Cambridge IGCSE Mathematics 0580 — 2021 May/June Paper 1 · Variant 1
0580/11/M/J/21 · 22 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 · Zachary asks the 30 students in his class which is their favourite sport
1 Zachary asks the 30 students in his class which is their favourite sport. The table shows the results. Netball Football Hockey Tennis 7 12 6 5 Complete the pictogram. Netball Football Hockey Tennis Key: represents 4 people [2]
Mark scheme: Question Answer Marks Partial Marks 1 Pictogram completed correctly 2 B1 for 2 rows completed correctly
Q2 · Find the value of 225
2 (a) Find the value of 225. ................................................. [1] 2 (b) Write down the reciprocal of . 3 ................................................. [1] (c) Work out three‑quarters of one‑third. ................................................. [1] (d) Work out - 7 - ( 6 - 8) . ................................................. [1]
Mark scheme: 2(a) 15 1 2(b) 1 1 12 oe 2(c) 1 1 oe 4 2(d) –5 1
Q3 · Write down the order of rotational symmetry of this diagram
3 (a) Write down the order of rotational symmetry of this diagram. ................................................. [1] (b) On the diagram, draw all the lines of symmetry. [2]
Mark scheme: 3(a) 4 1 3(b) 2 B1 for 2 or 3 correct lines drawn or for 4 correct lines and one wrong extra line
Q4 · The stem‑and‑leaf diagram shows the number of hours that each of 16 students studied last…
4 The stem‑and‑leaf diagram shows the number of hours that each of 16 students studied last week. 1 2 5 6 8 2 0 1 1 7 9 3 2 3 4 5 4 4 5 7 Key: 1q2 represents 12 hours Find (a) the median, ............................................... h [1] (b) the mode, ............................................... h [1] (c) the range. ............................................... h [1]
Mark scheme: 4(a) 28 1 4(b) 21 1 4(c) 35 1
Q5 · The volume of a cuboid is 24 cm3
5 The volume of a cuboid is 24 cm3. The base of the cuboid is 3 cm by 2 cm. Draw a net of the cuboid on the 1cm2 grid. [4]
Mark scheme: 5 Correct net of 6 faces drawn 4 B1 for height of 4 cm soi 24 or M1 for 3 × 2 B1 for a 3 cm by 2 cm face soi B1 for 3 more faces drawn in correct positions or for a complete net drawn with wrong height
Q6 · 8 7 6 5 Distance (km) 4 3 2 1 0 12 00 13 00 14 00 15 00 16 00 Time The travel graph shows…
6 8 7 6 5 Distance (km) 4 3 2 1 0 12 00 13 00 14 00 15 00 16 00 Time The travel graph shows a student’s journey. (a) Explain what is happening between 14 20 and 14 40. ..................................................................................................................................................... [1] (b) Complete the statement. The student is travelling fastest between the times ........................ and ........................ because ....................................................................................................................................... [2]
Mark scheme: 6(a) Student is stationary oe 1 6(b) 13 00 13 20 2 B1 for both times correct or correct gradient is steepest reason
Q7 · The probability that a train is late is 0.15
7 The probability that a train is late is 0.15 . Write down the probability that the train is not late. ................................................. [1]
Mark scheme: 7 0.85 oe 1
Q8 · Nazaneen changes $6500 into 5798 euros at a bank
8 Nazaneen changes $6500 into 5798 euros at a bank. Work out the exchange rate the bank uses. $1 = ........................................ euros [1]
Mark scheme: 8 0.892 1
Question 9
9 Work out. 6 8 (a) + e- 5o e- 1o [1] f p - 4 (b) 3 e 7o [1] f p
Mark scheme: 9(a) 14 1 −6 9(b) −12 1 21
Q10 · NOT TO 59° 37° SCALE a° c° b° The diagram shows two parallel lines intersected by two…
10 NOT TO 59° 37° SCALE a° c° b° The diagram shows two parallel lines intersected by two straight lines. Find the values of a, b and c. a = ................................................. b = ................................................. c = ................................................. [3]
Mark scheme: 10 [a =] 59 3 B1 for each [b =] 37 If 0 scored, SC1 for [c =] 84 their (a + b + c) = 180 if a, b, c > 0
Q11 · Write down the mathematical name for a polygon with 5 sides
11 (a) Write down the mathematical name for a polygon with 5 sides. ................................................. [1] (b) Work out the interior angle of a regular 18‑sided polygon. ................................................. [2]
Mark scheme: 11(a) Pentagon 1 11(b) 160 2 360 (18 − 2 ) × 180 M1 for 180 − or oe 18 18
Q12 · The nth term of a sequence is 6n - 4
