Cambridge IGCSE Mathematics 0580 — 2012 May/June Paper 2 · Variant 1
0580/21/M/J/12 · 21 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 · The price of a ticket for a football match is $124
1 The price of a ticket for a football match is $124 . For Examiner's (a) Calculate the amount received when 76 500 tickets are sold. Use Answer(a) $ [1] (b) Write your answer to part (a) in standard form. Answer(b) $ [1]
Mark scheme: Qu Answers Mark Part marks 1 (a) 9486000 1 (b) 9.486 × 106 1ft
Q2 · Gregor changes $700 into euros (€) when the rate is €1 = $1.4131
2 Gregor changes $700 into euros (€) when the rate is €1 = $1.4131 . Calculate the amount he receives. Answer € [2]
Mark scheme: 2 495.36 2 M1 for 700 ÷ 1.4131
Question 3
3 Factorise completely. 15p2 + 24pt Answer [2]
Mark scheme: 3 3p(5p + 8t) final answer 2 B1 for answer of 3(5p2 + 8pt) or p(15p + 24t) or SC1 for correct answer seen in working 8
Q4 · Write the following in order of size, smallest first
4 Write the following in order of size, smallest first. 8 0.47 0.22 tan 25° 17 Answer < < < [2]
Mark scheme: 8 4 tan 25 < 0.22 < 0.47 < 2 M1 correct conversion to decimals 0.466, 0.469, 0.471 17 x
Q5 · For Examiner's NOT TO Use 29 cm SCALE x cm 53.2° Calculate the value of x
5 For Examiner's NOT TO Use 29 cm SCALE x cm 53.2° Calculate the value of x. Answer x = [2]
Mark scheme: x 5 23.2 2 M1 for sin 53.2 = implicit form or better 29 8 + 4 + 8 + 9 + y
Q6 · Leon scores the following marks in 5 tests
6 Leon scores the following marks in 5 tests. 8 4 8 y 9 His mean mark is 7.2. Calculate the value of y. Answer y = [2]
Mark scheme: 8 + 4 + 8 + 9 + y 6 7 2 M1 = 7 .2 oe 5
Q7 · The sides of a rectangle are 6.3 cm and 4.8 cm, each correct to 1 decimal place
7 The sides of a rectangle are 6.3 cm and 4.8 cm, each correct to 1 decimal place. Calculate the upper bound for the area of the rectangle. Answer cm2 [2]
Mark scheme: 7 30.7975 cao 2 M1 6.35 and 4.85 seen
Q8 · Find r when (5) 3 = 125
8 Find r when (5) 3 = 125 . Examiner's Use Answer r = [2]
Mark scheme: 8 9 2 M1 125 = 5 3
Q9 · D A B (a) The point C lies on AD and angle ABC = 67°
9 D A B (a) The point C lies on AD and angle ABC = 67°. Draw accurately the line BC. [1] (b) Using a straight edge and compasses only, construct the perpendicular bisector of AB. Show clearly all your construction arcs. [2]
Mark scheme: 9 (a) 1 B1 C marked on AD unless the line stops at AD and angle of 67° at B also correct ruled line (b) 2 B1 correct arcs B1 correct ruled line perpendicular bisector of AB 750 × 5 × 2 5
Q10 · For 10 Shania invests $750 at a rate of 2 2 % per year simple interest
1 For 10 Shania invests $750 at a rate of 2 2 % per year simple interest. Examiner's Use Calculate the total amount Shania has after 5 years. Answer $ [3]
Mark scheme: 750 × 5 × 5.2 10 843.75 3 M2 for + 750 oe 100 750 × 5 × 5.2 or M1 for oe 100 or SC2 for answer 93.75 IGCSE – May/June 2012 0580 21
Q11 · Solve the simultaneous equations
11 Solve the simultaneous equations. 3x + 5y = 24 x + 7y = 56 Answer x = y = [3]
Mark scheme: 11 x = −7 3 M1 for consistent multiplication and addition/ y = 9 subtraction as appropriate. Allow computational errors A1 for x= –7 or y = 9 55 27 25 27
Q12 · 9 For 12 Without using your calculator, work out 1 +
5 9 For 12 Without using your calculator, work out 1 + . Examiner's 6 10 Use You must show your working and give your answer as a mixed number in its simplest form. Answer [3]
Mark scheme: 55 27 25 27 12 + oe or )1( + oe M1 for denominator of 30k 30 30 30 30 82 52 oe or )1( oe M1 for denominator of 30k dependent on previous M1 30 30 11 2 M2 must be scored A1 If M0 scored then SC1 for common denominator of 15 30k seen k
Q13 · Y is inversely proportional to x2
13 y is inversely proportional to x2. When x = 4, y = 3. Find y when x = 5. Answer y = [3]
Mark scheme: k 13 1.92 3 M1 y = 2 oe B1 for k = 48 x
Q14 · For y Examiner's Use 7 6 5 4 3 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 –1 The…
14 For y Examiner's Use 7 6 5 4 3 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 –1 The region R contains points which satisfy the inequalities 1 y Y x + 4, y [ 3 and x + y [ 6. 2 On the grid, label with the letter R the region which satisfies these inequalities. You must shade the unwanted regions. [3]
