Question 11 mark
Question
The temperature at midnight is -4 °C. The temperature at noon is 25 °C. Work out the difference between these two temperatures. …… °C [1]
Mark scheme
1 29 1
Mathematics 0580/22 May/June 2024: question paper and mark scheme
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_220580_s24_ms_220580/22/M/J/24
- Paper
- Paper 2 (Extended)
- Total marks
- 70
- Time
- 1 hour 30 minutes
- Code on the paper
- 0580/22/M/J/24
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
A gardener charges $6.55 for each hour he works plus a fixed charge of $15.50 . Calculate the total amount he charges when he works for 4 hours. $ …… [2]
Mark scheme
2 41.7[0] 2 M1 for 6.55 × 4 + 15.5
Question 33 marks
Question
A delivery driver records the number of pizzas she delivers each month for one year. 48 44 39 28 57 22 36 41 54 57 49 52 (a) Complete the stem-and-leaf diagram. 2 3 4 5 Key: 4 q8 represents 48 pizzas [2] (b) Find the median. …… [1]
Mark scheme
3(a) Correct table 2 B1 for two rows correct or for fully correct unordered stem-and-leaf diagram 2 2 8 3 6 9 4 1 4 8 9 5 2 4 7 7 3(b) 46 1
Question 43 marks
Question
Jonah has $750. 1 He spends of this money on travel and some of this money on food. 4 He now has $437.50 . Work out the fraction of the $750 he spends on food. …… [3]
Mark scheme
4 1 3 or equivalent fraction 6 625 B2 for oe 750 750 or M2 for 750 − − 437.5 oe 4 750 or M1 for 750 − oe 4 750 or + 437.5 oe 4 437.5 or oe 750
Question 52 marks
Question
The table shows part of a tram timetable. Newpoint Westhill 10 30 11 17 12 18 13 30 14 17 All the trams take the same number of minutes to complete the journey from Newpoint to Westhill. Complete the table. [2]
Mark scheme
5 13 05 or 1 05pm 2 M1 for 47 [minutes]
Question 61 mark
Question
Write 0.04628 correct to 2 significant figures. …… [1]
Mark scheme
6 0.046 cao 1
Question 71 mark
Question
A B On the Venn diagram, shade the region A , B . [1]
Mark scheme
7 1 A B
Question 83 marks
Question
Kai invests $5000 in an account paying simple interest at a rate of r % per year. At the end of 8 years, the value of his investment is $5700. Find the value of r. r = …… [3]
Mark scheme
8 1.75 3 ( 5700 − 5000 ) [×100] M2 for oe 5000 × 8 or ( 5700 − 5000 ) ×100 oe 5000 [× 8] 5000 × 8 × r or M1 for [5700 – 5000] = oe 100 or B1 for 87.5 or 0.14 or 1.14 If 0 scored SC1 for answer 14.25
Question 95 marks
Question
y 7 6 5 4 B 3 2 A 1 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 x –1 –2 –3 (a) Describe fully the single transformation that maps triangle A onto triangle B. …… [3] -4 (b) On the grid, draw the image of triangle A after a translation by the vector e o. [2] 3
Mark scheme
9(a) Enlargement 3 B1 for each [s f] 2 [centre] (1, −1) 9(b) image at ( −1, 4 )( −1, 5 )(1, 4 ) 2 −4 k B1 for translation by or k 3
Question 101 mark
Question
Write 174 000 in standard form. …… [1]
Mark scheme
10 1.74 ×105 1
Question 112 marks
Question
A company surveys 40 of its employees. In the survey, 3 employees say they walk to work. The company has a total of 1240 employees. Find the expected number of employees in the company who walk to work. …… [2]
Mark scheme
11 93 2 3 1240 M1 for [×1240] oe or [×3] oe 40 40 40 1240 or = oe 3 x
Question 122 marks
Question
NOT TO SCALE 14 cm x° 8.5 cm The diagram shows a right-angled triangle. Calculate the value of x. x = …… [2] 1 7
