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Notes Mark Scheme Syllabus

IGCSE EXAMINATIONS – JUNE 2003 0580/0581

TYPES OF MARK

Most of the marks (those without prefixes, and ‘B’ marks) are given for accurate results,drawings or statements.

� M marks are given for a correct method.

� B marks are given for a correct statement or step.

� A marks are given for an accurate answer following a correct method.

ABBREVIATIONS

a.r.t. Anything rounding tob.o.d. Benefit of the doubt has been given to the candidatec.a.o. Correct answer only (i.e. no ‘follow through’)e.e.o. Each error or omissiono.e. Or equivalentSC Special cases.o.i. Seen or impliedww Without workingwww Without wrong working�� Work followed through after an error: no further error made�� Work followed through and another error found

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June 2003

INTERNATIONAL GCSE

MARK SCHEME

MAXIMUM MARK: 56

SYLLABUS/COMPONENT: 0580/01, 0581/01

MATHEMATICS

Paper 1 (Core)

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Mark Scheme Syllabus Paper

IGCSE EXAMINATIONS – JUNE 2003 0580/0581 1

© University of Cambridge Local Examinations Syndicate 2003

* indicates that it is necessary to look in the working following a wrong answer.

1 (a) 19.55249(345)

(b) 19.55

1

1 √

2 (a) 3.3 to 3.7

(b) - 0.9

1

1 √

Allow negative values

2.6 - I(a)I

3(a)

50

33 67% 0.68

(b) 25

17

1

1

Allow 0.66, 0.67, 0.68 o.e.

4 42 2* M1 72 �12

5 781000 2* M1 for 550 000 x 1.42

6 366 2* M1 for "97.60" x 3.75

7

9

42* M1 for

4

9 or 0.44..... , 2

4

1, 3

2, 3

22

8 (a) - 30 c.a.o.

(b) v(4u – 3)

1

1 c.a.o.

9

2

1 3* M1 6 – 3x

M1 x + 3x = 6 – 4

10 (a) 0.004

(b) 4 x 10-3

2*

1 √

M1 figs 2 : 500000 or figs 4 inanswer

11 a = 3, b = -1 3* M1 adding or x 2nd equation by 3and subtracting

A1 A1 o.e. (Rearrange andsubstitute scores M1)

Working essential if only oneanswer is correct

12 (a) 88 c.a.o.

(b) 85.5, 86.5

1

1, 1

Not 88.0

B1 both correct and reversed

13 (a) 20 05

(b) (i) 0.4

(ii) 24

1

2*

1 √

Allow 20:05, 8.05pm. Not 20.5 or20h5m

M1 30 � 75

(i) � 60

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IGCSE EXAMINATIONS – JUNE 2003 0580/0581 1


14 (a) 6

43� =

6

7

(b) 5

6 x4

7 =

10

21

2*

2*

M1 for first term o.e.

M1 for improper fractions

15 (a) (i) 28

(ii) 176

(b) pyramid

2*

2 √

1

M1 for ½ x 8 x 7

M1 for 4 x ( i) + 82 A1√

16 (a) 90

(b) 7.71

(c) 113

1

2*

2*

M1 sin40 = PB/12 or 12 = PB sin(a) sin40

M1 � x 62

17 (a) 9.59

(b) 210

2*

3*

M1 8.32 + 4.82

M1 tan x = 3.8

8.4 M1 180 + x at P

If sin or cos used then allow √from (a). NO marks for scaledrawing

18 (a) (i) 35

(ii) 25

(b) similar

(c) 11(.0)

1

1 √

1

2*

60 – ( i)

M1 16.6 = CX o.e. Not 11.1 8.3 5.5

or M1 for 120sin

6.16 =

35sin

CX

TOTAL 56

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November 2003

INTERNATIONAL GCSE

MARK SCHEME

MAXIMUM MARK: 56


MATHEMATICS

Paper 1 (Core)

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IGCSE EXAMINATIONS – NOVEMBER 2003 0580/0581 1


Question Number

Mark Scheme Details Part Mark

1 400 (grams)

1 1

2

($)2.7(0)

2 M1 for 18100

15× o.e.

SC1 for 3.1518100

85=×

2

3 (a)

5

2

1 Accept equivalent fractions, decimals, percentages (with sign)

(b) 0

1 accept

k

0,

5

0 do not accept,

none, not but condone it with 0

2

4 (a) 126o

1

(b)

40(%)

2 M1 for 100360

144× o.e.

3

5 1.71(01…)

2 M1 for 5 sin 20o or 5 cos70° or 1.7

2

6

6 or 1

6

2 M1 for 10

60,

60

10

1,

6

1

1

2

7

144o

3 M2 for 10

90)4102( ×−×

or

10

180)210( ×−

or

180 – 10

360.

After 0, SC1 for answer 36o

3

8 1250 ≤ r.l. < 1350

1 + 1 SC1 if reversed 2

9 (a) 10x2 – 15xy

2 B1 for one term correct

(b) 6x (x + 2)

2 M1 for 6(x2 + 2x) or x(6x + 12) or 2(3x2 + 6x) or 2x(3x + 6) or 3(2x2 + 4x) or 3x(2x + 4)

4

10 (a) 87o

1

(b) 28o

1

(c) 62o √

1 f.t. is (90 – y)

3

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11

Any line through the centre

1

1

1

Lines may be freehand but must go completely through the shape

3

12 x = 4, y = 12

3 M1 for attempting to eliminate one unknown by a correct method A1 for one correct value (x or y)

3

13 (a) (i) 2.4096… (ii) 2.41 √

1

1

f.t. from (i)

(b) 19.3 or 19.32(16…)

2 B1 for 2.68 seen or implied by 19.2…

4

14 (a) Monday, Tuesday and Saturday

1 All three and no extras

(b) -2o

3 B1 for –14 seen + M1 for (their –14) ÷ 7

4

15 (a) (i) 0.28 (ii) 0.275 (iii) 0.2857… or 0.286

1

1

1

(b)

1000

275

, 28%, 7

2

or equivalent √

1

f.t. from (a)

4

16

(a)

4.58(m)

2 M1 for

2225 − s.o.i. e.g. √21

(b)

66.4o or 66.3o – 66.45o

2 M1 for cos-1

5

2 o.e. incl √

4

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17 (a) 3

1 108 etc. penalise once only

(b) -4

1 accept –04

(c) 0

1

(d) -2

1

4

18 (a) 0.4 or 2.6

2 B1 for one correct SC1 if (0.4,0) (2.6,0)

(b) (i) 0 (ii) Correct line from x = -1 to x = 4

1

1

Must be ruled

(c) (0,1), (4,5) √

2 B1 for one correct f.t. from (b) (ii)

6

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June 2004

INTERNATIONAL GCSE

MARK SCHEME

MAXIMUM MARK: 56


MATHEMATICS

Paper 1 (Core)

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MATHEMATICS – JUNE 2004 0580/0581 1

© University of Cambridge International Examinations 2004

11 (a) 110° 2 B1 for Q = 35° s.o.i.(can be on diagram) 70 seen implies B1.

12 (a) 3 1

(b) 0 1

13 (a)(i) 200 40 1

(a)(ii) 5f.t. 1 Only f.t. for simple mental calculation. E.g. 220 ÷ 40 = 5.5

or 200 ÷ 30 = 6 or 7 or 6 2

3 or 6.6 or 6.66 etc

(b) 5.6 1

14 B or 2nd – dependent on M1, M1

3 M1 for a correct method for 1 bottle, implied by figs 615 or 652 seen or figs 1625 or 153… seen. M1(dep) for a complete correct method with consistent units. (Implied by a correct pair of values seen. Alt. Method completely correct is M2

15

2.65 or 2.649(….)

3

M1 for sin 32° = h

5

M1 (dep) for h = 5sin 32° (2.6.…implies M2 provided no obvious scale drawing, which is zero) Other methods can be split similarly. From grads 2.409 or radians 2.757 implies M2

1 39 1

2 842 1 Ignore any or no units after answer. Allow 84200cm.

3 (a) 3

4 final answer 1

(b) 7

100 final answer 1

4 (a) 49 1

(b) 31 1

5 4.5(0) 2 M1 for 18 x 25 or 450 or 4m 50cm seen (18:450 and 18:4.5 also indicate M1)

6 4 1

2 or 9

2 or 18

4 or 4 2

4 2 M1 for 9

4 x 2

(1) seen.

Allow SC1 for 4.5 or 4 1

2oe seen with incomplete or

decimal working.( 9

4 or × 2

(1) oe or 2.25 ÷ 0.5)

Answer only, no working, is 0.

7 141.5, 142.5 2 1 for each answer SC1 for both values correct but wrong way round.

8 2x( 2y – 3z) 2 M1 for 2( 2xy – 3xz) or x( 4y – 6z ) or 2x(wrong expression) Allow omitted last bracket.

9 190.48 or 190.47 or 190 2 M1 for 200 ÷ 1.05, implied by 190.(…..) Not allow 190.5 or 190.4 or 190.00 for 2 marks

10 (a) 0 1 (a) and (b) reversed–no marks

(b) 2 1

18

13

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MATHEMATICS – JUNE 2004 0580/0581 1


16 (a) 13 2 M1 for –3 + 16 seen

(b) y – a or y – a oe b b b Allow a – y –b

2 M1 for a correct step, for clearly dividing by b or y – a seen.

17 Bar Chart 4 S1 correct scale and equal width bars. (Lost for vertical lines drawn) B2 all bars correct height or B1 for any 2 bars correct height. Dots or line graph is B0. L1 correct labels.

18 (a) $4.5(0) 2 M1 for 50 x ( 0.25 or 25) or $12.5(0) or 1250 seen,

or 0.25 – 8 ÷ 50 = (0.09)

or 25 – 800 ÷ 50 = ( 9)

(b) * 56.25 or 56 or 56.3 or 56.2 2f.t. M1 for their (a)/8 x 100 or

their profit for 1 orange × 100 their cost for 1 orange

19 (a) 2826 to 2828 or 2830

2 M1 for π x 302 or π × 0.3

2 and method not spoilt.

