Cambridge IGCSE Mathematics 0580 — 2021 May/June Paper 1 · Variant 3
0580/13/M/J/21 · 24 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 · A (a) Measure angle a
1 a (a) Measure angle a. ..................................................... [1] (b) Write down the mathematical name for this type of angle. ..................................................... [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 144 to 148 1 1(b) Obtuse 1
Q2 · NOT TO SCALE O B A Points A and B lie on a circle, centre O
2 NOT TO SCALE O B A Points A and B lie on a circle, centre O. (a) Write down the mathematical name for line AB. ..................................................... [1] (b) The circle has a diameter of 16.8 cm. Write down the radius of the circle. ................................................ cm [1]
Mark scheme: 2(a) Chord 1 2(b) 8.4 oe 1
Q3 · Write down the number that is 23 less than - .16
3 Write down the number that is 23 less than - .16 . ..................................................... [1]
Mark scheme: 3 –24.6 1
Q4 · Write as a fraction in its simplest form
4 Write as a fraction in its simplest form. (a) 72% ..................................................... [1] (b) 0.004 ..................................................... [1]
Mark scheme: 4(a) 18 1 cao 25 4(b) 1 1 cao 250
Q5 · X NOT TO SCALE 40° The diagram shows a pair of parallel lines and a straight line
5 x NOT TO SCALE 40° The diagram shows a pair of parallel lines and a straight line. Complete the statement with the correct geometrical reason. x = 40° because the angles are ............................................ [1]
Mark scheme: 5 Corresponding 1
Q6 · 18 28 7 15 41 19 31 53 Calculate the mean of these numbers
6 18 28 7 15 41 19 31 53 Calculate the mean of these numbers. ..................................................... [2]
Mark scheme: 6 26.5 2 M1 for (18 + 28 + 7 + 15 + 41 + 19 + 31 + 53) ÷ 8
Q7 · The diagram shows a box in the shape of a cuboid
7 The diagram shows a box in the shape of a cuboid. The box has an open top. NOT TO 4 cm SCALE 2 cm 5 cm (a) On the 1 cm 2 grid, draw a net of this box. [3] (b) The outside of the box is painted. Work out the total area that is painted. .............................................. cm2 [2]
Mark scheme: 7(a) Correct net 3 B2 for 3 or 4 correct faces in the correct place provided no more than 6 faces or B1 for 1 or 2 correct faces in the correct place SC2 for correct net with internal lines missing 7(b) 66 2 M1 for 2 × (5 × 4 + 2 × 4) + 5 × 2 oe If 0 scored, SC1 for 76 surface area of closed box
Q8 · NOT TO SCALE 100° y° y° Find the value of y
8 NOT TO SCALE 100° y° y° Find the value of y. y = ..................................................... [2]
Mark scheme: 8 130 2 M1 for 360 – 100 or better
Q9 · 12 18 29 49 91 125 From the list of numbers, write down (a) a cube number…
9 12 18 29 49 91 125 From the list of numbers, write down (a) a cube number, ..................................................... [1] (b) a prime number. ..................................................... [1]
Mark scheme: 9(a) 125 1 9(b) 29 1
Q10 · 5 10 (a) a = b = e - 4 o e2o Work out
3 5 10 (a) a = b = e - 4 o e2o Work out. (i) 8b [1] f p (ii) a – b [1] f p 5 (b) Point L has coordinates ( - 3, 6 ) and LM = e- 2o. Find the coordinates of point M. ( .................... , .................... ) [1]
Mark scheme: 10(a)(i) 40 1 16 10(a)(ii) −2 1 −6 10(b) 2 4 1
Q11 · Maria buys n pencils that cost p cents each
11 Maria buys n pencils that cost p cents each. She pays with a $y note. Find, in terms of n, p and y, the amount of change Maria receives. Give your answer in cents. ............................................. cents [2]
Mark scheme: 11 100y – np 2 B1 for 100y seen or for answer [10k] y – np
Q12 · Francesca spins a four-sided spinner numbered 1, 2, 3 and 4
12 Francesca spins a four-sided spinner numbered 1, 2, 3 and 4. The table shows some of the probabilities of landing on each number. Number 1 2 3 4 Probability 0.18 0.21 0.37 Complete the table. [2]
Mark scheme: 12 [0].24 2 M1 for 1 – ([0].18 + [0].21 + [0].37)
Q13 · Alex changes 190 euros (€) into pounds (£) when £1 = €1.1723
13 Alex changes 190 euros (€) into pounds (£) when £1 = €1.1723 . Calculate the amount Alex receives. Give your answer correct to 2 decimal places. £ ..................................................... [2]
Mark scheme: 13 162.07 cao 2 M1 for 190 ÷ 1.1723
Q14 · The exterior angle of a regular polygon is 36°
14 The exterior angle of a regular polygon is 36°. Find how many sides this polygon has. ..................................................... [1]
