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CAMBRIDGE INTERNATIONAL EXAMINATIONS 
International General Certificate of Secondary Education 
MARK SCHEME for the May/June 2014 series 
0580 MATHEMATICS 
0580/21 Paper 2 (Extended), maximum raw mark 70 
This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of 
the examination. It shows the basis on which Examiners were instructed to award marks. It does not 
indicate the details of the discussions that took place at an Examiners’ meeting before marking began, 
which would have considered the acceptability of alternative answers. 
Mark schemes should be read in conjunction with the question paper and the Principal Examiner 
Report for Teachers. 
Cambridge will not enter into discussions about these mark schemes. 
Cambridge is publishing the mark schemes for the May/June 2014 series for most IGCSE, GCE 
Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.
Page 2 Mark Scheme Syllabus Paper 
IGCSE – May/June 2014 0580 21 
Abbreviations 
cao correct answer only 
dep dependent 
FT follow through after error 
isw ignore subsequent working 
oe or equivalent 
SC Special Case 
nfww not from wrong working 
soi seen or implied 
Question Answers Mark Part Marks 
36 
2 
© Cambridge International Examinations 2014 
1 
1.37 
2 B1 for 0.866… or 
3 
or 0.5 or 
2 
1 
2 
or B1 for 1.366… as final answer 
2 
1 
18 
18 
2 M1 for 
2 
36 
+ or better 
3 
30 
2 M1 for n – 8 = 22 or 15 
2 
= 
n 
4 (a) 
5× 2 
20 
1 
(b) 
0.5 or 
1 
2 
cao 
1 
5 0.53 0.52 0.5 3 0.5 2 B1 for 0.25 , 0.125 and 0.793… seen 
or for three in correct order 
6 1.6[0] 3 M1 for 800 × 1.5 
and M1 for their 1200 ÷ 750 
7 4 ± y − 6 3 M1 for their 6 moved correctly 
M1 for their √ taken correctly 
M1 for their 4 moved correctly 
8 
2 
( 1) 
x x + 
3 B1 for common denominator x (x +1) seen 
M1 for 2 (x + 1) – 2x oe or better 
9 (a) 119 3 M2 for 18 × 6 + 11 oe 
or B1 for 18 or 11 or 108 
(b) [0] 1 [00] pm cao 
1 
10 (a) 
(a + b)(x + y) 2 B1 for a(x + y) + b(x + y) 
or x(a + b) + y(a + b) 
(b) (x – 1)(3x – 2) 2 B1 for (x – 1)(3(x – 1) + 1) 
If B0 then SC1 for (x + a)(3x + b) where 3a + b = – 5 
or ab = 2 or 3(x – 1)(x – ⅔)
Page 3 Mark Scheme Syllabus Paper 
IGCSE – May/June 2014 0580 21 
8 2 92 2 2 
9 2 8 2 2 
+ − 
22 
2 
2 
= or x + k 
3 
24 
1 
1 
3 = or 8 2 3 
1 
( 
1 
1 
or 3 8 or 8 = 23 or 3 ) 
© Cambridge International Examinations 2014 
11 
113.9 to 114.0 
4 M2 for [cos =] 
+ − 
2 × 8 × 
2 
or M1 for 92 = 82 + 22 – 2 × 8 × 2 × cos x 
A1 for −0.406 or −0.4063 to −0.4062 or 
13 
32 
− 
If 0 scored SC2 for 54.3[1…] or 11.7 or 11.71 to 
11.72 
SC1 for [cos =] 
9 2 2 2 2 
+ − 
82 × 9 × 
2 
or 
[cos =] 
2 × 9 × 
8 
12 (a) 2 × 1010 2 B1 for 20 × 109 or 20 000 000 000 
(b) 1.25 × 10−1 2 B1 for 0.125 oe 
13 (a) 32 
2 B1 for AOC = 116 
(b) 35 
2 B1 for CDA = 122 
14 
y = x − 2 
oe 
2 
3 
4 B1 for (9, 4) 
and 
2 
M2 for y = kx − 2 (k ≠ 0) or y = x + k 
3 
(k ≠ 0) or 
2 
3 
x − 
or M1 for y x 
3 
3 
(k ≠ 0) 
15 [0], 1, 2, 3 4 M1 for moving the 5 correctly 
M1 for collecting their terms 
A1 for a correct inequality for x eg [0 ≤ ] x < 4 
16 (a) 8 2 B1 for 212 or 4096 
3 
(b) 2 2 
q 
3 B2 for 2 
kq as the answer 
or 
1 
B1 for 2q2 and B1 for 2 
q oe nfww 
17 (a) correct working 
2 M1 for 1 holiday = 5 or 360 ÷ 72 = 5 
and B1 for 24 × 5 [= 120] 
or 
M2 for 360 
72 
× [=120] oe 
(b) 6 nfww 3 M1 for 150 + 120 + x + 2x = 360 oe 
A1 for 30 identified as the required angle 
18 (a) 
correct working 
2 B2 for 
2 
8 
10 
= AND 5 
2 
4 
= oe and 2 
2 
= 
oe 
or 
B1 for 3 
8 
2 
8 
=
Page 4 Mark Scheme Syllabus Paper 
IGCSE – May/June 2014 0580 21 
7 1 
2 
1 2 
1 2 
© Cambridge International Examinations 2014 
(b) 
147 or 146.5 to 146.6… 
4 M3 for π 4 10 
3 
8 
× × × × 
or 
M1 for π 4 10 
3 
× × × 
and 
M1 for π 2 5 
3 
× × × 
and 
M1 for subtracting their volumes 
19 
1.38 or 1.39 or 1.384 to 1.389 
1 × × 
7 M3 [Area Δ =] 8cos 60 8sin 60 
2 
or M1 for [ AE =] 8cos 60 and M1 for [ ED] = 8sin 60 
and 
30 
M1 for Area sector 2 π 8 
360 
× × 
and 
M1 for Area rectangle = 8 × 8cos60 or 8 × 4 
M1 for their 32 – (their 13.86 + their 16.76) or better

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IGCSE Math tutor for 0580 may june math paper 2,paper 4

  • 1. CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2014 series 0580 MATHEMATICS 0580/21 Paper 2 (Extended), maximum raw mark 70 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.