Mark scheme
12 52.6 or 52.61 to 52.62 2 8.5 M1 for cos[... =] oe 14
Question 133 marks
Question
Without using a calculator, work out 2 ' 1 . 4 8 You must show all your working and give your answer as a mixed number in its simplest form. …… [3]
Mark scheme
13 9 8 M2 × oe or 4 15 18 15 ÷ oe with common 8 8 9 15 denominator B1 for oe or oe 4 8 their 9 8 or M1 for × oe 4 their 15 1 A1 dep on M2 1 cao 5
Question 142 marks
Question
y 7 6 B 5 4 3 2 A 1 0 1 2 3 4 5 6 7 8 9 x A is the point (0, 2) and B is the point (8, 6). Find the equation of line AB. Give your answer in the form y = mx + c . y = …… [2]
Mark scheme
14 1 2 6−2 y= x + 2 oe M1 for oe 2 8−0 or for y = kx + 2
Question 153 marks
Question
North A NOT TO C SCALE B Three towns, A, B and C, are equidistant from each other. The bearing of C from A is 104°. Calculate the bearing of B from C. …… [3]
Mark scheme
15 224 3 M2 for a fully correct method e.g. 360 – (180 – 104 + 60) oe or B2 for 120, 136, 44, 46, 14, or 16 in the correct position or B1 for 60, 76, 104 or 284 in the correct position or for interior angle of triangle = 60 i.e. these positions for B2 or B1: 44 76 60 60 60 136 76 44 16 60 44 104 104 120 14 46 284
Question 164 marks
Question
The speed–time graph shows information about a car journey. 16 NOT TO Speed SCALE (m/s) 0 0 30 240 320 Time (s) (a) Find the deceleration of the car between 240 and 320 seconds. …… m /s 2 [1] (b) Calculate the total distance the car travels during the 320 seconds. …… m [3]
Mark scheme
16(a) 0.2 oe 1 16(b) 4240 3 1 M2 for × ( 210 + 320 ) × 16 oe 2 or M1 for one area correct
Question 172 marks
Question
W = {students who walk to school} G = {students who wear glasses} There are 20 students in a class. • 8 walk to school • 3 wear glasses and walk to school • 2 do not wear glasses and do not walk to school. Complete the Venn diagram. W G [2]
Mark scheme
17 2 B1 for 2 sections out of 4 correct W 10 G 5 3 2
Question 183 marks
Question
y 18 16 14 12 10 8 6 4 2 0 x 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 The graph of y = f (x) is drawn on the grid. (a) Draw the tangent to the graph at the point x = 3. [1] (b) Use your tangent to find an estimate for the gradient of the curve at the point x = 3. …… [2]
Mark scheme
18(a) tangent ruled at x = 3 1 18(b) 4.8 to 5.8 2 dep on a close attempt at a tangent rise M1 for also dep on close attempt at tangent run
Question 194 marks
Question
(a) y is directly proportional to `x - 1j . 2 When x = 4 , y = 3. Find y when x = 7 . y = …… [3] (b) m is inversely proportional to the square root of p. Explain what happens to the value of m when the value of p is multiplied by 9. …… [1]
Mark scheme
19(a) 12 3 M1 for y = k ( x − 1)2 oe M1 for y = their k ( 7 − 1) oe 2 19(b) divided by 3 oe 1
Question 203 marks
Question
Two parcels are mathematically similar. The larger parcel has volume 80 cm 3 and height 5.2 cm. The smaller parcel has volume 33.75 cm 3 . Calculate the height of the smaller parcel. …… cm [3]
Mark scheme
20 3.9 3 33.75 M2 for 5.2 × 3 oe 80 3 3 33.75 80 or M1 for 3 oe or 3 oe 80 33.75 h3 33.75 or 3 = oe 5.2 80
Question 215 marks
Question
Solve the simultaneous equations. You must show all your working. 4y + 3x = 13 y = x 2 - 18 x = …… y = …… or x = …… y = …… [5]
Mark scheme
