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June 2003

INTERNATIONAL GCSE

MARK SCHEME

MAXIMUM MARK: 104

SYLLABUS/COMPONENT: 0580/03, 0581/03

MATHEMATICS

Paper 3 (Core)

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Mark Scheme Syllabus Paper

IGCSE EXAMINATIONS – JUNE 2003 0580/0581 3

© University of Cambridge Local Examinations Syndicate 2003

1 (a) 7 1

(b) 42 1

(c) (i) 9 1

(ii) 8 2 M1 for evidence of idea of mid-value

(iii) 8.3 3 M1 for 4 x 5 + 7 x 6……+ 3 x 12 or 415M1 (dep) for � 50

(d) 5cm 2 M1 for 1cm to 2 students o.e.

(e) 36o 2 M1 for 5 x 360 50

(f) $7.5(0) 2 M1 � 3

(g) 22 2 M1 for 11 (x 100) 50SC1 for 19 (x 100) = 38% 50

(h) (i)

50

6 1

(ii)

50

14 1

(iii) 1 1

Accept equivalent fractions,decimals or percentages

19

2 (a) 120, ……….24, 20 1, 1, 1

(b) 7 correctly plotted points f.t.correct curve

P3C1

Deduct 1 for each error (�1mm)Must be a reasonable hyperbola

(c) 1.6 to 1.8 1 Accept f.t.

(d) 120, ……..0 2

(e) Straight line through 4 points L2 L1 if short or not ruledSC1 for √ if all straight lines

(f) (1.2 – 1.4, 92 – 96)(4.6 – 4.8, 24 - 26)

11 Accept f.t.

(g) -20 2 SC1 for 20 or M1 for rise/run seen(numerical attempt)

16

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3 (a) (i) 175 cents 1

(ii) 25b cents 1

(iii) $1.75 1 or √

(iv) $4

b (allow

100

25b) (0.25b) 1 or √ If involves b

(b) (i)

n

T 1

(ii) The cost of one bar 1

(c) (i) 4.5(0) 1

(ii) 4.2(0) 2 M1 for (36 – 6.60)/7

(iii)

x

y 1

(iv)

1

7

�

�

x

y 2 B1 for y – 7 or x – 1 seen

12

4 (a) (i) P with vertices (4, 11), (2, 11),(2, 12)

2 SC1 if translated by ��

��

�

4

3, ��

�

��

�

� 3

4 etc.

(ii) Q with vertices (9, 7), (11, 7),(11, 8)

2 SC1 if reflected in y = 8 or √ from P

(iii) R with vertices (7, 7), (7, 5),(6, 5)

2 SC1 if 90o clockwise from A or √ fromQ

(iv) S with vertices (7, 7), (3, 7),(3, 9)

2 SC1 if different scale factor about A orenlargement of triangle T s.f. 2 about Bor C

(b) (i) Translation

��

��

�

� 4

3

1

1

(ii) EnlargementScale factor 1/2

centre A

111

(c) (i) 90o (anti-clockwise) 1 Accept 270o clockwise

(ii) (3, 3) 2 B1 for 1 correct

16

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5 (a) (i) Accurate and with arcs 2 B1 without arcs or inaccurate

(ii) Accurate quarter-circle r = 5 2 SC1 for r > 4.8 or < 5.2 with compassor correct r but freehand

(b) Correct region shaded 1 or √ If convinced

(c) (i) 45o correct12cm correct

11

��2o

��1mm

(ii) Reasonable tangent 1 Must be ruled �5o

(iii) 6.8 to 7.2 1 Accept f.t. �0.1

9

6 (a) 3 x 1 x 1.5 + 9 x 1 o.e. 2 M1 for appropriate strategyM1 (dep.) for correct numbers used

