UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS

International General Certificate of Secondary Education

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MARK SCHEME for the May/June 2010 question paper for the guidance of teachers

0580 MATHEMATICS

0580/41 Paper 41 (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.

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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.

Page 2

Mark Scheme: Teachers’ version IGCSE – May/June 2010

Syllabus 0580

Paper 41

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 Qu. 1 (a) (b) (c) (d) (e) Answers 11:14 50 12 280 240 (ii) 5 (iii) 4.75 Mark 1 2 2 3 2 1 1 3 M1 for 1 × 2 + 1 × 3 + 17 × 4 + 12 × 5 + 6 × 6 + 3 × 7 condone one slip then M1 dependent result (190) ÷ 40 SC1 for their 190 + 3n SC1 for 2 correct vertices or an enlargement sf 1 with wrong centre 2 B1 each row SC1 for 2 correct ft vertices. Can also be correct regardless of (i) B1 Independent of (i) or (ii) Extra transformations lose all marks B1 Independent of (i) or (ii) B1 Extra transformations lose all marks 2 3 B1 B1 Extra transformations lose all marks B1 Allow word origin for (0, 0) B1 Allow – 90° or 270° (anti-clockwise) B1 each column M1 for (220 + 280) ÷ 10 o.e. M1 for 21 ÷ (4 + 3) × 4 (or 3) o.e. M1 for 0.35 × their 500 (175) M1 dependent × 1.60 M1 for dividing 264 by 1.1 oe Part Marks

2 (a) (i) 4

(b) 3 (a)

190 + 3n 40 + n

Triangle drawn with co-ords at (1, 4), (4, 2), (4, 4)

2 2

(b) (i)

−8 4

−8 8

− 2 8

2 2ft

(ii) Triangle drawn at (–8, 4), (–8, 8), (–2, 8) ft (i) (iii) Reflection cao y – axis or x = 0 cao (c) (i) Translation

2

− 10 o.e. − 10

(ii) Rotation (0, 0) 90° clockwise oe (d)

0 −1

1 0

2

© UCLES 2010

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Mark Scheme: Teachers’ version IGCSE – May/June 2010

Syllabus 0580

Paper 41

4

In (b) and (c) isw any cancelling or changing to other forms, after correct answer seen. Penalty of – 1 for 2 sf decimals or percentages. Do not accept ratio or worded forms. (a) B and

2 1 , oe 5 4

1

Allow any reasonable explanation, e.g. 2 out of 5 greater than 1 out of 4. B1 B1 B1 B1

(b) (i) (ii)

1 3 2 3 , , , 3 4 5 5

4 www 2 2

6 oe 12 42 oe 60

cao

1 2 3 , 0.5 etc M1 for × their i.e. product of 2 3 4 correct branches on their tree 7 , 0.7 etc 10

(iii)

cao

www2

2

1 3 M1 for their (ii) + their × their from their 3 5 tree

cao www2 2

1 , 0.0333(3……..) etc 30 2 1 1 2 1 M1 for × × 0 + × × 3 4 3 5 4

(c)

2 oe 60

5 (a) (b)

200.5… to 201 17.2 (0….)

www 2 www 4

2 4

M1 for 0.5 × 24 × 26 sin 40 A1

oe

M2 for 262 + 242 – 2 × 26 × 24 cos 40 26 2 + 24 2 − BD 2 or M1 for cos 40 = 2 × 24 × 26 A2 or A1 for 295.976.. B1 for Angle C = 110 soi accept on diagram 24 sin 30 oe or M2 for ( BC ) = sin 110 sin 110 sin 30 = oe i.e. a correct implicit M1 24 BC statement soi A1 M1 for their (c) × sin40 oe

(c)

12.8 (12.77…)

www 4

4

(d)

8.208 to 8.230

www 2

2

© UCLES 2010

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Mark Scheme: Teachers’ version IGCSE – May/June 2010

Syllabus 0580

Paper 41

6 (a)

32.5

cao

www4

4

M1 for mid-values seen...