Math Paper 4 2010 Mark Scheme
Math Paper 4 2010 Mark Scheme
Math Paper 4 2010 Mark Scheme
0580 MATHEMATICS
0580/42 Paper 42 (Extended), maximum raw mark 130
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 must be read in conjunction with the question papers and the report on the
examination.
• CIE will not enter into discussions or correspondence in connection with these mark schemes.
CIE is publishing the mark schemes for the May/June 2010 question papers for most IGCSE, GCE
Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.
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Page 2 Mark Scheme: Teachers’ version Syllabus Paper
IGCSE – May/June 2010 0580 42
Abbreviations
cao correct answer only
cso correct solution only
dep dependent
ft follow through after error
isw ignore subsequent working
oe or equivalent
SC Special Case
www without wrong working
100 × 9
(b) (i) 5 www 2 2 M1 for oe
90 × 2
(ii) 165 www 2 2 M1 for 99 ÷ 0.6 oe
(c) 162.24 final answer cao 2 M1 for 150 × 1.04 × 1.04 oe implied by
answer 162.2
1 1 1 1
(b) (i) v – c or (v – c) cao 2 M1 for CV soi
2 2 2 2
1 1
(ii) c + v again allowing brackets cao 2 M1 for OM e.g. OC + CM or better seen
2 2 or v – their (i)
or c + their (i)
1 1
(iii) v – c again allowing brackets cao 2 M1 for any correct route e.g. MV + VL
6 2 1
or their (i) – v
3
2
or v – their (b)(ii)
3
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Page 3 Mark Scheme: Teachers’ version Syllabus Paper
IGCSE – May/June 2010 0580 42
1 1 1
(b) (i) oe (0.0278) 2 Allow 0.02777 – 0.02778, M1 for ×
36 6 6
6 3 1
(ii) oe (0.167) www 2 2 Allow 0.1666 – 0.1667, M1 for × × 2 oe
36 6 6
1
(c) (i) oe 1
4
1
(ii) oe 1
2
n
4 2
(d) 5 (but not from rounding) 2 M1 for repeating × oe e.g.
6 3
4 (a) (i) Triangle with vertices (–4, 4), (–1, 4), 2 SC1 for translation − 7 or k
(–1, 6) k 3
(ii) Triangle with vertices (1, –3), (1, –6), 2 SC1 two correct vertices or 90° anticlockwise
(3, –6) about (0, 0)
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Page 4 Mark Scheme: Teachers’ version Syllabus Paper
IGCSE – May/June 2010 0580 42
0 − 1
(c) (i) −1 0 2 B1 each column
1 0 ft
(ii) 0 3 2ft ft factor in (b)(ii) only if stretch and can
recover to correct matrix
SC1ft for right-hand column
1 0 0 to 1 0 or n 0 1 0
(iii) 0 1 ft ft 1 to n
n
1ft 0 1
3 0 n 0 1 0 1
n ≠ 0, ± 1
1
for , allow 0.33 or better
3
2 2 2
180 + 115 − 90
5 (a) (cos) M2 M1 for correct implicit expression 902 = ……
2 × 180 × 115
24.98 – 24.99 A2 A1 for (cos) = 0.9064…
90 sin 30 TR 90
(d) M2 M1 for = or other correct
sin 70 sin 30 sin 70
implicit equation
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Page 5 Mark Scheme: Teachers’ version Syllabus Paper
IGCSE – May/June 2010 0580 42
(c) 8 points plotted ft, ignoring (0, 0) P3ft P2ft for 6 or 7 plotted , P1ft for 4 or 5 plotted
Reasonable increasing curve or C1ft Condone starting at (5, 12) and ft only if shape
polygon through their 8 points correct.
(e) (i) 22 – 23 1
(ii) 13.5 – 14.5 1
(iii) 25.5 – 26.5 1
(iv) 136 – 140 must be integer 2 SC1 for 60 – 64 seen and must be integer
8 (a) (p + q)2 – 5 oe final answer 2 SC1 for (p + q)2 oe seen
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Page 6 Mark Scheme: Teachers’ version Syllabus Paper
IGCSE – May/June 2010 0580 42
(b) (i) 96 1
(ii) 48 ft 1ft ft 0.5 their (b)(i)
(iii) 97 ft 1ft ft 145 – their (b)(ii)
(iv) 35 1
180(n − 2)
(c) 20n = 360 oe or = 160 oe M2 M1 for 9e = 180 oe allow diagram to show this
n if reasonably clear
or 180(n – 2) = 8 × 360 oe 8 × 360
360 360 or M1 for 8 × 360 or
or 8 = 180 − n
n n
18 www 3 A1
10 (a) Pentagon 1
Octagon 20 1, 1
(b)(i) 35 1
(ii) 54 1
(d) 31 cao 1
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