(b) 3780 3 M1 for volume is area x length, 13.5 x2.8 or 37.8B1 for 280 seen

(c) (i) 1.92 2 M1 for 2 x 1.2 x 0.8

(ii) 1 920 000 f.t. 2 M1 for (their) (i) x 106 or 200 x 120 x 80

(iii) 507 f.t. 2 M1 for (c) (ii) � (b) or 507. ... or 508

(d) One vertical line drawn 1 Within ��0.2cm of the centre

(e) (order) 1 or no symmetry 1

13

7 (a) (i) 84o 1

(ii) 22o 1

(b) 11 1 Accept 10.8 � 11, 10min 48sec �11min

(c) 16o 1

(d) (i) 32, (16), 8, 4 3 B1 for each

(ii) Halving o.e. 1

(e) 20o 1 Allow answer >20 and <22

9

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8 (a) 3 new lines from the vertex tothe base 2

(b) 6, 7, n + 2 3 B1 for each

(c) 15, 21, 55 3 B1 for each

(d) 12 2 SC1 for 10 or 11

10

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November 2003

INTERNATIONAL GCSE

MARK SCHEME

MAXIMUM MARK: 104


MATHEMATICS

Paper 3 (Core)

9Dwebsite.tk



MATHEMATICS – NOVEMBER 2003 0580/0581 3


Question Number

Mark Scheme Part Marks

Notes Question Total

1 a) 24 1 b) 25 or 52 1 c) 27 or 33 1 d) 23

29 1 1

e) 26 1 condone 6, 26 or 6 x 26 f) 28 cao 1 g) 21 and 27 1 condone 21 x 27 8

2 a) i) 1300 or 1 pm 1 ii) 1030 1 allow 10.30, 10:30 etc iii) 9 2 B1 for either 24 or 33 seen

or M1 for 2 correct horizontal lines drawn or 24 and 33 marked on axis

b) i) 4.35, 8.7(0) 2 B1 for one correct ii) Correct straight line

(through (10, 8.6 to 8.8) 2 P1 for (5, 4.2 to 4.4) or (10, 8.6 to

8.8)

iii) 9.2(0) (± 0.1) 1 no ft. iv) 575 (± 5) 1 no ft. 10

18

3 a) 6000 2 M1 for 25 x 30 x 8 b) i) art 4400 3 M2 for π x 102 x 14

or SC1 for π x 52 x 14

ii) art 10400 1 √ ft their a + bi iii) art 13.9 3 √ ft for (their bii) ÷ (25 x 30)

M2 for (their bii) ÷ (25 x 30) oe or M1 for (their bi) ÷ (25 x 30) 9

4 a) 4, 7, 6, 4, 4, 2, 3 2 SC1 for 5 or 6 correct or 7 correct tallies

b) 1 cao 1 c) 2 cao 2 M1 for attempt at ranking list seen

d) 2.5 cao _

2 M1 their ( ) ∑∑ ÷ fxf imp by 2.5

seen

e) i) 0.23(3....) or

30

7 1 √ allow 23%

ft from their table

ii) 0.3 or

30

9

10

3or 1 √ ft from their table

f) 40 1 √ ft their table x 10. Allow 40/300 10

19

5 a) 6 –4

1 1

b) i) Rotation through 180° about (2.5, 6) o.e.

M1 A1 A1

Half turn M1 Al, –1 for "symmetry" allow correct description of point

ii) Enlargement s.f. 3 centre (1,7)

B1 B1 B1

accept scale 3, x3 etc accept'B' for (1,7)

c) i) 3 cao 1 ignore units ii) 1 : 9 cao 2 SC1 for 27 seen

M1 for correct answer nlt

d) 9

6'

3

2 −−

, –0.66 or better 2

SC1 for 3

2 oe or –k

13

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6 a) i) 27 1 ii) 6 2 M1 for (39 - 3) ÷ 6 iii)