  • 2. Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0580 21 Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Question Answers Mark Part Marks 36 2 © Cambridge International Examinations 2014 1 1.37 2 B1 for 0.866… or 3 or 0.5 or 2 1 2 or B1 for 1.366… as final answer 2 1 18 18 2 M1 for 2 36 + or better 3 30 2 M1 for n – 8 = 22 or 15 2 = n 4 (a) 5× 2 20 1 (b) 0.5 or 1 2 cao 1 5 0.53 0.52 0.5 3 0.5 2 B1 for 0.25 , 0.125 and 0.793… seen or for three in correct order 6 1.6[0] 3 M1 for 800 × 1.5 and M1 for their 1200 ÷ 750 7 4 ± y − 6 3 M1 for their 6 moved correctly M1 for their √ taken correctly M1 for their 4 moved correctly 8 2 ( 1) x x + 3 B1 for common denominator x (x +1) seen M1 for 2 (x + 1) – 2x oe or better 9 (a) 119 3 M2 for 18 × 6 + 11 oe or B1 for 18 or 11 or 108 (b) [0] 1 [00] pm cao 1 10 (a) (a + b)(x + y) 2 B1 for a(x + y) + b(x + y) or x(a + b) + y(a + b) (b) (x – 1)(3x – 2) 2 B1 for (x – 1)(3(x – 1) + 1) If B0 then SC1 for (x + a)(3x + b) where 3a + b = – 5 or ab = 2 or 3(x – 1)(x – ⅔)
  • 3. Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0580 21 8 2 92 2 2 9 2 8 2 2 + − 22 2 2 = or x + k 3 24 1 1 3 = or 8 2 3 1 ( 1 1 or 3 8 or 8 = 23 or 3 ) © Cambridge International Examinations 2014 11 113.9 to 114.0 4 M2 for [cos =] + − 2 × 8 × 2 or M1 for 92 = 82 + 22 – 2 × 8 × 2 × cos x A1 for −0.406 or −0.4063 to −0.4062 or 13 32 − If 0 scored SC2 for 54.3[1…] or 11.7 or 11.71 to 11.72 SC1 for [cos =] 9 2 2 2 2 + − 82 × 9 × 2 or [cos =] 2 × 9 × 8 12 (a) 2 × 1010 2 B1 for 20 × 109 or 20 000 000 000 (b) 1.25 × 10−1 2 B1 for 0.125 oe 13 (a) 32 2 B1 for AOC = 116 (b) 35 2 B1 for CDA = 122 14 y = x − 2 oe 2 3 4 B1 for (9, 4) and 2 M2 for y = kx − 2 (k ≠ 0) or y = x + k 3 (k ≠ 0) or 2 3 x − or M1 for y x 3 3 (k ≠ 0) 15 [0], 1, 2, 3 4 M1 for moving the 5 correctly M1 for collecting their terms A1 for a correct inequality for x eg [0 ≤ ] x < 4 16 (a) 8 2 B1 for 212 or 4096 3 (b) 2 2 q 3 B2 for 2 kq as the answer or 1 B1 for 2q2 and B1 for 2 q oe nfww 17 (a) correct working 2 M1 for 1 holiday = 5 or 360 ÷ 72 = 5 and B1 for 24 × 5 [= 120] or M2 for 360 72 × [=120] oe (b) 6 nfww 3 M1 for 150 + 120 + x + 2x = 360 oe A1 for 30 identified as the required angle 18 (a) correct working 2 B2 for 2 8 10 = AND 5 2 4 = oe and 2 2 = oe or B1 for 3 8 2 8 =
  • 4. Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0580 21 7 1 2 1 2 1 2 © Cambridge International Examinations 2014 (b) 147 or 146.5 to 146.6… 4 M3 for π 4 10 3 8 × × × × or M1 for π 4 10 3 × × × and M1 for π 2 5 3 × × × and M1 for subtracting their volumes 19 1.38 or 1.39 or 1.384 to 1.389 1 × × 7 M3 [Area Δ =] 8cos 60 8sin 60 2 or M1 for [ AE =] 8cos 60 and M1 for [ ED] = 8sin 60 and 30 M1 for Area sector 2 π 8 360 × × and M1 for Area rectangle = 8 × 8cos60 or 8 × 4 M1 for their 32 – (their 13.86 + their 16.76) or better