Mark scheme: 14 10 1
Question 15
15 Expand and simplify. 6 ( t - q) - 2 ( t - 3q ) ..................................................... [2]
Mark scheme: 15 4t final answer 2 B1 for 6t – 6q or – 2t + 6q or 2t – 6q or for 4t or 0q in the final answer
Q16 · 116 Without using a calculator, work out 1 ' 7
2 116 Without using a calculator, work out 1 ' 7 . 3 2 You must show all your working and give your answer as a fraction in its simplest form. ..................................................... [3]
Mark scheme: 16 5 2 M2 5 15 × oe or B1 for oe or oe 3 15 3 2 5 2 or M1 for their ×their 10 45 3 15 ÷ oe with common 6 6 denominator 2 A1 cao 9
Q17 · These are the first four terms of a sequence
17 These are the first four terms of a sequence. 7 11 15 19 Find the nth term. ..................................................... [2]
Mark scheme: 17 4n + 3 oe 2 B1 for 4n + j or kn + 3 (k ≠ 0) as answer or 4n + 3 oe seen then spoilt
Q18 · Calculate the volume of a cylindrical vase with radius 14.2 cm and height 18 cm
18 (a) Calculate the volume of a cylindrical vase with radius 14.2 cm and height 18 cm. .............................................. cm3 [2] (b) Change your answer to part (a) into litres. ............................................. litres [1]
Mark scheme: 18(a) 11 400 or 11 400 to 11 404 2 M1 for π × 14.22 × 18 oe 18(b) 11.4 or 11.4 to 11.40… 1 FT their (a) ÷ 1000
Q19 · Write 0.000 74 in standard form
19 (a) Write 0.000 74 in standard form. ..................................................... [1] (b) Calculate 4.6 # 10 2 # 6 .7 # 10 5 . Give your answer in standard form, correct to 2 significant figures. ..................................................... [2]
Mark scheme: 19(a) 7.4 × 10-4 1 19(b) 3.1 × 108 2 B1 for figs 31 or 3.082 × 108
Q20 · A group of 120 students take two tests, mathematics and English
20 (a) A group of 120 students take two tests, mathematics and English. Here is some information about the number of students who pass mathematics (M ) and who pass English (E ). • 61 students pass mathematics. • 27 students pass both mathematics and English. • 19 students do not pass mathematics and do not pass English. M E (i) Complete the Venn diagram. [3] (ii) Use the Venn diagram to find n(E ). ..................................................... [1] (b) A B Use set notation to describe the shaded region. ..................................................... [1]
Mark scheme: 20(a)(i) 3 B2 for 2 or 3 numbers in the correct place or B1 for 1 correct number in the correct place 20(a)(ii) 67 1 FT their diagram 20(b) A ∩ B 1
Q21 · Y 5 4 3 2 L 1 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 Find the equation of line L in the…
21 (a) y 5 4 3 2 L 1 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 Find the equation of line L in the form y = mx + c . y = ..................................................... [2] (b) Find the equation of the line which is • parallel to the line y = 3x - 5 and • passes through the point (0, 17). ..................................................... [1]
Mark scheme: 21(a) 1 2 B1 for −0.5x + c oe or mx + 2 oe (m≠0) −0.5x + 2 or – x + 2 2 21(b) y = 3x + 17 cao 1
Q22 · E NOT TO B SCALE 85 cm 34 cm A C 28 cm D F Triangle ABC is similar to triangle DEF
22 E NOT TO B SCALE 85 cm 34 cm A C 28 cm D F Triangle ABC is similar to triangle DEF. Calculate DF. DF = ................................................ cm [2]
Mark scheme: 22 70 2 DF 85 DF 28 M1 for = or = oe or better 28 34 85 34
Q23 · Simplify 3x 3 # 4x 4
23 Simplify 3x 3 # 4x 4 . ..................................................... [2] Question 24 is printed on the next page.
Mark scheme: 23 12x 7 final answer 2 B1 for 12xj or kx7 (j,k ≠ 0) as final answer
Q24 · NOT TO 30 cm SCALE 18 cm x° The diagram shows a right-angled triangle
24 NOT TO 30 cm SCALE 18 cm x° The diagram shows a right-angled triangle. Show that the value of x is 36.9, correct to 1 decimal place. [2]
Mark scheme: 24 sin [x =] 18 ÷ 30 oe or better M1 36.87 or 36.86… A1
What was in this paper
The subtopics covered by these 24 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
4Fractions, decimals and percentages2Algebraic manipulation1Area and perimeter1Averages and range1Equations of linear graphs1Geometrical terms1Indices II1Introduction to probability1Money1Powers and roots1Ratio and proportion1Right-angled triangles1Sequences1Sets1Similarity1Standard form1Surface area and volume1The four operations1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2021 May/June, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.