(b) * 226.(080) to 226.(240) or 226.(4…)

2f.t.

M1 for his (a) × 80 s.o.i. or correct f.t. answer seen in cubic centimetres.

20 (a) 9 2 M1 for 31 + 5 or 31 – 5 or x – 1.25 = 7.75 4

(b) 14 2 M1 for 4y – 20 = 36 or y – 5 = 9 or better.

21 (a) 00 15 or 12 15am Ignore am added to 00 15

1 Allow a clear time in words. E.g. 15 minutes after midnight. Not 12 15 or 24 15

(b)(i) * 7 h 30min

Allow 7 1

2 or 7.5 hours

1f.t. f.t. their (a)

(b)(ii) * 749.(33….) f.t. 3f.t. B1 for their 7.5 or 7 1

2 or their 450 minutes and

(finally) multiplied by 60 used. M1 for 5620/their time (independent of B1) (f.t. dependent on B1 and M1)

[Watch for 5620 ÷ 7.3 = 769.(86…) implies B0 M1.]

16

9

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November 2004

INTERNATIONAL GCSE

MARK SCHEME

MAXIMUM MARK: 56


MATHEMATICS

Paper 1 (Core)

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Number Answers Mark Notes

1 17 1 Not -17

2 (10 - 5) x (9 + 3) 1 Ignore omission of final bracket only

3 0.56 2 B1 for 5 ÷ 9 or digits 55 (….) or digits 56 Common answer for B1 is 0.55

4 (a) 100 (b) 400

1 1

5 1.5 (0...) 2 M1 for

)534(

5

++

x 3.6

SC1 for 1.2 or 0.9 (ie. Wrong ingredient)

6 (a) 270 (b) (0)45

1 1

7 Obtuse Reflex

1 1

8

0

5

1 + 1 One mark each component. If only number 5 in bracket allow 1 mark.

If 0 scored SC1 for

−

4

2 or

− 4

2

seen, or

5

0

Ignore a line between Components

9

5

3x

7

10

35

30=7

6 or

71

23

×

×

=7

6

M1

E1

Only acceptable method.

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10

(a) a7 (b) b

1 1

Allow b1

11 (a) < (b) =

1 1

12 (a) 3 (b) 2

1 1

Ignore any added words

13 Net of the pyramid. A square with 4 equal isosceles triangles correctly positioned.

2 1 for a square 1 for all 4 triangles, isosceles or equilateral. Reasonable accuracy by eye. Ignore any tabs shown.

14 16.66 cao 3 M1 for 0.15 x 19.60 (implied by 2.94 seen) M1 for 19.60 – his 2.94 (allow if 2.94 is rounded to 2.90, method only) or M2 for 0.85 x 19.60 [allow for (1 – 0.15) x 19.60] Answer 1666 2 marks, 1670 1 mark ww. 16.7(0) implies M2

15 24500 3 M1 for 350 x 350 x 200 or 3.5 x 3.5 x 2 soi A1 for 24500000 or 24.5 seen B1 for his ‘volume’ correctly converted to litres.

16 (a) (i) (base) = 7.5 (ii) (height) = 5.5

1 1

Allow 2 marks for correct answers reversed. Allow 1 mark for one of the answers seen in either (i) or (ii).

(b) 20.6 (25) or 20.62 or 20.6 (3) f.t.

1 A correct calculation of the area using his values of base and height regardless of his values.

17 (a) 1018 (b) 89.38 final answer ft.

1 2

M1 for his (a) x 8.78 soi or SC1 for answer in cents.

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18 (a) 1,2,3,5,6,10,15,30 cao or 1 x 30, 2 x 15, 3 x 10, 5 x 6 cao (b) 2,3,5 or 2 x 3 x 5

2

1f.t.

B1 for 4 correct factors, none incorrect. All the correct primes from his part (a), and at least one prime and no non-primes.

19 (a) 6 (hours) 45 (minutes)

(b) rounds to 52.6 or 52 27

16

1

3f.t.

B1 for 6.75 or 64

3oe used or

his time correctly converted to hours. M1 for 355 ÷ his time. (any form) (55.0…or 0.87….ww implies M1) A1 f.t. provided his (a) correctly converted to hours.

20 (a) 10

(b) 35

4 oe or 0.114 (...)

or 11.4%

2 2

M1 for 7

2 x 35

M1 for 1 -

+5

3

7

2 soi or

[35 - (his (a) + 5

3 x 35] ÷ 35

0.11 or 11% seen imply M1

21 (a) 2.34 x 103 (b) 1.26 x 106

2 2

SC1 for figs 234 seen or 2.3 x 103

SC1 for figs 126 seen or 1.3 x 106

22 (a) diameter (b)(i) rounds to 30.8 or 30.9

(ii) rounds to 56.5 or 56.6

1 2 2

M1 for 0.5 x π x 12 or 12 +

π x 12

(implied by rounding to18.8 or 18.9 or 49.7 seen)

M1 for using π x 62 (implied by 113 (. ) seen

9Dwebsite.tk


June 2005

IGCSE

MARK SCHEME

MAXIMUM MARK: 56


MATHEMATICS

Paper 1 (Core)

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IGCSE – JUNE 2005 0580/0581 1


Question Answers Mark Notes

1 1393000 1 Allow 1393000.0 or 1.393 × 10 6 2 9

30 or 3

10 or 0.3 or 30% isw 1 isw only for incorrect cancelling

3 40 1

4 35 : 8 ignore consistent units

2 M1 for 3500 or 0.8 seen. SC1 Reversed SC1 for 1: 8

35 or 4 3

8:1 ( 35

8:1) or 35k : 8k

(decimal form for SC1 correct to 3sf) 5 1

64 2 B1 for 1

43

or 1

4( )3 or (±) 64 seen.

decimal form only B0

6 (a) 12 only (b) 3 only

1 1

7 63 2 M1 for 28 ÷ 4 x 9 (can be implied by 4

252 )

63.64 or 63.63 implies M1 8 –9 www 2 B1 for – 27 or (+)18 seen

9 255 ≤ weight < 265 2 1 mark for each. Allow 255.0 and 265.0 SC1 for fully correct but reversed

10 3.31 or 3.308 or 3.307(….) 2

17

M1 for 12sin16 (implied by 12 × 0.28 or better) Grads 2.98…. implies M1. 3.3ww no marks

11 900 2 M1 for (5000 x 3 x 6) ÷ 100 oe or B1 for 300 seen SC1 for 5900

12 (s =) (p + q)/t or p + q oe t

2 B1 for p + q seen or correct ÷ by t or p/t = s – q/t or (p –q)/t SC1 for p + q/t or p/t + q

13 (a) similar (b) 145

1 1

14 rounds to 1410 isw (isw only for incorrect rounding eg 1413 = 141)

2 M1 for π × 15 2 × 2 (or π × 1.5 2 × 0.2 )

SC1 if π × 30 2 × 2 calculated correctly

(rounds to 5650 or 5660) (allow 3(.0)used)

1.41 cm 3 is 2 marks, 1.41 or 5.65 implies M1

15 (a) multiple of 24

(b) 11

24

1 2

ignore extras if lowest correct M1 for a correct attempt at two equivalent fractions (e.g.. 5×8

48 and 3×6

48 seen or better)

ww. and decimals alone zero 16 (a) 23 isw

(b) 43 (c) 4n + 3 oe final answer

1 1ft 1

14

ignore extras even if incorrect their (a) + 20 allow any unsimplified form e.g. 7 + (n – 1) × 4 or 7 + 4n – 4

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IGCSE – JUNE 2005 0580/0581 1


17 (a) 4x + 17 final answer (b) x (5x – 7)

2 1

B1 for –3x + 12 or 4x or +17 seen (+17 strictly www) condone missing final bracket

18 2.45 3 B1 for 1.20 or 1.35 seen. (or 120 or 135) M1 for 5 – their (1.5 × 0.8 + 3 × 0.45) or 500 – their (1.5 × 80 + 3 × 45)

19

(a) (i) 9 – 3 × 2 3

(ii) (equals) 1 (b) 1.01

1

1ft

1

allow slip of denominator as 3.0 or 3.00 (not allow zeros in other figures) their (a)(i) provided order of operation is as seen and both (a)(i) and (a)(ii) are to a maximum of 1dp apart from zeros

20 (a) Panama, (Guyana), Colombia, Brazil (b) 5

1 2

allow figures if correct

M1 for (1.14 × 10 6) ÷ (2.15 × 10 5) implied by figs 53(0……)

21 (a) 5.6(0) oe (allow 5 3

5)

(b) 2.4(0) oe www (allow 2 2

5)

2

1ft

15

M1 for 35 ÷ 100 × 16 SC1 for $10.40 $8 – their (a) if positive result from their (a) allow saving calculated from comparing costs or savings

22 (a) 10 (b) 20 (c) on the graph (d) 12 (allow 10 < time < 15) (allow 12 from calculation)

2 1 1

1ft

M1 for use of distance ÷ time with figures. 5/0.5, 5/30, 5/6, 5/0.30 only. Not 5/8.00, 5/0.3 ruled single line from 8.00 am home continued to school, 12 km line. Ignore beyond 12 km line must cross within square ft their intended single ‘straight’ line (need not be ruled) and within a square, not on the boundary unless actually on a boundary

23 (a) 90 (b) 65 (c) 25

1 2ft 2ft

10

M1 for 180 – 25 – their (a) [155 – their (a)] ft. 90 – their (b) B1 for angle DEB = 90° used or B1 for angle CEB = 65° seen

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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS

International General Certificate of Secondary Education

MARK SCHEME for the November 2005 question papers

0580/0581 MATHEMATICS 0580/01, 0581/01 Paper 1 (Core), maximum raw mark 56

This mark scheme is published as an aid to teachers and students, to indicate the requirements of the examination. It shows the basis on which Examiners were initially instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began. Any substantial changes to the mark scheme that arose from these discussions will be recorded in the published Report on the Examination. All Examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes must be read in conjunction with the question papers and the Report on the

Examination.

