Cambridge IGCSE Mathematics 0580 — 2017 May/June Paper 1 · Variant 2
0580/12/M/J/17 · 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write 0.071 64 correct to 2 significant figures
1 Write 0.071 64 correct to 2 significant figures. ................................................. [1]
Mark scheme: Question Answer Marks Part Marks 1 [0].072 1
Q2 · The probability that Stephanie wins her next tennis match is 0.85
2 The probability that Stephanie wins her next tennis match is 0.85 . Find the probability that Stephanie does not win her next tennis match. ................................................. [1]
Mark scheme: 2 [0].15 oe 1
Q3 · Calculate 120 + 3.8 2 - 25
3 Calculate 120 + 3.8 2 - 25 . ................................................. [1]
Mark scheme: 3 [0].394 1 or [0].3944 to [0].3945
Q4 · Work out 85 cents as a percentage of $2.03
4 Work out 85 cents as a percentage of $2.03 . ............................................ % [1]
Mark scheme: 4 41.9 or 41.87… 1
Q5 · Change 6200 cm2 into m2
5 Change 6200 cm2 into m2. ........................................... m2 [1]
Mark scheme: 5 [0].62 1
Question 6
6 Factorise. 14x - 21y ................................................. [1]
Mark scheme: 6 7(2x – 3y) final answer 1
Q7 · The daily temperature, in °C, at 3 pm in a town is shown below
7 The daily temperature, in °C, at 3 pm in a town is shown below. Monday Tuesday Wednesday Thursday Friday Saturday Sunday 3 -2 1 2 -4 3 5 (a) Which day had the coldest temperature? ................................................. [1] (b) Work out the difference in the temperatures on Friday and Saturday. ............................................°C [1]
Mark scheme: 7(a) Friday 1 7(b) 7 1
Q8 · Write these numbers in order of size, smallest first
8 Write these numbers in order of size, smallest first. 7 1 0.3 33% 22 3 ........................ 1 ........................ 1 ........................ 1 ........................ [2] smallest
Mark scheme: 8 7 1 2 B1 for 0.32 or 0.31[8…], 0.33 and 0.333 0.3 33% or percentages 22 3
Q9 · The shape above is a rhombus
9 The shape above is a rhombus. Draw all the lines of symmetry on the shape. [2]
Mark scheme: 9 Two correct lines only 2 B1 for one correct line only
Q10 · Write 0.03 as a percentage
10 (a) Write 0.03 as a percentage. ............................................ % [1] (b) Write 37% as a fraction. ................................................. [1]
Mark scheme: 10(a) 3 1 10(b) 37 1 100
Q11 · Find the value of 5a - 3b when a = 7 and b =- 2
11 Find the value of 5a - 3b when a = 7 and b =- 2 . ................................................. [2]
Mark scheme: 11 41 2 M1 for 5(7) – 3(– 2)
Q12 · NOT TO p° 70° SCALE q° The diagram shows a straight line intersecting two parallel lines
12 NOT TO p° 70° SCALE q° The diagram shows a straight line intersecting two parallel lines. Find the value of p and the value of q. p = ................................................ q = ................................................ [2]
Mark scheme: 12 110 1 70 1
Question 13
13 Solve. 2 - x = 5 x + 1 x = ................................................ [2]
Mark scheme: 13 1 2 M1 for 2 – 1 = 5x + x oe oe 6
Q14 · Write 0.0605 in standard form
14 (a) Write 0.0605 in standard form. ................................................. [1] (b) Calculate 0.1 # 5 .1 # 104 , giving your answer in standard form. ................................................. [1]
Mark scheme: 14(a) 6.05 × 10 –2 1 14(b) 5.1 × 10 3 1
Q15 · The mass, m kilograms, of a cat is 2.7 kg, correct to 1 decimal place
15 The mass, m kilograms, of a cat is 2.7 kg, correct to 1 decimal place. Complete the statement about the value of m. ......................... G m 1 ......................... [2]
Mark scheme: 15 2.65 1 2.75 1 If zero scored, SC1 for correct answers but reversed
Q16 · 7 cm NOT TO 4 cm SCALE x° Calculate the value of x
16 7 cm NOT TO 4 cm SCALE x° Calculate the value of x. x = ................................................ [2]
Mark scheme: 16 34.8 or 34.84 to 34.85 2 4 M1 for sin [=] 7
Q17 · Y B 10 9 8 7 6 5 4 3 2 1 A x 0 1 2 3 4 5 Find the gradient of the line AB
17 y B 10 9 8 7 6 5 4 3 2 1 A x 0 1 2 3 4 5 Find the gradient of the line AB. ................................................. [2]
