Cambridge IGCSE Mathematics 0580 — 2022 May/June Paper 1 · Variant 1
0580/11/M/J/22 · 23 questions · 56 marks · ≈63 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper12 pages
Mark scheme6 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Students at an activity centre choose one of four activities
1 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: Question Answer Marks Partial Marks 1(a) Correct bar height and width 1 1(b) Climbing 1 FT through their hiking bar
Q2 · L Draw a line that is perpendicular to line L
2 L Draw a line that is perpendicular to line L. [1]
Mark scheme: 2 Perpendicular line 1
Q3 · The diagram shows a circle
3 (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
Q4 · The scale drawing shows the positions of town A and town B
4 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
Q5 · Change 0.56 kilometres into metres
5 Change 0.56 kilometres into metres. .............................................. m [1]
Mark scheme: 5 560 1
Q6 · Write these numbers in order, starting with the smallest
6 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
Q7 · NOT TO y° SCALE x° 68° The diagram shows two parallel lines and a straight line crossing…
7 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
Q8 · Here is some information about six numbers: • The lowest number is 37
8 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
Q9 · Calculate 4 5 - 5 4
9 Calculate 4 5 - 5 4 . ................................................. [1]
Mark scheme: 9 399 1
Q10 · Jason starts a run at 10.05 am and finishes at 1.02 pm
10 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]
Mark scheme: 10 2 [h] 57 [m] 1
Q11 · - 0.711 Calculate , giving your answer correct to 4 significant figures
1 - 0.711 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
Q12 · Kirsty changes $380.80 into pounds (£) when £1 = $1.19
12 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
Q13 · A 4-sided spinner is numbered 1, 2, 3 and 4
13 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]
Mark scheme: 13 [0].23 oe 2 M1 for 1 − [0].27 − [0].18 − [0].32 oe
Q14 · 214 Without using a calculator, work out -
3 214 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
Q15 · C NOT TO SCALE 15 cm 38° A B The diagram shows a right-angled triangle, ABC
15 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 M1 for sin[38 BC] or better 15
Q16 · V = 3 - 5t (a) Work out the value of v when t = 4
16 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
Q17 · Kim has a 6-sided spinner numbered 1 to 6
17 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 18 7y(2x – y) final answer 2 2 B1 for 7 2 xy y or y 14 x 7 y or 7 y 2 x y seen then spoilt
Q19 · Lin invests $16 000 at a rate of r % per year simple interest
19 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 1 920 or 100 or 16000 17920 100 1 00 16000 their 1920 or 100 or figs 384 5
Q20 · 22, 17, 12, 7, 2, … (a) Find the next term of the sequence
20 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
Q21 · Write down an irrational number with a value between 10 and 20
21 Write down an irrational number with a value between 10 and 20. ................................................. [1]
Mark scheme: 21 An irrational number between 10 and 20 1
Q22 · The table shows the population and area of three countries in 2020
22 The table shows the population and area of three countries in 2020. Country Population Area (km2) Nigeria .206 # 108 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 Population density = 2 > area(km ) H ................................................. [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
Q23 · 204 mm NOT TO SCALE 72 mm 180 mm Work out the area of this trapezium
23 204 mm NOT TO SCALE 72 mm 180 mm Work out the area of this trapezium. ........................................ mm2 [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 1 and M1 for (72 + their168) × 180 2 oe If zero scored, then SC1 for 72 × 180 alone or as part of total area calculation
Q24 · C R NOT TO 6 cm SCALE A B P Q 8 cm 6 cm Triangle ABC is mathematically similar to…
24 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
What was in this paper
The subtopics covered by these 23 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Rates2Algebraic manipulation1Angles1Area and perimeter1Circles, arcs and sectors1Fractions, decimals and percentages1Introduction to probability1Ordering1Perpendicular lines1Powers and roots1Ratio and proportion1Right-angled triangles1Scale drawings1Sequences1Similarity1Statistical charts and diagrams1The four operations1Time1Types of number1Units of measure1What you needed in this session
Cambridge’s own grade thresholds for 2022 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.