• CIE will not enter into discussion or correspondence in connection with these mark schemes.

The minimum marks in these components needed for various grades were previously published with these mark schemes, but are now instead included in the Report on the Examination for this session. CIE is publishing the mark schemes for the November 2005 question papers for most IGCSE and GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

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IGCSE – NOVEMBER 2005 0580/0581 1



1 1.01(00) x 104 1

2 x(3y – 2)

1

3 6950 1

4 √5 1

5 5x = 8 + 7 or better seen. (x = ) 3

M1 A1

(Correct first step)

6 12 2 SC1 correct method seen

18

1

2

1÷ or better.

7 (a) (b)

10 (allow –10) 12

1 1

8 P – 2b = 2a

2

2bP −

oe

M1 A1

9 (a) 100

7

1 Allow 0.07 or 7%

(b) 72% 1 Allow 0.72 or

100

72

(c) 0.072 and 7.2% 1 In this form. [15]

10 (a) (b) (c)

61 or 67 63 64

1 1 1

11 (a)

− 2

5

2 1 mark for each correct component.

(b) Correct Vector Drawn 1

12

2.121sin

height=

° oe or better

M1 (alt. method) 1200 seen B1 C’s 1200 sin 21o M1 430 (.0...) A1 f.t.

0.43(0……) 430(.0….)

A1 B1ft

13 (Decrease) 200 000 B1 (alt. method)

2700000

2500000x 100 or 92.5 B1

subtract answer from 100 M1

1000002700

000200×

Their

M1

7.41 or 7.40(7….) A1

14 (a) (b) (c)

> < <

1 1 1 [15]

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IGCSE – NOVEMBER 2005 0580/0581 1



15 (a) (b) (i) (ii)

0.5 not 0.50 10 – 6 x c’s 0.5 = 7 7.0908

1 1f.t. 1

Only f.t. c’s (a) if it is 0.4 (0) or 0.50 or 0 Allow 7.6 or 8 from 0.4

16 (a) (b) (c)

3r – 3s or 3(r – s) q or q1 p4

1 1 1

17 (a) (b)

A clear attempt to multiply each by 3 and add, or equivalent. 60 9

M1 A1 1f.t.

Must be a clear use of Dalila’s intended total from (a) subtract 12

18 (a) (b)

160 Their (a) π÷

50.9(…..) or 51

1 M1 A1

19 (a) (b) (c)

29.25 or 29.2 or 29.3 18 Their (a) ÷2.20 14

1 1 M1 A [16]

Implied by 13.3 or 13.2 (...) seen

20 (a) (b)

90010035 ×÷

=315 (Payments) 720 Deposit + Payments – 900 135

M1 A1 B1 M1 A1 f.t.

Implied by 1035 seen No follow through for negative answer

21 (a) 62 1 (b)

2

12

1

(c) (i) Ruled line through (0, 0) and (1, 16) Through and further than (5, 80)

B1 B1

Dependent

(ii) 5 1f.t. [10]

Intersection of their line with the given line.

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MARK SCHEME for the May/June 2006 question paper

0580 and 0581 MATHEMATICS

0580/01 and 0581/01 Paper 1, maximum raw mark 56

These mark schemes are published as an aid to teachers and students, to indicate the requirements of the examination. They show the basis on which Examiners were initially instructed to award marks. They do not indicate the details of the discussions that took place at an Examiners’ meeting before marking began. Any substantial changes to the mark scheme that arose from these discussions will be recorded in the published Report on the Examination. All Examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes must be read in conjunction with the question papers and the Report on the

Examination. The minimum marks in these components needed for various grades were previously published with these mark schemes, but are now instead included in the Report on the Examination for this session.

• CIE will not enter into discussion or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the May/June 2006 question papers for most IGCSE and GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

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IGCSE – May/June 2006 0580 and 0581 01


1 –27 1

2 0.09 9%

100

9

1

3 10000 or 1 x 104 oe. 1

4 (a) 7 1

(b) Any multiple of 70 (e.g. 490) 1

5 2.71(4….) 2 M1 for attempt at cube root of 20

6 (a) 0.075976(….) 1

(b) 0.076 1 f.t. f.t. candidates (a)

7 345000 355000 1, 1

8 2x(x – 3y) 2 M1 for 2(x2 – 3xy) or x(2x – 6y) or 2x(……)

9 (a) (i)

10

4 oe.

1

(ii) 0 1

(b)

12

7 o.e.

1

10 (a) p5 1

(b) q7 1

(c) r6 1

19

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11 (a) ($) 25 1

(b) ($) 551.25 2 M1 for 500 x 1.052 or (c’s (a) + 500) x 1.05

12 (a) A-2 correct lines and B-6 correct lines 1, 1 Allow not ruled and small inaccuracies.

(b) 2 1

13 (x=) 5, (y=)–3 3 M1 correct method to eliminate y or x. (add equations or correct multiply and subtract)

A1, A1

ww allow SC1 for 1 correct answer.

ww both correct, full marks.

14 (a) 6 (h) 50 (min) 1

(b) 37.5 (%) 2 B1 for 9 (hours) seen or M1 for c’s 9 ÷ 24 x 100

15 (a)

−

12

3

1

(b) Parallel oe. 1

CD is 3 times as long as AB oe. 1

16 (a) (hockey) 105, (cricket) 30 2 1 mark each correct entry.

(b) Correct line on pie chart to divide hockey and cricket. (30 ± 2) degrees to left of vertical oe.

1ft ft only if the angles in (a) total 135°

(c) Football 1

19

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17 (a) 54 2 M1 for 90 ÷ 5 x 3

(b) 9.15(….) 2 M1 for 57.5 ÷ (2π) or SC1 for 57.5 ÷ π. (implied by 18.3…)

18 (a) Net of the cuboid 2 M1 for a net with 6 correct size rectangles.

A1 for a fully correct net.

(b) 52 2ft M1 for 5 or 6 areas calculated and added

or SC1 for answer of 26.

ft only if 5 or 6 rectangles are shown in part (a).

8

19 (Joseph $) 17.5(0) 2 M1 for 30 ÷ 12 x 7.

(Maria $) 9 2 M1 for 30 ÷ 100 x 30.

(Rebecca $) 3.50 1ft 30 – c’s Joseph – c’s Maria.

20 (a) 1.13 x 106 2 M1 for 2000 x 565 seen or B1 for figs 113

(b) 4.42(….) x 10–2 3 M1 for 25 ÷ 565 soi and B1 for figs 442(….)

10

Total 56

9Dwebsite.tk



International General Certificate of Secondary Education MARK SCHEME for the October/November 2006 question paper

0580, 0581 MATHEMATICS

0580/01, 0581/01 Paper 1 (Core), maximum raw mark 56

This mark scheme is published as an aid to teachers and students, 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.

All Examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated.

Mark schemes must be read in conjunction with the question papers and the report on the examination. The grade thresholds for various grades are published in the report on the examination for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 2006 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

9Dwebsite.tk



IGCSE - OCT/NOV 2006 0580, 0581 1

© UCLES 2006


1 −13.1 1

2 2 × ( 3 − 4 ) + 5 = 3 1 & no other brackets

3 Negative (allow –ve) 1 Not allow ‘N’ or ‘n’ or ‘No’ 4 18 1 5 12.09 or 12.1 1 Not 12.10 6 2a( ab − 3 ) final answer. 2 SC1 for 2( a 2

b − 3a ) or a( 2ab − 6 ) or 2a( ab + 3 ) or 2a( ab – 6 ) final answer.

7

(a) 0.0561 (b) 15300

1 1

(Answers may be in standard form)

8 3x6y

3 or 3(x 2y) 3 2 SC1 for x 6or y 3 seen in final answer

9 (a) 79507

(b) 80000

1 1ft

ft provided (a) > 500 and not a multiple of 1000.

10

10

6

50

33

3

2

2 SC1 for reverse order. M1- at least 2 fractions correctly compared in the same form. (decimal, percentage or common denominator)

11 (x = )

5

6 oe isw

2 M1 for -2 + 8 = 10x – 5x oe or better.

12 B (and) D 1,1 Either way round. -1 each extra letter. 13 3.51 × 10 3− 2 B1 for figures 351 seen

14 15.55 ( ≤ length < ) 15.65 2 1 mark for each. SC1 for fully correct but reversed.

15 (a) 3.2 (b) 384

1 1 ft

their (a) × 120.

16 (a) 3 or 2 3 = 8

(b) −4 or 3 −4 = 81

1 1

SC1 for 2 3 and 3 4− in the answer spaces

17 (a) art 314

(b) π4

A oe

1

2

M1 for π4

Aseen

18 (a)(i) 30 (ii) Straight line from (11 00, 20) to (11 45, 80) (b) ‘Correct’ horizontal line ‘Correct’ return journey line

1

1 1 1

Ignore all beyond (11 45, 80) Horizontal line @ 80, 4 units long. Line to (14 30, 0)

15

19

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IGCSE - OCT/NOV 2006 0580, 0581 1

© UCLES 2006

19 (a) 52.2(0) 83.7(2)

(b) 7.8(0)

(c) art 36.4 allow –ve. Accept 36www

1 1ft

2ft

60 − their ($3.48 × 15) M1 for ((their 83.72 − 15 × 3.55)/their 83.72) × 100 or 100 − ((15 × 3.55)/their 83.72) × 100

20 (a) 2 correct lines on H 1 correct line on W (b) 1 2

1 1 1

1

Ruled not essential in either. Judge by eye. No extraneous lines on either. Allow 0 or indication of no rotational symmetry.

