Cambridge IGCSE Mathematics 0580 — 2017 May/June Paper 2 · Variant 2
0580/22/M/J/17 · 23 questions · 70 marks · ≈79 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 · Change 6200 cm2 into m2
3 Change 6200 cm2 into m2. ........................................... m2 [1]
Mark scheme: 3 [0].62 1
Q4 · Calculate 120 + 3.8 2 - 25
4 Calculate 120 + 3.8 2 - 25 . ................................................. [1]
Mark scheme: 4 [0].394 1 or [0].3944 to [0].3945
Q5 · Work out 85 cents as a percentage of $2.03
5 Work out 85 cents as a percentage of $2.03 . ............................................ % [1]
Mark scheme: 5 41.9 or 41.87 1
Question 6
6 Factorise. 14x - 21y ................................................. [1]
Mark scheme: 6 7(2x – 3y) final answer 1
Q7 · Find the value of 5a - 3b when a = 7 and b =- 2
7 Find the value of 5a - 3b when a = 7 and b =- 2 . ................................................. [2]
Mark scheme: 7 41 2 M1 for 5(7) – 3(–2)
Q8 · NOT TO p° 70° SCALE q° The diagram shows a straight line intersecting two parallel lines
8 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: 8 110 1 70 1
Q9 · 19 Without using a calculator, work out -
5 19 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]
Mark scheme: 9 5 3 M1 5 k 3k – oe oe for − 6 6 6 k 6 k 1 A1 cao final answer 3
Question 10
10 Solve. 2 - x = 5 x + 1 x = ................................................ [2]
Mark scheme: 10 1 2 M1 for 2 – 1 = 5x + x oe oe 6
Q11 · Write 0.0605 in standard form
11 (a) Write 0.0605 in standard form. ................................................. [1] (b) Calculate 0.1 # 5.1 # 104 , giving your answer in standard form. ................................................. [1]
Mark scheme: 11(a) 6.05 × 10–2 1 11(b) 5.1 × 103 1
Q12 · 7 cm NOT TO 4 cm SCALE x° Calculate the value of x
12 7 cm NOT TO 4 cm SCALE x° Calculate the value of x. x = ................................................ [2]
Mark scheme: 12 34.8 or 34.84 to 34.85 2 4 M1 for sin [=] 7
Question 13
13 Solve the inequality. 3n - 11 2 5n - 18 ................................................. [2]
Mark scheme: 13 n < 3.5 oe final answer 2 M1 for 18 – 11 > 5n – 3n oe
Question 14
14 Work out. 2 3 (a) 125 ................................................. [1] J N- 2 1 (b) KK OO 3 L P ................................................. [1]
Mark scheme: 14(a) 25 1 14(b) 9 1
Q15 · Make q the subject of the formula p = 2 q 2
15 Make q the subject of the formula p = 2 q 2 . q = ................................................ [2]
Mark scheme: 15 p 2 p 2 [ ± ] oe M1 for = q or p = 2 q 2 2 p p or [q =] their or [q =] 2 their 2
Q16 · B A C (a) Using a straight edge and compasses only, construct the bisector of angle BAC
16 B A C (a) Using a straight edge and compasses only, construct the bisector of angle BAC. [2] (b) Shade the region inside the triangle that is nearer to AC than to AB. [1]
Mark scheme: 16(a) Correct bisector with correct arcs 2 B1 for correct bisector but no arcs or correct arcs but no line 16(b) Correct region shaded 1
Q17 · 8.15 m C B 30° NOT TO SCALE 110° A Calculate AC
17 8.15 m C B 30° NOT TO SCALE 110° A Calculate AC. AC = ........................................... m [3]
Mark scheme: 17 4.34 or 4.336 to 4.337 3 .815 sin 30 M2 for sin 110 sin 110 sin 30 or M1 for = oe .815 AC
Q18 · A rectangle has length 62 mm and width 47 mm, both correct to the nearest millimetre
18 A rectangle has length 62 mm and width 47 mm, both correct to the nearest millimetre. The area of this rectangle is A mm2. Complete the statement about the value of A. ......................................... G A 1 ......................................... [3]
Mark scheme: 18 2859.75 2968.75 cao 3 B2 for one correct seen final answer or B1 for 62.5 or 61.5 or 46.5 or 47.5 seen or M1 for (62 + 0.5) × (47 + 0.5) or (62 – 0.5) × (47 – 0.5)
Q19 · In a triangle PQR, PQ = 8 cm and QR = 7 cm
19 In a triangle PQR, PQ = 8 cm and QR = 7 cm. The area of this triangle is 17 cm2. Calculate the two possible values of angle PQR. Angle PQR = ........................ or ........................ [3]
Mark scheme: 19 37.4 or 37.38… 3 B2 for one correct and or M1 for 0.5 × 8 × 7 sin = 17 oe 142.6 or 142.6… If zero or M1 only scored, SC1 for two answers with a sum of 180
Q20 · Write as a single fraction in its simplest form
20 Write as a single fraction in its simplest form. 2x - 1 2 - 3 x + 1 ................................................. [3]
Mark scheme: 20 2 x 2 + x − 7 2 x 2 + x − 7 3 M1 for (2x – 1)(x + 1) – 2 × 3 oe with an or attempt to expand the brackets 3 ( x +1) 3 x + 3 final answer B1 for 3(x + 1) or 3x + 3 for denominator
Q21 · Y is inversely proportional to 1+ x
21 y is inversely proportional to 1+ x . When x = 8 , y = 2 . Find y when x = 15 . y = ................................................ [3]
Mark scheme: 21 3 1 3 k 1.5 or or M1 for 2 12 1 + x their k M1 for y = 1 + 15 2 y or M2 for = 1 + 15 1 + 8
Question 22
22 Factorise completely. (a) 9t 2 - u 2 ................................................. [2] (b) 2c - 4d - pc + 2pd ................................................. [2]
Mark scheme: 22(a) ( 3t + u )( 3t − u ) final answer 2 B1 for ( at + bu )( ct + du ) final answer where ac = 9 or ad + bc = 0 or bd = – 1 22(b) ( c − 2 d )(2 − p ) or ( p − 2)(2 d − c ) 2 M1 for 2 ( c − 2 d ) − p ( c − 2 d ) final answer or c ( 2 − p ) − 2 d ( 2 − p ) or p ( 2 d − c ) − 2 ( 2 d − c ) or 2 d ( p − 2) − c ( p − 2 )
Q23 · = {students in a class} P = {students who study physics} C = {students who study…
23 (a) = {students in a class} P = {students who study physics} C = {students who study chemistry} The Venn diagram shows numbers of students. P C 5 11 8 7 (i) Find the number of students who study physics or chemistry. ................................................. [1] (ii) Find n P k C l ^ h. ................................................. [1] (iii) A student who does not study chemistry is chosen at random. Find the probability that this student does not study physics. ................................................. [1] (b) On the Venn diagram below, shade the region D j E l. D E [1]
Mark scheme: 23(a)(i) 24 1 23(a)(ii) 5 1
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.
2Equations2Introduction to probability2Limits of accuracy2Non-right-angled triangles2Algebraic fractions1Angles1Fractions, decimals and percentages1Geometrical constructions1Inequalities1Introduction to algebra1Percentages1Powers and roots1Ratio and proportion1Right-angled triangles1Standard form1The four operations1Units of measure1What you needed in this session
Cambridge’s own grade thresholds for 2017 May/June, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.