21 4 x 2 + 3 x − 85 [ = 0] M2 13 − 3 x or 16 y 2 − 113 y + 7 [ = 0] ( ) M1 for 4 x 2 − 18 + 3 x = 13 or x 2 − 18 = 4 oe simplified 2 13 − 4 y or y = − 18 oe or better 3 correct method to solve their M1 −3 ± 32 − 4 × 4 × − 85 quadratic equation e.g. factors, oe, (4x – 17)(x + 5) quadratic formula, completing the 2× 4 square − ( −113) ± ( −113)2 − 4 ×16 × 7 oe, 2 ×16 (16y – 1)(y – 7) x = −5 y = 7 B2 B1 for one correct pair or two correct x values or 17 1 two correct y values x= oe y = oe If B0 scored and at least 2 method marks scored, 4 16 SC1 for correct substitution of both of their x values or their y values into 4y + 3x = 13 or y = x2 – 18
Question 227 marks
Question
(a) For each sketch, put a ring around the correct type of function shown. (i) y O x linear cubic quadratic reciprocal exponential [1] (ii) y O x linear cubic quadratic reciprocal exponential [1] (b) (i) On the grid, sketch the curve y = sin x for 0° G x G 360° . y 1 0 x 180° 360° –1 [2] (ii) Solve the equation sin x + 0.4 = 0 for 0° G x G 360° . x = …… or x = …… [3]
Mark scheme
22(a)(i) cubic 1 22(a)(ii) reciprocal 1 22(b)(i) correct sine curve sketch through 2 (0, 0), (180, 0) and (360, 0) M1 for correct sine curve shape through the origin 22(b)(ii) 203.6 and 336.4 3 B2 for one correct or M1 for sin x = −0.4 oe If 0 or M1 scored, SC1 for two reflex angles with a sum of 540 or two non-reflex angles with a sum of 180
Question 233 marks
Question
E F 8 1 6 1 2 3 5 4 S The Venn diagram shows information about the number of students in a class. Some study English (E ), some study French (F ), some study Spanish (S ) and some do not study any of these languages. (a) Find n `(E , F)l , Sj . …… [1] (b) One student is picked at random from those who study Spanish. Find the probability that this student studies exactly two languages. …… [2] Question 24 is printed on the next page.
Mark scheme
23(a) 15 1 23(b) 1 2 oe nfww 2 2+3 4 +1 M1 for oe or 1 − oe 2 +1+ 3 + 4 2 +1+ 3 + 4 with either the numerator or denominator correct
Question 245 marks
Question
P M Q NOT TO SCALE a N O S b R O is the origin and OPQR is a parallelogram. M is the midpoint of PQ and N divides QR in the ratio 2 : 1. OP = a and OR = b . (a) Find MN . Give your answer in terms of a and/or b and in its simplest form. MN = …… [2] (b) The lines MN and OR are extended to meet at S. Find the position vector of S. Give your answer in terms of a and/or b and in its simplest form. …… [3]
Mark scheme
24(a) 1 2 2 1 2 b− a B1 for answer b + ka or jb − a 2 3 2 3 or correct unsimplified in terms of a and b 24(b) 5 3 b ρ 1 4 M2 for RS = b oe 4 ρ 3 1 2 or MS = b − a oe 2 2 3 ρ 1 1 2 or NS = b − a oe 2 2 3 or M1 for a correct route in terms of vertices and/or a and/or b or B1 for answer jb where j > 1 ρ 1 ρ ρ 1 ρ or RS = MQ , RS = OR , oe 2 4 ρ 1 ρ ρ 3 ρ NS = MN , MS = MN 2 2 ρ 1 ρ NS = MS 3
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Where can I find the 0580/22 May/June 2024 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/22, May/June 2024 (0580_s24_ms_22), and the question paper (0580_s24_qp_22), to read or download, with each question's marking points written out underneath.
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Mathematics 0580/22 for May/June 2024 is out of 70 marks, with 1 hour 30 minutes to answer it.
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