21

(a)

4

0 Final ans

(b)

− 24

30Final ans

2 2

Ignore ‘fraction’ lines in (a) and (b) Allow coordinate form 1 mark for each correct component. 1 mark for each correct component.

22 (a)

)1020(5

2010

÷−

+

(b) 10 cao. (c) 9.49 cao.

2

1

2

SC1 for 3 or 4 of the numbers given to 1 significant figure. B1 for 9.485(5)… to 9.493 seen. (Allows for 22 ÷ 13 rounded to 3sf) If zero, SC1 for 9.5www as final answer (Not 9.50 but check for possible B1)

23 (a) (i) 36

31 oe isw 1 Fraction, decimal or percentage only.

(ii) 0 Final ans 1 6

0 , 36

0 , 0% or zero. Not allow ‘no’, none,7

0 or 0/0.

(iii) 1 1 Allow 6

6 or 36

36 or 100%.

(b) 99

17 isw 1 If decimal, allow art 0.172

(c) Piero’s 1 Can be indicated by 102

21

Total for the paper is 56 marks

17

5

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0580/0581 MATHEMATICS

0580/01 and 0581/01 Paper 1 (Core), maximum raw mark 56

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.


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 2007 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

9Dwebsite.tk



IGCSE – May/June 2007 0580/0581 01

© UCLES 2007

1 −2 B1

2 0.58 <

5

3 < 62(%)

B1 Accept answer in alternative form

provided equivalence is clear.

3 7 (h) 55 (min) B1

4 24 B1

5 Negative B1

6 (a)

(b)

Jan

26(.0)

B1

B1

Not just –10.2 but ignore if included.

Allow −26

7 145 + 180 or

360 − their acute angle at L

325

M1

A1

Must be clearly indicated in working

or diagram.

[9]

8 (a)

(b)

−

3

1

(–2, –1)

B1

B1

SC1 for both answers with

components of (a) and coordinates of

(b) reversed.

i.e.

−1

3for (a) and (–1, –2) for (b)

9 2x2+ 3xy or x(2x + 3y) B2 B1 for 3x

2 − x2+ 3xy or

x(3x – x + 3y) seen.

SC1 for answer 2x2 − 3xy oe

or 2x2 seen in final answer of 2 terms.

10 75° B2 B1 for 25° or 50° seen on diagram or

clear in working that angle BCD is

25° or angle DCE is 50°.

Minimum - arc seen in diagram.

11 (a)

(b)

Equilateral

(Triangular) prism

B1

B1

Not equal

If qualified must be triangular

(or triangle).

[8]

9Dwebsite.tk

sennsh

1st variant Mark Scheme



IGCSE – May/June 2007 0580/0581 01

© UCLES 2007

12 (y =) 3x − 1 B2 B1 for mx – 1 or 3x + c where m and

c are integers with m ≠ 0 and

c ≠ 5.

13 (a)

(b)

(c)

10

3

−2

B1

B1

B1

SC2 for 410, 23 and 5–2.

SC1 for two of the above

14 (a)

(b)

250 ÷ 1.19886

208 to 210.084…..

1.20

M1

A1

B1

Allow division by 1.19 to 1.2

One and only one zero is essential

15 180 –

6

360

(x =) 120

(y =) 150

M1

A1

B1ft

Alt. (2 × 6 – 4) × 90 ÷ 6 oe

360 – (90 + their x) ft if positive

ww. reversed answers 2 marks.

Alt. (y first) 6

360+ 90 M1 150 A1

(x=) 120 B1ft

16 (a)

(b)

15 × 5.40 + 5 × 3 − 80

16

20

M1

A1

B1ft

ft their (a) ÷ 80 × 100

(provided profit >0)

If 0 scored in parts (a) and (b) allow

SC1 for 96 seen

[14]

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IGCSE – May/June 2007 0580/0581 01

© UCLES 2007

17 (a)

(b)

5.1 ×108

29.4 × their (a)/ 100

art 1.5 × 108 oe

B2

M1

A1cao

B1 for 5.1 ×10n where n is an integer

greater than 1

Calculator form; penalise 1 mark

each form.

May revert to given value.

Answer does not need to be in

standard form. (e.g. 149940000)

If M0, SC1 for 3.6 × 108

18 (a)

(b)

(AB2 = ) 12002 + 9002

1500

tan (=) 900/1200 oe

art 36.9

M1

A1

M1

A1cao

Indicated by 2250000 seen

Allow art 1500 if sin or cos used and

(b) done before (a).

For sin or cos method allow their (a)

for M1 only.

19 (a)

(b)

(c)

263

Correct construction with arcs

109.5

B1

B2

B1

B1 without arcs, accuracy 2mm

SC1 for ‘correct’ mirror image with

arcs.

[12]

20 (a) (i)

(a) (ii)

(a) (iii)

(b)

50

Sum divided by 15

43.9(3…….)

Attempt to order estimates

47

(Low) Extreme values oe

B1

M1

A1

M1

A1

B1

Indicated by answer of 43 to 45 or

calculation shown.

(Total = 659)

Must be at least 7 values

Two very low values etc.

Must not refer to extreme high

values.

21 (a)

(b)

(c) (i)

(c) (ii)

30 + 60 (seconds)

90 (seconds)

D to E

1280(m)

400 used

their (c)(i) divided by 400 (only)

3.2

M1

A1

B1

B1

B1

M1

A1ft

SC1 for 30 or 60 seen.

Any clear indication of section

Allow 1270 to 1280

Also indicated by

310 or (400 – their (a)).

ft correct to 3 significant figures.

[13]

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IGCSE – May/June 2007 0580/0581 01

© UCLES 2007

1 −5 B1

2 0.79 <

5

4 < 81%

B1 Accept answer in alternative form

provided equivalence is clear.

3 7 (h) 45 (min) B1

4 24 B1

5 Negative B1

6 (a)

(b)

Jan

13.2

B1

B1

Not just –10.2 but ignore if included.

Allow −13.2

7 125 + 180 or

360 − their acute angle at L

305

M1

A1

Must be clearly indicated in working

or diagram.

[9]

8 (a)

(b)

−

3

1

(–2, –1)

B1

B1

SC1 for both answers with

components of (a) and co-ordinates of

(b) reversed.

i.e.

−1

3for (a) and (–1, –2) for (b)

9 3x2+ 2xy or x(3x + 2y) B2 B1 for 4x

2 − x2 + 2xy or

x(4x – x + 2y)seen.

SC1 for answer 3x2− 2xy oe or

3x2 seen in final answer of 2 terms.

10 80° B2 B1 for 35° or 45° seen on diagram or

clear in working that angle BCD is

35º or angle DCE is 45°.

Minimum - arc seen in diagram.

11 (a)

(b)

Equilateral

(Triangular) prism

B1

B1

Not equal.

If qualified must be triangular

(or triangle).

[8]

9Dwebsite.tk

sennsh

2nd variant Mark Scheme



IGCSE – May/June 2007 0580/0581 01

© UCLES 2007

12 (y =) 2x − 3 oe B2 B1 for mx – 3 or 2x + c where m and

c are integers with m ≠ 0 and

c ≠ 3

13 (a)

(b)

(c)

9

5

−2

B1

B1

B1

SC2 for 39, 25 and 6–2.

SC1 for two of the above

14 (a)

(b)

270 ÷ 1.19886

225 to 226.891

1.20

M1

A1

B1

Allow division by 1.19 to 1.2

One and only one zero is essential.

15 180 –

6

360

(x =) 120

(y =) 150

M1

A1

B1ft

Alt. (2 × 6 – 4) × 90 ÷ 6

360 – (90 + their x) ft if positive

ww. reversed answers 2 marks.

Alt. (y first) 6

360 + 90 M1 150 A1

(x=) 120 B1ft

16 (a)

(b)

15 × 5.80 + 5 × 3 − 90

12

13(.3…..)

M1

A1

B1ft

ft their (a) ÷ 90 × 100

(provided profit >0)

If 0 scored in parts (a) and (b) allow

SC1 for 102 seen.

[14]

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IGCSE – May/June 2007 0580/0581 01

© UCLES 2007

17 (a)

(b)

5.1 ×108

29.4 × their (a)/ 100

art 1.5 × 108oe

B2

M1

A1cao

B1 for 5.1 ×10n where n is an integer

greater than 1.

Calculator form; penalise 1 mark each

form.

May revert to given value.

Answer does not need to be in

standard form. (e.g. 149940000)

If M0, SC1 for 3.6 × 108

18 (a)

(b)

(AB2 = ) 11002 + 8002

art 1360

tan (=) (800/1100) oe

36 to 36.03

M1

A1

M1

A1cao

Indicated by 1850000 seen.

For sin or cos method allow their (a)

for M1 only.

19 (a)

(b)

(c)

276

Correct construction with arcs

119.5

B1

B2

B1

B1 without arcs, accuracy 2mm

SC1 for ‘correct’ mirror image with

arcs.

[12]

20 (a) (i)

(a) (ii)

(a)(iii)

(b)

50

Sum divided by 15

44.1(3…..)

Attempt to order estimates

48

(Low) Extreme values oe

B1

M1

A1

M1

A1

B1

Indicated by answer of 43 to 45 or

calculation shown.

(Total = 662)

Must be at least 7 values

Two very low values etc.

Must not refer to extreme high values.

21 (a)

(b)

(c) (i)

(c) (ii)

30 + 60 (seconds)

90 (seconds)

D to E

1280 (m)

400 used

their (c)(i) divided by 400(only)

3.2

M1

A1

B1

B1

B1

M1

A1ft

SC1 for 30 or 60 seen.

Any clear indication of section.

Allow 1270 to 1280

Also indicated by

310 or (400 – their (a)).

ft correct to 3 significant figures.