Mark scheme: 17 3 cao 2 M1 for rise ÷ run
Q18 · A NOT TO SCALE D 15 cm 5 cm B C E F 16.5 cm Triangles ABC and DEF are similar
18 A NOT TO SCALE D 15 cm 5 cm B C E F 16.5 cm Triangles ABC and DEF are similar. Find the length of EF. EF = ......................................... cm [2]
Mark scheme: 18 5.5 2 5 15 M1 for [× 16.5 ] or [16.5÷] or better 15 5
Q19 · The exchange rate between dollars and euros(€) is €1 = $1.158
19 The exchange rate between dollars and euros(€) is €1 = $1.158 . (a) Felicity changes €4900 into dollars. Work out how many dollars she receives. $ ................................................ [1] (b) Ricky changes $2895 into euros. Work out how many euros he receives. € ................................................ [2]
Mark scheme: 19(a) 5674.2[0] 1 19(b) 2500 2 1 M1 for 2895 ÷ 1.158 or 2895 × 1.185
Q20 · B NOT TO SCALE C 42° A A, B and C are points on the circumference of a circle with…
20 B NOT TO SCALE C 42° A A, B and C are points on the circumference of a circle with diameter AB. A tangent is drawn at A. Find (a) angle BAC, Angle BAC = ................................................ [1] (b) angle ABC. Angle ABC = ................................................ [2]
Mark scheme: 20(a) 48 1 20(b) 42 2FT FT ‘90 − their (a)’ provided their (a) < 90 B1 for angle BCA = 90 or marked as a right angle
Q21 · 121 (a) Without using a calculator, work out -
5 121 (a) Without using a calculator, work out - . 6 2 Show all the steps of your working and give your answer as a fraction in its simplest form. ................................................. [2] (b) Show that 4 1 4 1 6 # 1 5 = 7 2 . Do not use a calculator and show all the steps of your working. [2]
Mark scheme: 21(a) 5 3 M1 5 k 3k − oe oe for − 6 6 6 k 6 k 1 A1 cao final answer 3 21(b) 25 9 225 B2 25 9 × = oe B1 for or 6 5 30 6 5
Q22 · Each diagram shows the net of a solid
22 (a) Each diagram shows the net of a solid. Write down the mathematical name of each solid. (i) ................................................. [1] (ii) ................................................. [1] (b) The cross section of this prism is a trapezium. NOT TO SCALE 8 cm 5 cm 18 cm 14 cm Calculate the volume of the prism. ......................................... cm3 [3]
Mark scheme: 22(a)(i) pyramid 1 22(a)(ii) triangular prism 1 22(b) 990 3 1 M2 for (8+14) × 5 × 18 oe 2 1 or M1 for (8+14) × 5 2
Q23 · Pablo has $16 400 to invest in one of these savings plans
23 Pablo has $16 400 to invest in one of these savings plans. Plan A pays compound interest at a rate of 4% per year. Plan B pays simple interest at a rate of 4% per year. Pablo invests the $16 400 for 3 years. Calculate how much more he will receive from Plan A than from Plan B. Give your answer correct to 2 decimal places. $ ................................................ [5] Question 24 is printed on the next page.
Mark scheme: 23 79.76 or 79.77 5 Total amounts method 4 3 M2 for 16400 1 + oe 100 4 2 or M1 for 16400 1 + oe 100 and 16400 × 4 × 3 M2 for + 16400 100 16400 × 4 × 3 or M1 for 100 Interests method B3 for 2047 to 2048 or M3 for 656 + 682[.24] + 709[.5296] 4 3 or for 16400 1 + – 16400 100 and 16400 × 4 × 3 M1 for 100
Q24 · Work out the area of a circle with radius 6 cm
24 (a) Work out the area of a circle with radius 6 cm. ......................................... cm2 [2] (b) A solid cylinder has length 15 cm and radius 6 cm. NOT TO SCALE 6 cm 15 cm Calculate the total surface area of the cylinder. ......................................... cm2 [4]
Mark scheme: 24(a) 113 or 113 to 113.12 2 M1 for π × 62 24(b) 792 or 791 or 791.4 to 791.8 4 M2 for 2 × π × 6 ×15 and M1FT for 2 × their (a) or 2 × π × 62
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.
3Algebraic manipulation2Fractions, decimals and percentages2Limits of accuracy2Surface area and volume2Angles1Circle theorems1Equations1Gradient of linear graphs1Introduction to probability1Ordering1Powers and roots1Ratio and proportion1Right-angled triangles1Similarity1Standard form1Symmetry1Units of measure1What you needed in this session
Cambridge’s own grade thresholds for 2017 May/June, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.