Mark scheme: 14 2 R 3 1 3 2 0 1 2
Q15 · The scale of a map is 1 : 500 000
15 The scale of a map is 1 : 500 000 . (a) The actual distance between two towns is 172 km. Calculate the distance, in centimetres, between the towns on the map. Answer(a) cm [2] (b) The area of a lake on the map is 12 cm2. Calculate the actual area of the lake in km2. Answer(b) km2 [2]
Mark scheme: 15 (a) 34.4 2 SC1 figs 344 seen (b) 300 2 SC1 figs 3 seen − 1 2
Q16 · 5 2 − 1 − 2 For Examiner's16 M = N = − 3 4 2 6 Use Calculate…
5 2 − 1 − 2 For Examiner's16 M = N = − 3 4 2 6 Use Calculate (a) MN, Answer(a) MN = [2] (b) M−1, the inverse of M. Answer(b) M–1 = [2]
Mark scheme: 1 2 16 (a) 2 B1 any two entries correct 11 30 1 4 − 2 1 a b 4 − 2 (b) oe 2 B1 or k 26 3 5 26 c d 3 5 4 3c
Q17 · Make w the subject of the formula
17 Make w the subject of the formula. 4 + w c = w + 3 Answer w = [4]
Mark scheme: 4 − 3c 17 w = www 4 M1 clearing denominator and removing brackets c − 1 M1 correctly collecting terms in w on one side only M1 factorising correctly M1 divide by coefficient of w
Q18 · For 20 Examiner's Use 15 Speed 10 (m / s) 5 0 10 20 30 40 50 60 70 80 90 100 110 120 Time…
18 For 20 Examiner's Use 15 Speed 10 (m / s) 5 0 10 20 30 40 50 60 70 80 90 100 110 120 Time (s) The diagram shows the speed-time graph for the first 120 seconds of a car journey. (a) Calculate the acceleration of the car during the first 25 seconds. Answer(a) m/s2 [1] (b) Calculate the distance travelled by the car in the first 120 seconds. Answer(b) m [4]
Mark scheme: 18 (a) 0.8 1 (b) 1850 4 M1 for area = distance travelled M1 for two correct area statements M1 for complete correct area statement IGCSE – May/June 2012 0580 21
Q19 · For S R Examiner's Use T Q t O P p O is the origin and OPQRST is a regular hexagon
19 For S R Examiner's Use T Q t O P p O is the origin and OPQRST is a regular hexagon. = p and = t. Find, in terms of p and t, in their simplest forms, (a) , Answer(a) = [1] (b) , Answer(b) = [2] (c) the position vector of R. Answer(c) [2]
Mark scheme: 19 (a) −p + t 1 (b) p + 2t 2 M1 for a correct route from P to R or unsimplified answer (c) 2(p + t) or 2p + 2t 2ft M1 for OR or a correct route or ft p + their (b) unsimplified provided their (b) is a vector PT
Q20 · For R Examiner's Use NOT TO O SCALE 78° 5 cm P T R and T are points on a circle, centre…
20 For R Examiner's Use NOT TO O SCALE 78° 5 cm P T R and T are points on a circle, centre O, with radius 5 cm. PR and PT are tangents to the circle and angle POT = 78°. A thin rope goes from P to R, around the major arc RT and then from T to P. Calculate the length of the rope. Answer cm [6] Question 21 is printed on the next page.
Mark scheme: PT 20 64.8 to 64.9 6 M2 5 tan 78 soi by 23.5 or M1 tan 78 = or 5 5 5 sin 78 or tan 12 sin 12 360 − 2 × 78 M2 × 2 × π × 5 soi by 17.8 360 or M1 for 2π5 seen used M1 for their arc + 2 (their PT) 1 3 2
Q21 · In this question, give all your answers as fractions
21 In this question, give all your answers as fractions. For Examiner's A box contains 3 red pencils, 2 blue pencils and 4 green pencils. Use Raj chooses 2 pencils at random, without replacement. Calculate the probability that (a) they are both red, Answer(a) [2] (b) they are both the same colour, Answer(b) [3] (c) exactly one of the two pencils is green. Answer(c) [3]
Mark scheme: 1 3 2 21 (a) 2 M1 × 12 3 + 2 + 4 (their 9 ) − 1 5 4 × 3 2 (× 1) (b) 3 M2 their(a) + + 18 their 72 their 72 4 × 3 2 (× 1) or M1 or their 72 their 72 5 4 5 (c) 3 M2 2 × × 9 3 + 2 + 4 (their 9 ) − 1 4 5 or M1 × 3 + 2 + 4 (their 9 ) − 1
What was in this paper
The subtopics covered by these 21 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Ratio and proportion3Area and perimeter1Averages and measures of spread1Circles, arcs and sectors1Equations1Fractions, decimals and percentages1Geometrical constructions1Graphs in practical situations1Limits of accuracy1Ordering1Percentages1Powers and roots1Probability of combined events1Right-angled triangles1The four operations1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2012 May/June, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.