[13]

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MARK SCHEME for the October/November 2007 question paper






• CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 2007 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

9Dwebsite.tk



IGCSE – October/November 2007 0580/0581 01

© UCLES 2007


1 −13 1 Not 13–

2 ($) 10

2 M1 for 35 ÷ (5 + 2) or better. SC1 for ($) 25 only or 25:10 or 25 and 10 in the answer space.

3 (x = ) − 1 2 M1 for 1 − 4 = x + 2x oe Not embedded unless x = –1 seen.

4 60 2 M1 for 52.50 ÷ 0.875. SC1 for answers 59.659 rot or 60.3448 rot (from rounding 0.875 to 0.88 or 0.87.)

5 2x(2y − 1) final answer 2 SC1 for x(4y − 2) or 2(2xy − x) or 2x(2y +1) Or SC1 for 2x(2y – 1) not as final answer.

6 art39.8 2 M1 for tan p = 25

30 oe

7 1250 (≤ d <) 1350 2 13

1 mark for each in correct order

8 (a) Two correct lines of

symmetry, No extra lines

(b) Parallelogram

1

1

Lines must be a minimum of length and height of the figure.

9 (a) 15 (b) 11

9 oe

22

18 − 15

18 = 7

18 oe

1 B1 E1

Eg 66

54 Allow 9

9 + 2

9 or better

Must be finally reduced to 7

18

10 (a) 30 (b) 12

1 2ft

M1 for 360 ÷ either 30 or their (a) ft. answer only when calculation gives an integer > 2

11 art38.3 3

11

M1 for d

50 = cos (180 – 140) oe soi

M1dep. for ( d =) 50 cos (180 – 140) oe SC1 for 32.1 (distance east)

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maigna

First variant




© UCLES 2007


12 (a) −3

(b) (y =) −3x + 3 Final answer

1 2ft

B1 for their (a)x or +3 as intercept seen in the equation. Not y = 3

13 (a) 55 or art 54.6 (b) 15

2 2

M1 for 131 ÷ 240(× 100) implied by 54.5

M1 for 6.25 ÷ 100 × 240 SC1 for answer 225

14 (a) art 25.1 www (b) 61 (Can be on diagram)

2

2

M1 for π × 8 or 2π × 8 ÷ 2 implied by answer of 25 M1 for 90 – 29 or 180 – 90 – 29

SC1 for angle Q = 90° soi

15 (a) 1

(b) x 6

(c) x2

9

1 1 2

15

M1 for 1

( 3x)2

or better. E.g. ( x

3) 2

B1 if answer contains x 2 as numerator or

3 2(or 9) as denominator.

16 (a)(i) 18 000

(ii) 1.8 × 10 4 (b) 0.056

1 1 ft 2

1.7598 × 10 4 gets 0 B1 for 0.06 or 0.0565 or 0.05649 or 0.057 seen SC1 for final answer 0.0560(0)

17 (a) ($) 16.2(0)

(b) ($) 16.3(2) or 16.3(0)

2

2

M1 for (200 × 4.05 × 2)/100 SC1 for 216.2(0)

M1 for 200(1.04) 2 − 200oe SC1 for 216.3(2). SC1 for both 8.(00) and 8.3(2) seen

18 (a)(i) Vector KL drawn (ii) (0,2)

(b) (1, −1)

1

1 ft 2

12

If arrow shown, it must be correct. Only ft their point if labelled L. M1 for vector PS drawn or for

(PS =) 4

2

SC1 Point S on diagram at (1, –1)

19 (a)(i) 60 (m/min) (ii) 3.6 (km/h) (b) 3 (km/h)

1 2cao

2

5

M1 for their (a) × 60 ÷ 1000

or 1.2 ÷ 0.33 or better

M1 for total distance(figs 15) ÷ total time Values seen, but independent of units.

9Dwebsite.tk

maigna

First variant

maigna

Second variant




© UCLES 2007


1 −12 1 Not 12–

2 ($) 25 2 M1 for 45 ÷ (4 + 5) or better SC1 for ($) 20 only or 20:25 or 25 and 20 in the answer space.

3 (x = ) − 2 2 M1 for 2 − 10 = x + 3x oe Not embedded unless x = –2 seen.

4 80 2 M1 for 70.80 ÷ 0.885 SC1 for answers 79.55 rot or 80.45 rot from rounding 0.885 to 0.89 or 0.88)

5 2q(p − 2) final answer 2 SC1 for q(2p − 4) or 2(pq − 2q) or 2q(p + 2) or SC1 for 2q(p – 2) not as final answer.

6 art34.5 2 M1 for tan p = 22

32 oe

Grads 38.3 or rads 0.6023 check for M1 A0 only.

7 8750 (≤ d <) 8850 2

13

1 mark for each in correct order SC1 for fully correct but reversed

8 (a) Two correct lines of

symmetry. No extra lines.

(b) Parallelogram

1

1

Lines must be a minimum of length and height of the figure.

9 (a) 15 (b) 17

12 oe

34

24 − 15

24 = 19

24 oe

1 B1

E1

Eg 68

48 Allow 12

12 + 5

12 or better

Must be finally reduced to 19

24

10 (a) 20 (b) 18

1 2ft

11

M1 for 360 ÷ either 20 or their (a) Ft answer only when calculation gives an integer >2

11 art34.6 www 3 M1 for d

40 = cos (180 – 150) oe soi

M1dep for ( d =) 40 cos (180 – 150) oe SC1 for 20 (distance east) Grads 35.6 or rads 6.17 check M2 A0 only.

9Dwebsite.tk

maigna

Second variant




© UCLES 2007


12 (a) −2

(b) (y =) −2x + 4 Final answer.

1 2ft

Allow –2

1 and –4

2 or 2

–1 or 4

–2

B1 for their (a) x or +4 as intercept seen in the equation. Not y = 4

13 (a) 48 or art 47.8 (b) 12

2 2

M1 for 153 ÷ 320 (× 100)

M1 for 3.75 ÷ 100 × 320 SC1 for answer 308

14 (a) art 40.8 or art 40.9 (b) 57

2

2

M1 for π × 13 or 2π × 13 ÷ 2 implied by answer of 41 M1 for 90 – 33 or 180 – 90 – 33

SC1 for angle Q = 90° soi

15 (a) 1

(b) y 8

(c) p2

25

1 1 2

15

M1 for 1

5

p( )2 or better. E.g. (

p

5) 2

B1 if answer contains p 2 as numerator or

5 2(or 25) as denominator

16 (a)(i) 16 000

(ii) 1.6 × 10 4 (b) 0.0037

1 1 ft 2

1.5583 × 10 4 gets 0. B1 for 0.004 or 0.00372 or 0.003718 seen. SC1 final answer 0.00370(0)

17 (a) ($) 48.4(0)

(b) ($) 49.4(4) or 49.4(0)

2

2

M1 for (400 × 6.05 × 2)/100 SC1 for 448.4(0)

M1 for 400(1.06) 2 − 400 SC1 for 449.44 SC1 for 24 and 25.4(4) seen

18 (a)(i) Vector KL drawn correctly (ii) (0, 2) (b) (2, 0)

1

1 ft 2

12

If arrow shown, it must be correct Allow L not labelled. Only ft their point if labelled L. M1 for vector PS drawn or for

(PS =) 6

4

Ignore ‘fraction’ line.

SC1 Point S on diagram at (2, 0)

19 (a)(i) 45 (m/min) (ii) 2.7 (km/h) (b) 3.2 (km/h)

1 2cao

2

5

M1 for their (a) × 60 ÷ 1000

or 0.9 ÷ 0.33 or better

M1 for total distance(figs 16) ÷ total time Values seen, but independent of units.

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Second variant











9Dwebsite.tk

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First variant



IGCSE – May/June 2008 0580, 0581 11

Abbreviations

aro Answer rounding to BOD Benefit of the doubt is to be given to the candidate CAO Correct answer only eeo Each error or omission NR Answer space is completely blank o.e. or equivalent SC Special Case www Without wrong working ft or √ Work has been followed through after an error dep Dependent on the previous mark

Qu Answer Mark Part Marks/Notes

1 13 1

2 2 (h) 16 (min) cao 1 If not in the answer space units must be clear. E.g. Not 2:16 or 2.16.

3 196 1

4 10 1

5 33(%) < 1/3 < 0.35 1 Accept the values in any form. 1/3 must be to 3 or more s.f.

6 –14 1

7 3.62 × 10–3 cao 1

8 (a) 2 1

(b) 2 1

9 ($)1278 2 M1 284 ÷ 2 × 9 or 284 ×

2

9 or better.

10 11.5 Ğ h < 12.5 1 + 1 1 mark for each value in correct place.

11 ($)1.40 or 140 cents 2 M1 2.45 ÷ (4 + 3) implied by 0.35. SC1 for answer 140. For answer in cents units must be stated.

12 (a) 24

13 isw 1

(b)

20

11 isw 1

Ignore further attempts at cancelling in (a) and (b). Allow equivalent fractions in (a) and (b). SC1 Both correct but written as decimals or %. (Give mark in part (b)).

13 7.5 or 7½ 2 M1 ½ × 8 × h = 5 × 6 or better.

Implied by 4

30 or

2

15seen.

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First variant



IGCSE – May/June 2008 0580, 0581 11

14 (a) 35.81415(6…) or 35.8188 or 35.796

1

(b) 36 (cm) (Ignore trailing zeros)

1 ft

π from calculator value or 3.142 or 3.14 respectively. 36 or follow through from their (a) but only if the answer to (a) is greater than 1.

15 Vertices (3,1), (5,1), (2,4), (0,4) and ruled parallelogram drawn.

2 M1 3 or 4 vertices correctly plotted. If M0, SC1 Correct reflection in y = 3. (3,5), (1,5), (4,2), (6,2).

16 4.578 to 4.58 2 M1 2.42 + 3.92 or better. Square root not essential for M1. Implied by 20.97 or 5.76 + 15.21 seen.

