
- Time
- 1 hour 30 minutes
- Code on the paper
- 0580/22/M/J/22
0580/22 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 22 marks
Question
Thibault records the number of cars of each colour in a car park. Colour Black White Silver Red Number of cars 8 5 4 3 He draws a pie chart to show this information. Calculate the sector angle for the red cars. …… [2]
Mark scheme
2 54 2 360 3 M1 for [×3] or [×360] oe 8+5+ 4+3 8+5+ 4+3
Question 33 marks
Question
Figs cost 43 cents each. Lyra has $5 to buy some figs. Calculate the largest number of figs Lyra can buy and the amount of change, in cents, she receives. …… figs and …… cents change [3]
Mark scheme
3 11 27 3 M1 for 500 ÷ 43 oe M1 for 500 − their 11 × 43 oe their 11 must be an integer from 2 to 11
Question 41 mark
Question
Find the value of 68 # 153 . …… [1]
Mark scheme
4 102 1
Question 53 marks
Question
Find the total surface area of a cuboid with length 8 cm, width 6 cm and height 3 cm. …… cm 2 [3]
Mark scheme
5 180 3 M2 for [ 2 ×] ( 8 × 6 + 8 × 3 + 3 × 6 ) oe or M1 for 8 × 6 or 8 × 3 or 3 × 6
Question 62 marks
Question
Some cards have either a square, a circle or a triangle drawn on them. Piet chooses one of the cards at random. Complete the table to show the probability of choosing a card with each shape. Shape Square Circle Triangle Probability 0.2 0.32 [2]
Mark scheme
6 0.48 oe 2 M1 for 1 − ( 0.2 + 0.32 ) oe
Question 72 marks
Question
The price of a coat is $126. In a sale, this price is reduced by 18%. Find the sale price of the coat. $ …… [2]
Mark scheme
7 103.32 cao 2 18 M1 for 126 × 1 − oe 100 or B1 for 22.68
Question 82 marks
Question
The nth term of a sequence is n 2 + 12 . Find the first three terms of this sequence. …… , …… , …… [2]
Mark scheme
8 13 16 21 2 B1 for 2 correct terms in correct position or SC1 for 12, 13, 16
Question 92 marks
Question
North B NOT TO SCALE A The bearing of B from A is 059°. Work out the bearing of A from B. …… [2] 2 -1
Mark scheme
9 239 2 M1 for 180 + 59 or 360 – (180 − 59) oe or indicates correct angle on diagram
Question 104 marks
Question
p=e o q =e o 8 4 (a) Find (i) p - q, f p [1] (ii) 6p. f p [1] (b) Find p - q . …… [2] p
Mark scheme
10(a)(i) 3 1 4 10(a)(ii) 12 1 48 10(b) 5 2 M1 for (their 3) 2 + (their 4) 2 or better
Question 111 mark
Question
Find the value of p when 6 # 6 4 = 6 28 . p = …… [1]
Mark scheme
11 24 1
Question 126 marks
Question
Annette cycles a distance of 70 km from Midville to Newtown. Leaving Midville, she cycles for 1 hour 30 minutes at a constant speed of 20 km/h and then stops for 30 minutes. She then continues the journey to Newtown at a constant speed of 16 km/h. 80 60 Distance (km) 40 20 0 0 1 2 3 4 5 Time (h) (a) On the grid, draw the distance–time graph for the journey. [3] (b) Calculate the average speed for the whole journey. …… km/h [3] 1 5
Mark scheme
12(a) correct graph 3 B1 for line from (0, 0) to (1.5, 30) B1 for horizontal line from (their 1.5, their 30) for 0.5 hours B1 for a line from (their 2, their 30) ending at distance 70 with a gradient of 16 Provided it fits on the grid and their 30 is <70 12(b) 15.6 or 15.55 to 15.56 3 M2 for 70 ÷ (their final time in hours) nfww 70 – their 30 (final time =) 1.5 + 0.5 + 16 or 4.5 or their final time from graph or M1 for 70 ÷ any time
Question 133 marks
Question
Without using a calculator, work out 4 - 2 . 8 6 You must show all your working and give your answer as a mixed number in its simplest form. …… [3]
Mark scheme
13 33 17 1 5 B1 Correct step for dealing with mixed numbers or 2 − 8 6 8 6 33k 17 k Allow or 8k 6k 99 68 3 20 M1 Correct method to find common denominator and [ 2] − 3 20 24 24 24 24 e.g. 4 and 2 24 24 7 A1 1 cao and correct working 24
Question 143 marks
Question
Carlos invests $4540 at a rate of r % per year compound interest. At the end of 10 years he has earned $1328.54 in interest. Calculate the value of r. r = …… [3]
Mark scheme
14 2.6[0] or 2.600… 3 1328.54 + 4540 M2 for 10 4540 or M1 for 4540 ×k 10 = 1328.54 + 4540 for any k If 0 scored SC1 for answer –11.6 or –11.56…
Question 152 marks
Question
Find the highest common factor (HCF) of 12a 3 b and 20a 2 b 2 . …… [2]
Mark scheme
