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Cambridge IGCSE Mathematics (0580), Paper 1 (Core), 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_110580_s22_ms_110580/11/M/J/22
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
Students at an activity centre choose one of four activities. The bar chart shows some of their choices. 8 7 6 5 Frequency 4 3 2 1 0 Climbing Hiking Swimming Woodcraft (a) 5 students choose hiking. Complete the bar chart. [1] (b) Write down the most popular activity. …… [1]
Mark scheme
1(a) Correct bar height and width 1 1(b) Climbing 1 FT through their hiking bar
Question
L Draw a line that is perpendicular to line L. [1]
Mark scheme
2 Perpendicular line 1
Question
(a) The diagram shows a circle. On the diagram, draw a chord. [1] (b) Another circle has a diameter of 28 cm. Find the radius of this circle. …… cm [1]
Mark scheme
3(a) Chord drawn 1 3(b) 14 1
Question
The scale drawing shows the positions of town A and town B. The scale is 1 cm represents 15 km. North North B A Scale: 1 cm to 15 km (a) Find the actual distance between town A and town B. …… km [2] (b) Measure the bearing of town B from town A. …… [1]
Mark scheme
4(a) 111 [km] 2 M1 for 7.2[cm] to7.6[cm] seen or for their measurement [in cm] multiplied by 15 evaluated 4(b) [0]71 1
Question
Change 0.56 kilometres into metres. …… m [1]
Mark scheme
5 560 1
Question
Write these numbers in order, starting with the smallest. 6 9 34% 0.345 17 25 …… 1 …… 1 …… 1 …… [2] smallest
Mark scheme
6 6 9 2 M1 for [0].35… [0].34 [0].36 34% 0.345 17 25 or B1 for three in the correct order
Question
NOT TO y° SCALE x° 68° The diagram shows two parallel lines and a straight line crossing them. Find the value of x and the value of y. x = …… y = …… [2]
Mark scheme
7 112 68 2 B1 for each
Question
Here is some information about six numbers: • The lowest number is 37. • The range is 24. • The mode is 43. • The median is 46. • One number is a multiple of 11. Find the other five numbers. 37, ……, ……, ……, ……, …… [4]
Mark scheme
8 [37] 43 43 49 55 61 in any order 4 B1 for 43 43 B1 for 49 B1 for 55 B1 for 61
Question
Calculate 4 5 - 5 4 . …… [1]
Mark scheme
9 399 1
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
10 2 [h] 57 [m] 1
Question
Calculate , giving your answer correct to 4 significant figures. 0.45 - 0.38 …… [2]
Mark scheme
11 4.286 cao 2 30 B1 for 4.285[7...] or 4.29 or or 7 2 4 7 or for correctly rounding their more accurate decimal to 4sf
Question
Kirsty changes $380.80 into pounds (£) when £1 = $1.19 . Calculate the amount Kirsty receives. £ …… [2]
Mark scheme
12 320 2 M1 for 380.8[0] ÷ 1.19 oe
Question
A 4-sided spinner is numbered 1, 2, 3 and 4. The table shows the probability of the spinner landing on 1, 2 and 4. Number 1 2 3 4 Probability 0.27 0.18 0.32 Complete the table. [2] 3 2
Mark scheme
13 [0].23 oe 2 M1 for 1 − [0].27 − [0].18 − [0].32 oe
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]
Mark scheme
14 9 2 M1 Allow any correct denominator 21k and oe 21 21 1 A1 cao and correct working 3
Question
C NOT TO SCALE 15 cm 38° A B The diagram shows a right-angled triangle, ABC. AC = 15 cm and angle BAC = 38°. Calculate BC. BC = …… cm [2]
Mark scheme
15 9.23 or 9.234 to 9.235 2 BC M1 for sin[38 =] or better 15
Question
v = 3 - 5t (a) Work out the value of v when t = 4. v = …… [1] (b) Make t the subject of the formula. t = …… [2]
Mark scheme
16(a) −17 1 16(b) 3−v v−3 2 M1 for or final answer 5 −5 v 3 5t = 3 – v or v – 3 = −5t or = −t 5 5
Question
Kim has a 6-sided spinner numbered 1 to 6. She spins it 63 times and her scores are shown in the table. Score on spinner 1 2 3 4 5 6 Frequency 12 7 15 11 8 10 (a) Find the relative frequency of scoring a 5 with this spinner. …… [1] (b) Work out the mean score. …… [3]
Mark scheme
17(a) 8 1 or [0].127 or 12.7% 63 17(b) 3.41 or 3.412 to 3.413 3 M1 for 1×12 + 2×7 + 3×15 + 4×11 + 5×8 + 6×10 M1 dep for their 215 ÷ 63
Question
Factorise completely. 14xy - 7y 2 …… [2]
Mark scheme
18 7y(2x – 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
Lin invests $16 000 at a rate of r % per year simple interest. At the end of 5 years, she has a total amount of $17 920. Find the value of r. r = …… [3]
Mark scheme
19 2.4 3 B2 for 0.024 seen or M2 for oe or better r 17 920 – 16 000 = × 5 × 16000 [100] or 17 920 = 16 000 × (1 + 5r)[×100] or M1 for any of these, oe or better r 17 920 – 16 000 or × 5 × 16000 [100] their 1920 or [×100] or 16000 17920 [×100] − 1[ 00] 16000 their 1920 or [×100] or figs 384 5
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
20(a) −3 1 20(b) 27 – 5n oe final answer 2 B1 for j – 5n or 27 – kn, k ≠0 or for 27 – 5n seen then spoilt
Question
Write down an irrational number with a value between 10 and 20. …… [1]
Mark scheme
21 An irrational number between 10 and 20 1
Question
The table shows the population and area of three countries in 2020. Country Population Area (km 2 ) Nigeria 2.06 # 10 8 9.11 # 10 5 Comoros 8.70 # 10 5 1.86 # 10 3 Vietnam 9.73 # 10 7 3.10 # 10 5 (a) Calculate the difference in population between Nigeria and Vietnam. …… [1] (b) Which of Comoros or Vietnam has the greater population density? You must show all your working. >Population density = H population area (km 2) …… [3]
Mark scheme
22(a) 108 700 000 1 or 1.087 × 108 22(b) 8.70 × 105 ÷ 1.86 × 103 oe M1 9.73 × 107 ÷ 3.10 × 105 oe M1 Comoros A1 Dependent on M2
Question
204 mm NOT TO SCALE 72 mm 180 mm Work out the area of this trapezium. …… mm 2 [5] Question 24 is printed on the next page.
Mark scheme
23 21 600 5 B3 for 168 OR M2 for 2042 – 1802 or better or M1 for […]2 + 1802 = 2042 oe A1 for 96 dep on M2 and M1 for 1 (72 + their168) × 180 2 oe If zero scored, then SC1 for 72 × 180 alone or as part of total area calculation
Question
C R NOT TO 6 cm SCALE A B P Q 8 cm 6 cm Triangle ABC is mathematically similar to triangle PQR. Calculate QR. QR = …… cm [2]
Mark scheme
24 4.5 oe 2 8 6 M1 for = oe or better 6 QR
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Mathematics 0580/11 for May/June 2022 is out of 56 marks, with 1 hour to answer it.
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