17 ($)1.14 or 114 cents 2 M1 8 × 0.68 – 2 × 2.15 or 8 × 68 – 2 × 215. For answers in cents units must be stated.

18 3x(2 – 3xy) final answer 2 SC1 3(2x – 3x2y) or x(6 – 9xy) or 3x(2 + 3xy) as answers.

19 (a) (i) –27 (ii) –48

1 1

(b) z 1 Allow z1.

20 (a) 4 or 2 1

(b) 81 or 9 1

(c) 64 or 8 1

(d) 14 or 3.7(4…) 1

21 (a) 25 1

(b) 43 1

(c) 3n + 10 oe final ans. 2 SC1 3n + k oe (k ¸ 10) as answer.

22 (a) 12 1

(b) (i) 0.83(3…) or

12

10 oe isw

(ii) 49.8 to 50

1 1 ft ft 60 × their (b)(i) correct to 3sf.

(c) 46 2 W1 for (CD = ) 12 seen in working space, or answer line or between dotted lines at C and D.

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First variant



IGCSE – May/June 2008 0580, 0581 11

23 (a) ($)1020 2 M1 for 100

8.534000 ××

or SC1 for 5020 final ans.

(b) ($)1038.85 Allow 1039 or 1038.848 or

1038.8 or 1038.9 or 1038.84

3 M2 for

3

100

814000

+× or better.

or M1 for

2

100

814000

+× or better.

Alt. M1 for (4000 + 4000 × 0.08) × 0.08. M1 dep for ‘4665.60 × 0.08. (NB Interest only method)

24 (a) (i)

4

0 2 1 mark for each component.

(ii)

−

4


(b) Line segment from P to (–1, 6) 2 W1 for (–1, 6) indicated or

−

4

2 seen anywhere.

If zero, SC1 for line segment from P to (–1, k) or to (k, 6) or a line through P and (–1, 6).

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First variant











9Dwebsite.tk

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Second variant



IGCSE – May/June 2008 0580, 0581 12

Abbreviations

aro Answer rounding to BOD Benefit of the doubt is to be given to the candidate CAO Correct answer only eeo Each error or omission NR Answer space is completely blank o.e. or equivalent SC Special case www Without wrong working ft or √ Work has been followed through after an error dep Dependent on the previous mark

Qu Answer Mark Part Marks/Notes

1 9 1

2 3 (h) 29 (min) cao 1 If not in the answer space units must be clear. E.g. Not 3:29 or 3.29.

3 196 1

4 20 1

5 33(%) < 1/3 < 0.35 1 Accept the values in any form. 1/3 must be to 3 or more s.f.

6 –9 1

7 3.62 × 10–3 cao 1

8 (a) 2 1

(b) 2 1

9 ($)1012 2 M1 276 ÷ 3 × 11 or 276 ×

3

11 or better.

10 11.5 Ğ h < 12.5 1 + 1 1 mark for each value in correct place.

11 ($)1.25 or 125 cents 2 M1 2.25 ÷ (5 + 4) implied by 0.25. SC1 for answer 125. For answer in cents units must be stated.

12 (a) 29

17 isw 1

(b)

20

13 isw 1

Ignore further attempts at cancelling in (a) and (b). Allow equivalent fractions in (a) and (b). SC1 Both correct but written as decimals or %. (Give mark in part (b)).

13 13.5 or 13½ 2 M1 ½ × 8 × h = 6 × 9 or better.

Implied by 4

54 or

2

27seen.

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Second variant



IGCSE – May/June 2008 0580, 0581 12

14 (a) 32.67256(3…) or 32.6768 or 32.656

1

(b) 33 (Ignore trailing zeros)

1 ft

π from calculator value or 3.142 or 3.14 respectively. 33 or follow through from their (a) but only if the answer to (a) is greater than 1.

15 Vertices (3,1), (5,1), (2,4), (0,4) and ruled parallelogram drawn.

2 M1 3 or 4 vertices correctly plotted. SC1 Correct reflection in y = 3. (3,5), (1,5), (4,2), (6,2).

16 4.4598 to 4.4611 2 M1 1.52 + 4.22 or better. Square root not essential for M1. Implied by 19.89 or 2.25 + 17.64 seen.

17 ($)1.14 or 114 cents 2 M1 8 × 0.68 – 2 × 2.15 or 8 × 68 – 2 × 215. For answers in cents units must be stated.

18 3x(2 – 3xy) final answer 2 SC1 3(2x – 3x2y) or x(6 – 9xy) or 3x(2 + 3xy) as answers.

19 (a) (i) –64 (ii) –144

1 1

(b) z 1 Allow z1.

20 (a) 4 or 2 1

(b) 81 or 9 1

(c) 64 or 8 1

(d) 14 or 3.7(4…) 1

21 (a) 25 1

(b) 43 1

(c) 3n + 10 oe final ans. 2 SC1 3n + k oe (k ¸ 10) as answer.

22 (a) 12 1

(b) (i) 0.83(3…) or

12

10 oe isw

(ii) 49.8 to 50

1 1 ft ft 60 × their (b)(i) correct to 3sf.

(c) 46 2 W1 for (CD = ) 12 seen in working space, or answer line or between dotted lines at C and D.

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Second variant



IGCSE – May/June 2008 0580, 0581 12

23 (a) 1332 2 M1 for 100

7.436000 ××

or SC1 for 7332 final ans.

(b) 1350.26 Allow 1350 or 1350.258 or

1350.25 or 1350.2 or 1350.3

3 M2 for

3

100

716000

+× or better.

or M1 for

2

100

716000

+× or better.

Alt. M1 for (6000 + 6000 × 0.07) × 0.07. M1 dep for ‘6869.4’ × 0.07. (NB Interest only method)

24 (a) (i)

4


(ii)

−

4


(b) Line segment from P to (–1, 6) 2 W1 for (–1, 6) indicated or

−

4

2 seen anywhere.

If zero, SC1 for line segment from P to (–1, k) or to (k, 6) or a line through P and (–1, 6).

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Second variant











9Dwebsite.tk

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First Variant Mark Scheme



IGCSE – October/November 2008 0580 and 0581 11

© UCLES 2008

Abbreviations

cao correct answer only

ft work has been followed through after an error

isw ignore subsequent working

oe or equivalent

SC Special Case

soi seen or implied

ww without working

Qu. Answers Mark Part Marks

1 28 1

2 2 1

3 −13 1

4 6.5 1

5 12 − 13x cao final answer 2 W1 for (+)12 or −13x seen anywhere

6 11.5 2 M1 for 4.6 × figs 25 or W1 for figs 115

7 (a)

(b)

>

=

1

1

8 15.77 cao 2 M1 for 20 ÷ 1.2685 or

W1 for answers from 15 to 17

9 (x=) 10.2 or 10

5

1 isw

2 M1 for (53 − 2) ÷ 5 soi

10 6650 ≤ L < 6750 1, 1 1 mark for each value correctly placed.

SC1 both correct but reversed

11 (a)

(b)

12

24

1

1

12 (k=) 8 2 M1 for 0 = 2 × 4 − k or better

13 (a)

(b)

(c)

5.78 × 10 3−

0.0058

0.01

1

1

1

Accept 5.8 × 10−3

Accept 1 × 10−2

14

4

15seen

8

5 × their

15

4

6

1

W1

M1

A1

Must be inversion of an improper fraction

Can be implied by ÷

8

5 '

120

20''

4

' 15= .

ww no marks

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© UCLES 2008


15 (a)

(b)

(c)

Point marked at (3, 2)

( −2, 1)

−0.5 or 2

1−

1

1

1

Missing label not penalised.

More than 1 point seen, must be labelled

By eye 2mm

16 (a)

(b)

(c)

1

q 11

r 6− or 6

1

r

1

1

1

17 (a)

(b)

12 seen on diagram

at A and B

or 180o −168

o= 12

o.

AND 12 + 78 (= 90)

123o

1

2

Allow 168o + 12

o = 180

o only

Allow 90o − 78

o = 12

o or 90

o −12

o = 78

o

if the first condition is satisfied

W1 for angle BAC (or angle BCA) = 45o

18 (a)

(b)

1083300 to 1084000 or

1080000 or 1083000

Final answer

Their (a) ÷ 10 6 evaluated

2

1ft

M1 for π × 50 2 × 138 or π × 0.52 × 1.38

19 (a)

(b)

64

172

2

2ft

M1 for 2 × (10 + 22) or

22 + 10 + 14 + 6 + (22 – 14) + (10 – 6)

M1 for (22 × 10) − 6 × ‘8’ or

(140 × 10) + ‘8’ × ‘4’ or 14 × 6 + 22 × ‘4’

20 (a)

(b) (i)

(ii)

(iii)

15(%) or 0.15 or 100

15 oe

4

15

oe cao

10

15

oe cao

0 or 15

0 cao

1

1

1

1

isw for change of form or cancelling only in all

parts. Not ratio.

Allow 0.267 or 0.266(6….) or % form

Minimum 3 significant figures

Allow 0.667 or 0.666(6…) or % form


Consistent use of wrong denominator in all of

(b), −1 once.

Allow nil, none or zero only. No other

denominator allowed.

21 (a)

(b)

(c)

Similar

15

292

1

2

2

M1 for 10 ÷ 8 × 12 or equivalent method

M1 for 360 − 68

22 (a)

(b)

45

5

75

All sectors correct ± 2°

‘Correctly’ labelled

1

1

1ft

1ft

1

Their ‘5’ × 15 or 120o – ‘45’

Ft provided angles total 360°

Independent. Labelling of the other 3 sectors.

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9Dwebsite.tk

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Second Variant Mark Scheme




© UCLES 2008

Abbreviations




oe or equivalent

SC Special Case

soi seen or implied

ww without working


1

36 1

2

2 1

3

−13 1

4

7.4 1

5 10 − 17x cao final answer 2 W1 for (+)10 or −17x seen anywhere

6 9.5 2 M1 for 3.8 × figs 25 or W1 for figs 95

7 (a)

(b)

>

=

1

1

8 23.65 cao 2 M1 for 30 ÷ 1.2685 or

W1 for answers from 23 to 25

9 (x=) 10.6 or 10

5

3 isw

2 M1 for (54 − 1) ÷ 5 soi

10 6650 Y L < 6750 1, 1 1 mark for each value correctly placed.