15 4a 2b final answer 2 M1 for two correct parts out of three from 4, a2 and b in final answer
Question 164 marks
Question
The Venn diagram shows the number of students in a class of 40 who study physics (P), mathematics (M) and geography (G). P M 2 4 11 9 5 3 6 G (a) Use set notation to describe the shaded region. …… [1] (b) Find n ((P + G) , M l ) . …… [1] (c) A student is chosen at random from those studying geography. Find the probability that this student also studies physics or mathematics but not both. …… [2]
Mark scheme
16(a) ( M G ) P′ 1 16(b) 22 1 16(c) 8 2 oe M1 for 23 k k 8 3+ 5 or or or c≠1 23 3+9+5+6 c c or for 8 and 23 identified
Question 175 marks
Question
(a) Sketch the graph of y = sin x for 0° G x G 360° . y 1 O x 360 –1 [2] (b) Solve the equation 3 sin x + 1 = 0 for 0° G x G 360° . x = …… or x = …… [3]
Mark scheme
17(a) 2 Correct sketch to go through B1 for correct sine curve shape through the origin (0, 0), (180, 0) and (360, 0) 17(b) 199.5 or 199.47… 3 B2 for one correct and 340.5 or 340.52 to 340.53… 1 or M1 for sin x = − oe 3 If 0 scored SC1 for two reflex angles with sum of 540 or two non-reflex angles with sum of 180
Question 184 marks
Question
(a) y is directly proportional to the cube root of (x + 1) . When x = 7 , y = 1. Find the value of y when x = 124 . y = …… [3] (b) F is inversely proportional to the square of d. Explain what happens to F when d is halved. …… [1] 4
Mark scheme
18(a) 2.5 3 M1 for y = k × 3 x + 1 M1 for y = theirk × 3 124 + 1 18(b) multiplied by 4 oe 1
Question 194 marks
Question
f (x) = 7x - 8 g (x) = +5 h (x) = 2 x + 1 x (a) Find f -1 (x) . f -1 (x) = …… [2] (b) Find the value of x when h (x) = g e o. 1 3 x = …… [2]
Mark scheme
19(a) x +8 2 y 8 final answer M1 for x = 7 y − 8 or y + 8 = 7 x or = x− 7 7 7 19(b) 4 2 1 M1 for 4 ÷ + 5 oe or better 3
Question 205 marks
Question
Factorise completely. (a) 2m + 3p - 8km - 12kp …… [2] (b) 5x 2 - 20y 2 …… [3]
Mark scheme
20(a) ( 2m + 3 p )(1 − 4k ) final 2 B1 for 2m + 3 p − 4k ( 2m + 3 p ) or better answer or 2m (1 − 4k ) + 3 p (1 − 4k ) or correct answer seen and spoilt 20(b) 5 ( x − 2 y )( x + 2 y ) final 3 B2 for (5x – 10y)(x + 2y) or (x – 2y)(5x + 10y) answer or correct answer seen then spoilt ( or B1 for 5 x 2 − 4 y 2 ) or for ( x − 2 y )( x + 2 y )
Question 215 marks
Question
The nth term of a sequence is an 2 + bn - 4 . The first term is - 3 and the second term is 2. Find the value of a and the value of b. a = …… b = …… [5]
Mark scheme
21 [a =] 2 5 M2 for correct method to find two simultaneous [b =] − 1 equations e.g. two from a × 12 + b × 1 − 4 = −3 a × 22 + b × 2 − 4 = 2 3a + b = 2 – – 3 or M1 for 1 correct equation M1 for correctly eliminating one variable for their simultaneous equations A1 for a = 2 A1 for b = − 1
Question 222 marks
Question
A D B x NOT TO SCALE y O 3 4 OA = x , OB = y and OD = x + y . 7 7 Calculate the ratio AD : DB. …… : …… [2]
Mark scheme
22 4 : 3 oe 2 M1 for ρ 4 4 ρ 3 3 AD = − x + y oe or DB = − x + y oe 7 7 7 7
Question 234 marks
Question
6.2 cm NOT TO SCALE l The diagram shows a solid metal shape made from a cone and a hemisphere, both with radius 6.2 cm. The total surface area of the solid shape is 600 cm 2 . Calculate the slant height, l, of the cone. [The surface area, A, of a sphere with radius r is A = 4rr 2 .] [The curved surface area, A, of a cone with radius r and slant height l is A = rrl .] l = …… cm [4]
Mark scheme
23 18.4 or 18.40… 4 1 600 − × 4 × π × 6.22 M3 for 2 oe 6.2 × π or M2 for 1 × 4 × π × 6.22 + π × 6.2 × l = 600 oe 2 600 − 4 ×π × 6.22 or or better 6.2 ×π 1 or M1 for × 4 × π × 6.22 or π × 6.2 × l 2
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0580/22 questions
Where can I find the 0580/22 May/June 2022 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/22, May/June 2022 (0580_s22_ms_22), and the question paper (0580_s22_qp_22), to read or download, with each question's marking points written out underneath.
How many marks is 0580/22 out of?
Mathematics 0580/22 for May/June 2022 is out of 70 marks, with 1 hour 30 minutes to answer it.
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Yes. Upload your answers to 0580/22/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.