12 The nth term of a sequence is 6n - 4 . (a) Write down the first 3 terms in this sequence. ...................., ...................., .................... [1] (b) The kth term of this sequence is 422. Work out the value of k. k = ................................................. [2]
Mark scheme: 12(a) 2 8 14 1 12(b) 71 2 M1 for 6k – 4 = 422 or better
Q13 · The radius of a circle is 42 cm
13 The radius of a circle is 42 cm. Work out the circumference of the circle. Give your answer in terms of r. ............................................ cm [2]
Mark scheme: 13 84π final answer 2 M1 for 42 × 2 × π soi
Q14 · Change 680 000 cm3 into m3
14 Change 680 000 cm3 into m3. ............................................ m3 [1]
Mark scheme: 14 [0].68 1
Q15 · The length, l metres, of a piece of rope is 5.67 m, correct to the nearest centimetre
15 The length, l metres, of a piece of rope is 5.67 m, correct to the nearest centimetre. Complete this statement about the value of l. ............................. G l 1 ............................. [2]
Mark scheme: 15 5.665 5.675 2 B1 for each in correct order If 0 scored, SC1 for correct answers reversed or for 566.5 and 567.5 in correct places
Q16 · 516 Without using a calculator, work out 1 -
3 516 Without using a calculator, work out 1 - . 8 6 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [3]
Mark scheme: 16 11 5 3 1 B1 Correct step for dealing with mixed − + number 8 6 8 6 11k Allow 8 k 33 20 9 4 M1 Correct method to find common and and denominator 24 24 24 24 9 20 e.g. 124 and 24 13 A1 cao 24
Q17 · 7 (a) Write as a power of 2
117 (a) Write as a power of 2. 2 # 2 # 2 # 2 # 2 ................................................. [1] (b) (i) 3 18 ' 3 t = 3 6 Find the value of t. t = ................................................. [1] (ii) Simplify. 8w 10 # 6w 5 ................................................. [2]
Mark scheme: 17(a) 2–5 1 17(b)(i) 12 1 17(b)(ii) 48w15 final answer 2 B1 for answer 48wk or kw15 (k ≠ 0)
Q18 · Annie invests $8300 at a rate of 5.6% per year compound interest
18 Annie invests $8300 at a rate of 5.6% per year compound interest. Calculate the value of her investment at the end of 6 years. $ ................................................. [2]
Mark scheme: 18 11 500, 11 510, 11 509, 11 509.6[…] 2 6 5.6 M1 for 8300 × 1 + 100
Q19 · Write down an irrational number, n, where 31 1 n 1 32
19 Write down an irrational number, n, where 31 1 n 1 32 . n = ................................................. [1]
Mark scheme: 19 An irrational number satisfying inequality 1
Q20 · By rounding each number in the calculation correct to 1 significant figure, estimate the…
20 By rounding each number in the calculation correct to 1 significant figure, estimate the value of 38.7 # 3.115 . 20.3 - 4.12 You must show all your working. ................................................. [2]
Mark scheme: 20 40 × 3 M1 Allow M1 for 3 out of 4 values correctly 2 rounded 20 − 4 or for all correct but with any trailing zeros 30 cao A1 Dep on M1 with no errors or trailing zeros
Q21 · Solve the simultaneous equations
21 Solve the simultaneous equations. You must show all your working. 2x + y = 3 x - 5y = 40 x = ................................................. y = ................................................. [3]
Mark scheme: 21 Correctly eliminating one variable M1 [x =] 5 A1 [y =] – 7 A1 If M0 scored, SC1 for two values satisfying one of the original equations
Q22 · There is a straight road between town A and town B of length 130 km
22 There is a straight road between town A and town B of length 130 km. Maxi travels from town A to town B. Pippa travels from town B to town A. Both travel at a constant speed of 40 km/h. Maxi leaves 30 minutes before Pippa. Work out how far from town A they will be when they pass each other. ............................................ km [4]
Mark scheme: 22 75 4 B3 for 55 or B2 for 110 or B1 for 20 seen OR 30 M1 for × 40 or better seen 60 M1dep for 130−their 20 their110 M1dep for 2 OR M1 for 130 ÷ 40 or better seen M1 for their 3.25 – 0.50 2.75 M1 for their × 40 2
What was in this paper
The subtopics covered by these 22 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Angles2Fractions, decimals and percentages2Averages and range1Circles, arcs and sectors1Equations1Estimation1Indices I1Introduction to probability1Limits of accuracy1Percentages1Sequences1Statistical charts and diagrams1Surface area and volume1Symmetry1Types of number1Units of measure1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2021 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.