SC1 both correct but reversed

11 (a)

(b)

12

24

1

1

12 (k=) 8 2 M1 for 0 = 2 × 4 − k or better

13 (a)

(b)

(c)

6.56 × 10 3−

0.0066

0.01

1

1

1

Accept 6.6 × 10−3

Accept 1 × 10−2

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© UCLES 2008


14

3

20 seen

9

4 × their

20

3

15

1

W1

M1

A1

Must be inversion of an improper fraction

Can be implied by '

180

12''

3

20'

9

4=÷

ww no marks

15 (a)

(b)

(c)

Point marked at (3, 2)

(−2, 1)

−0.5 or 2

1−

1

1

1

Missing label not penalised.

More than 1 point seen, must be labelled.

By eye 2mm

16 (a)

(b)

(c)

1

q 8

r 8− or 8

1

r

1

1

1

17 (a)

(b)

12 seen on diagram

at A and B

or 180o −168

o = 12

o.

AND 12 + 78 (= 90)

123o

1

2

Allow 168o + 12

o = 180

o

Allow 90o – 78

o = 12

o or 90

o – 12

o = 78

o

If the first condition is satisfied

W1 for angle BAC (or angle BCA) = 45o

18 (a)

(b)

1458216 to 1459145 or

1460000 or 1459000

Final answer

Their (a) ÷ 106 evaluated

2

1ft

M1 for π × 602 × 129 or π × 0.6

2 × 1.29

19 (a)

(b)

64

172

2

2ft

M1 for 2 × (10 + 22) or

22 + 10 + 14 + 6 + (22 – 14) + (10 – 6)

M1 for (22 × 10) − 6 × ‘8’ or

(140 × 10) + ‘8’ × ‘4’ or 14 × 6 + 22 × ‘4’

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© UCLES 2008


20 (a)

(b) (i)

(ii)

(iii)

15(%) or 0.15 or 100

15 oe

4

15

oe cao

10

15

oe cao

0 or 15

0cao

1

1

1

1

isw for change of form or cancelling only in

all parts. Not ratio.

Allow 0.267 or 0.266(6….) or % form


Allow 0.667 or 0.666(6…) or % form


Consistent use of wrong denominator in all of

(b), −1 once.

Allow nil, none or zero only. No other

denominator allowed

21 (a)

(b)

(c)

Similar

19.95 to 20.04

297

1

2

2

M1 for 12 ÷ 9 × 15 or equivalent method

M1 for 360 − 63

22 (a)

(b)

45

5

75

All sectors correct ± 2°

‘Correctly’ labelled

1

1

1ft

1ft

1

Their ‘5’ × 15 or 120o − ‘45’

Ft provided angles total 360°

Independent. Labelling of the other 3 sectors.

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for the guidance of teachers



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.



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Mark Scheme: Teachers’ version Syllabus Paper

IGCSE – May/June 2009 0580, 0581 11

© UCLES 2009

Abbreviations




oe or equivalent

SC Special Case

soi seen or implied

ww without working


1 < 1 ( accept ≤ or both symbols)

2 (a)

(b)

0.00193(4….)

or 1.93(4…) × 10–3

7.63 × 10–2

1

1cao

3 22 2 M1 for 4500 ÷ 200 or 4.5 ÷ 0.2

4 30 2 M1 for a + 5a = 180 or 6a = 180 or

5a + 5a + a + a =360 or better

5 6.999…. to 7 2 M1 for 156.5 or 163.499… to 163.5 seen

6 (a)

(b)

3

y = 3x oe

1cao

1ft

Allow y = 3x + 0 or y = 3x − 0

Must be an equation. i.e. y = …..

7 328 ± 2 (ie 326 to 330) 2 W1 for angle of 32 ± 2 or 58 ± 2 or

148 ± 2 seen on diagram or

in working or in the answer space.

8 9.33 or 9.327(…) 2 M1 for 162 − 132 as chosen method.

Alt. Trig must be complete correct method

for M1.

9 35.68 2cao M1 30700 ÷ 79.6

SC1 for 2840(KES). Units need to be seen

in the working or on answer line.

10 (a)

(b)

7c − 20d www final answer

q(p − q) www

2

1

M1 for 15c − 20d − 8c or better or

W1 for 7c or − 20d seen as terms in final

answer

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IGCSE – May/June 2009 0580, 0581 11

© UCLES 2009

11 (a)

(b)

63

63

)9587(

their

×−×

oe

63

11 final answer

1

M1

A1ft

ft their (a)

12 (a)

(b)

(z =) − 13

(x =) 2

yz + oe final answer

1cao

2

M1 for z + y = 2x or 2

z

= x − 2

y or

–2x = –z – y

SC1 for answer of form 2±

±± yz

13 (a)

(b)

Correct ruled line with correct arcs and

at 30° to 34° to the line AB.

105(m) to 112.5(m)

W2

1ft

W1 for correct ruled line, 30° to 34° to AB

(i) with correct arcs but short of BC or (ii)

reaching BC with wrong or absent arcs.

15 × their DB (±2mm)

14 (a)

(b)

(c)

(d)

81

64

87

73

1cao

1cao

1cao

1cao

15 (a)

(b)

15p4 final answer

3q5 final answer

2

2

W1 for 15pn (n ≠ 0) or kp4 (k ≠ 0)

W1 for 3qn (n ≠ 0) or kq5 (k ≠ 0)

16 21.45 to 21.6 www 4 M1 10 × 10 or 100

M1 indep π × r2 where r is 5, 4.4 or 4.5

M1 dep Subtraction of the two areas.

Dependent on both first two M1’s

or Alternative method

Alt. M1 r × r where r is 5, 4.4 or 4.5

M1 ind 4

1 π × r2 where r is 5, 4.4 or 4.5

M1 dep 4 × subtraction of the two areas.


Follow one method only.

or W3 art 36.4 or art 39.2 www

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IGCSE – May/June 2009 0580, 0581 11

© UCLES 2009

17 (a)

(b)

(c)

D plotted at (3, 7)

−

4

4

3

3

1

2ft

1cao

Within 1 mm by eye.

1 mark for each component

−1 if in working, no brackets

SC1 Both (b) and (c) correct but written as

coordinates.

18 (a) (i)

(ii)

(b)

(c)

Isosceles

Equilateral

2 or two

Correct horizontal and vertical ruled

lines. By eye and to or beyond the

edges of the plan.

1

1

1

1, 1

Allow order (=) 2

SC1 Both freehand and ‘correct’ accuracy

by eye to or beyond edge of the plan or

both short of the full figure.

−1 for each additional line.

19 (a) ×

×

× (b) (i)

(ii)

(iii)

14×

×

335×

334

25

×2×

×

×2×

1cao

1cao

M1 for 350 × 4 ÷ 100

or M1 for 350 − (350 × 96 ÷ 100)

M1 Attempt at sum of the 5 values ÷ 5

SC1 for mean and median correct but

reversed

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9Dwebsite.tk

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IGCSE – May/June 2009 0580, 0581 12

© UCLES 2009

Abbreviations




oe or equivalent

SC Special Case

soi seen or implied

ww without working


1 > 1 ( accept ≥ or both symbols)

2 (a)

(b)

0.00153(48….) or 0.001535 or

1.53(4…) × 10–3 or 1.535 × 10–3

5.84 × 10–2

1

1cao

3 17 2 M1 for 3500 ÷ 200 or 3.5 ÷ 0.2

4 30 2 M1 for a + 5a = 180 or 6a = 180 or

5a + 5a + a + a =360 or better

5 8.999…. to 9 2 M1 for 158.5 or 167.499… to 167.5 seen

6 (a)

(b)

3

y = 3x oe

1cao

1ft

Allow y = 3x + 0 or y = 3x − 0

Must be an equation. i.e. y = …..

7 328 ± 2 (ie 326 to 330) 2 W1 for angle of 32 ± 2 or 58 ± 2 or 148 ± 2

seen on diagram or in working or in the

answer space.

8 9.64 or 9.643(6…) or 9.644 2 M1 for 172 − 142 as chosen method.

Alt. Trig must be complete correct method

for M1.

9 35.68 2cao M1 30700 ÷ 79.6

SC1 for 2840(KES). Units need to be seen

in the working or on answer line.

10 (a)

(b)

13c − 12d www

m(m − n) www

2

1

M1 for 20c − 12d − 7c or better or

W1 for 13c or − 12d seen as terms in final

answer

9Dwebsite.tk

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IGCSE – May/June 2009 0580, 0581 12

© UCLES 2009

11 (a)

(b)

63

63

)9587(

their

×−×

oe

63

11 final answer

1

M1

A1ft

ft their (a)

12 (a)

(b)

(z =) − 13

(x =) 2

yz + oe final answer

1cao

2

M1 for z + y = 2x or 2

z

= x − 2

y or

–2x = –z – y

SC1 for answer of form 2±

±± yz

13 (a)

(b)

Correct ruled line with correct arcs and

at 30° to 34° to the line AB.

105(m) to 112.5(m)

W2

1ft

W1 for correct ruled line, 30° to 34° to AB

(i) with correct arcs but short of BC or (ii)

reaching BC with wrong or absent arcs.

15 × their DB (±2mm)

14 (a)

(b)

(c)

(d)

81

64

87

73

1cao

1cao

1cao

1cao

15 (a)

(b)

24d

5 final answer

4t

7 final answer

2

2

W1 for 24d

n (n ≠ 0) or kd

5 (k ≠ 0)

W1 for 4t

n (n ≠ 0) or kt

7 (k ≠ 0)

16 21.45 to 21.6 www 4 M1 10 × 10 or 100

M1 indep π × r2 where r is 5, 4.4 or 4.5

M1 dep Subtraction of the two areas.


or Alternative method

M1 r × r where r is 5, 4.4 or 4.5

M1 ind 4

1 π × r2 where r is 5, 4.4 or 4.5

M1 dep 4 × subtraction of the two areas.


Follow one method only.

or W3 art 36.4 or art 39.2 www

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IGCSE – May/June 2009 0580, 0581 12

© UCLES 2009

17 (a)

(b)

(c)

D plotted at (3, 7)

−

4

4

3

3

1

2ft

1cao

Within 1 mm by eye.

1 mark for each component

−1 if in working, no brackets

SC1 Both (b) and (c) correct but written as

coordinates.

18 (a) (i)

(ii)

(b)

(c)

Isosceles

Equilateral

2 or two

Correct horizontal and vertical ruled

lines. By eye and to or beyond the

edges of the plan.

1

1

1

1, 1

Allow order (=) 2

SC1 Both freehand and ‘correct’ accuracy

by eye to or beyond edge of the plan or

both short of the full figure.

−1 for each additional line.

19 (a) ×

×

× (b) (i)

(ii)

(iii)

18×

×

335×

334

25

×2×

×

×2×

1cao

1cao

M1 for 360 × 5 ÷ 100

or M1 for 360 − (360 × 95 ÷ 100)

M1 Attempt at sum of the 5 values ÷ 5

SC1 for mean and median correct but

reversed

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0580 MATHEMATICS

0580/11 Paper 11 (Core), maximum raw mark 56




9Dwebsite.tk



IGCSE – October/November 2009 0580 11

© UCLES 2009


1 2 × 8 − (5 − 4) = 15 1

2 28% < 0.283 < 7

2 1

3 12.2 or 12.17 or 12.167 1

4 252 2 W1 for 108 or 72 correctly shown on the diagram

at B.

Or M1 for 180 + 72 or 360 − (180 − 72) soi

5 15500 Y N < 16500 1, 1 If zero, SC1 for correct but reversed

6

4

15 and

7

8 seen

28

120 oe fraction or 4

28

8 oe

M1

A1

isw incorrect cancelling after 28

120 oe

Final answer is a decimal, maximum M1.

7 Correct angle bisector (±2°) with two

pairs of correct arcs.

Line (±2 mm) from B.

2 W1 correct bisector without arcs or incorrect arcs

or absent arcs. Line (±2 mm) from B.

8 (a) 25 or 5

(b) 8 isw

1

1

9 (a) 14 23 isw or 2.23 pm isw.

(b) 94

1

2cao

Not 02 23 or 2 23 alone. Not 14h(ours)23

M1 for 235 ÷ 2.5 (or 2h 30min or 150)

Method mark is for formula with values.

10 (x =) 4 and (y =) 5 www 3 M1 for complete correct method for one value

A1 for 1 correct answer.

ww both correct W3

ww one correct W0

Reversed answer, look in working to be convinced

of transcription error.

11 (a) Ruled line from (0, 0) to (24, 15)

End point between (23.5, 15) and

(24.5, 15).

Start point within 1 mm of (0, 0)

(b) 18.8 to 19.6

2

1ft

W1 for correct freehand or short of (24, 15) but

within allowed limits and to at least 12 miles.

If zero SC1 Ruled line from (0, 0) to

(23.5, 15) or to (24.5, 15)

Answer in range.

If 0 or W1 gained in part (a) follow through line

with positive gradient only ± 1 mm

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12 Correct net layout

2 accurate, 7 cm by 4 cm, rectangles on

top and bottom.

2 accurate equilateral triangles at the

sides (height 3.3 cm to 3.7 cm)

1

1

1

2 rectangles and 2 equilateral triangles (one on

each side) in correct position to make a net.

within 2 mm of central grid line

13 (a) (–2, 1)

(b)

4

6

(c) H at (2, –2)

1

1

1

All coordinates/components reversed.

ie (a) (1, −2), (b)

6

4, (c) (−3, 3)

mark 0, 0, SC1

14 (a) –3 final answer

(b) 6 final answer

(c) 4s3 or 3

4

−

s

final answer

1

1

2

W1 for 4sn (n ≠ 0) or ks3 (k ≠ 0) seen

15

(a) 15

(b) (d =) m

J3

2

2

M1 for 35 = 3

7d or better.

M1 for 3J = md or m

J =

3

d

16 (a) 1.67 × 103

(b) 464 or 463.8(3…..)

2

2

W1 for 1.67 × 10n (n ≠ 0)

or 1.(…..) × 103 as answer

If zero SC1 for figs 167 in answer.

M1 for 1669.8 × 1000 ÷ 3600

17 (a) x(5x + 4y) final answer

(b) 5x + 13y www

1

3

Ignore check by expansion.

W1 for 14x + 7y

and W1 for –9x + 6y

If zero ww SC1 for 5x or (+)13y in answer

18 (a) 75 Angle(s) (on a straight) line (=)

180

(b) 67 Angle(s) (in a) triangle (sum to)

180

(c) 67 (vertically) opposite

1, 1

1ft,1

1ft,1

Or reference to straight line and 180

or exterior angle (of triangle is) sum of interior

(opposite) angles

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19 (a) 60

(b) 36 ÷ 240 × 360 oe

54

(c) (i) 116 to 118

(ii) 32.5 or their (c) (i) ÷ 3.6

1

M1

A1

1

2ft

oe e.g. 36 × 90 ÷ 60

W2 54 with some relevant working shown

M1 for their (c) (i) ÷ 360 × 100

Or for their (c) (i) × (60 ÷ 90) ÷ 240 × 100

Allow revised angle in range 116 – 118 seen with

working

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0580 MATHEMATICS

0580/12 Paper 12 (Core), maximum raw mark 56




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1 2 × 8 − (5 − 4) = 15 1

2 28% < 0.283 < 7

2 1

3 54.9 or 54.87 or 54.872 1

4 252 2 W1 for 108 or 72 correctly shown on the diagram

at B.

Or M1 for 180 + 72 or 360 − (180 − 72) soi

5 15500 Y N < 16500 1, 1 If zero, SC1 for correct but reversed

6

3

8 and

11

12 seen

33

96 oe fraction or 2

33

30oe

M1

A1

isw incorrect cancelling after 33

96 oe

Final answer is a decimal, maximum M1.

7 Correct angle bisector (±2°) with two

pairs of correct arcs.

Line (±2 mm) from B.

2 W1 correct bisector without arcs or incorrect arcs

or absent arcs. Line (±2 mm) from B.

8 (a) 25 or 5

(b) 8 isw

1

1

9 (a) 15 18 isw or 3.18 pm isw.

(b) 98

1

2cao

Not 03 18 or 3 18 alone. Not 15h(ours)18

M1 for 441 ÷ 4.5 (or 4h 30min or 270)

Method mark is for formula with values.

10 (x =) 3 and (y =) 4 www 3 M1 for complete correct method for one value

A1 for 1 correct answer.

ww both correct W3

ww one correct W0

Reversed answer, look in working to be convinced

of transcription error.

11 (a) Ruled line from (0, 0) to (24, 15)

End point between (23.5, 15) and

(24.5, 15).

Start point within 1 mm of (0, 0)

(b) 11 to 11.5

2

1ft

W1 for correct freehand or short of (24, 15) but

within allowed limits and to at least 7 miles.

If zero SC1 Ruled line from (0, 0) to

(23.5, 15) or to (24.5, 15)

Answer in range.

If 0 or W1 gained in part (a) follow through line

with positive gradient only ± 1 mm

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© UCLES 2009

12 Correct net layout

2 accurate, 7 cm by 4 cm, rectangles on

top and bottom.

2 accurate equilateral triangles at the

sides (height 3.3 cm to 3.7 cm)

1

1

1

2 rectangles and 2 equilateral triangles (one on

each side) in correct position to make a net.

within 2 mm of central grid line

13 (a) (–2, 1)

(b)

4

6

(c) H at (–1, 2)

1

1

1

All coordinates/components reversed.

ie (a) (1, −2), (b)

6

4, (c) (1, 0)

mark 0, 0, SC1

14 (a) –3 final answer

(b) 6 final answer

(c) 4s3 or 3

4

−

s

final answer

1

1

2

W1 for 4sn (n ≠ 0) or ks3 (k ≠ 0) seen

15

(a) 12

(b) (d =) m

J3

2

2

M1 for 32 = 3

8d or better.

M1 for 3J = md or m

J =

3

d

16 (a) 1.67 × 103

(b) 464 or 463.8(3…..)

2

2

W1 for 1.67 × 10n (n ≠ 0)

or 1.(…..) × 103 as answer

If zero SC1 for figs 167 in answer.

M1 for 1669.8 × 1000 ÷ 3600

17 (a) p(3m + 7p) final answer

(b) 14m + 23p www

1

3

Ignore check by expansion.

W1 for 24m + 8p

and W1 for –10m + 15p

If zero ww SC1 for 14m or (+)23p in answer

18 (a) 75 Angle(s) (on a straight) line (=)

180

(b) 67 Angle(s) (in a) triangle (sum to)

180

(c) 67 (vertically) opposite

1, 1

1ft,1

1ft,1

Or reference to straight line and 180

or exterior angle (of triangle is) sum of interior

(opposite) angles

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© UCLES 2009

19 (a) 60

(b) 36 ÷ 240 × 360 oe

54

(c) (i) 116 to 118

(ii) 32.5 or their (c) (i) ÷ 3.6

1

M1

A1

1

2ft

oe e.g. 36 × 90 ÷ 60

W2 54 with some relevant working shown

M1 for their (c) (i) ÷ 360 × 100

Or for their (c) (i) × (60 ÷ 90) ÷ 240 × 100

Allow revised angle in range 116 – 118 seen with

working

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