6

3−P oe

2 M1 for P–3 seen or

6

36

6

+=

xP oe

seen

b) i) 4x + 3 M1 for 9x + 4 – 2x – (3x + 1) oe allow 9x + 4 – 2x – 3x + 1 oe for M1 or SC1 for 4x or (+)3 in answer space

ii) 10, 16 and 23 3 M1 for 9x + 4 = 49 oe A1 for x = 5 10 23

7 a) i) 44 2 SC1 for 40 to 48 ii) 52 3 B1 for 6 or 8 or 12 or 9 or 21 or 28

or 32 or 112 seen +M1 for adding 6 rectangles o.e.

iii) cuboid or rectangular prism

1 allow rectangular cuboid but not cube or cubical

iv) 52 1 √ ft from their aii (not strict ft) v) 24 2 M1 for 2 x 3 x 4 b) i) 2(pq + qr + pr) oe as final

answer 2 SC1 for pq or qr or pr seen or imp.

for both parts. Other letters used consistently MR–1

ii) pqr as final answer 2 M1 for pqr seen 13 8 a) 12.5

NB 4021 answer 12.5 working uses 75 and 800

3 M1 for 7.5 x 12 oe or 80/12 oe seen

+M1 for 10080

8090x

−

(explicit) or

100....66.6

....66.650.7x

−

(explicit)

after M0 SC2 for figs 124 to 126 ww or SC1 for 112.5

b) 120 minutes 3 B1 for

5

2or 180 or

5

3 x 300 seen

+M1 for 5

2 x 300 oe or 300-180

c) i) Accurate ┴ bisector of AB, with arcs ±1°±1mm complete inside figure Accurate bisector of <C with arcs as above

2

2

SC1 if accurate without arcs or incomplete line. Ignore extra lines SC1 if accurate without arcs or incomplete line as above

ii) correct area shaded

2 √ Areas marked as diagram ft from clear intention to draw perp. bisector and angle bisector

12

9 a) i) 150 (km) 1 ii) 15 000 000 oe (√) 2 Ml for their a)i) x 100 x 1000

or SC1 for their a)i) x 10n when n>0

b) i) 1270 to 1320 2 M1 for their 8.6 x their 150 must have some evidence for their 8.6

ii) (0)45 to (0)48 oe 1 iii) 245 to 248 2 SC1 for any answer in the range

180 < x < 270 8 20

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10 a) 1 6 15 20 15 6 1 Sum 64 1 7 21 35 35 21 7 1 Sum 128

1 1 2 1

SC1 if 6 or 7 correct

b) i) 512 accept 29 2 SC1 for 256 ii) 2n 2 SC1 for 2 x 2 x 2 seen or description c) 165 330 462

The first 6 numbers repeated in reverse order

1 1

11

_ _ 11 TOTAL 104

9Dwebsite.tk


June 2004

INTERNATIONAL GCSE

MARK SCHEME

MAXIMUM MARK: 103


MATHEMATICS

Paper 3 (Core)

9Dwebsite.tk



MATHEMATICS – JUNE 2004 0580/0581 3

© University of Cambridge International Examinations 2004

FINAL MARK SCHEME 0580/3 June 2004

Question Number

Answer Marks Comments Total

1 a i 51 1

ii 49 2 M1 for clear evidence of ranking

iii 46 2 M1 for total/10, allowing errors in addition

b i 20 60 160 80 40 (360) 2 M1 for evidence of ×4 oe seen or SC1 for 3 or 4 correct

ii correct pie chart (±2°) correct labels

2 L1

5 sectors only. Any order. Or SC1 for 3 or 4 correct or ft correct 4 or 5 correct or ft correct

iii a 4/9 oe 1 allow (0).44…,44.….%, but not 0.4

iii b 1/3 oe 2 M1 for their((D+E)/T) from their table. Can be implied. For both parts −1 once for incorrect notation eg 4 out of 9, 1:3, 4 in 9 etc 0.3 ww is zero

13 13

2 a 9 1

b i 6 1

ii 18 1√ ft for 3× their bi (not strict ft)

c i (0).6 2 M1 for 3× 0.2

ii 30 2√ M1 for their bii/ci (not strict ft) or 2×3/0.2

d (0).02 2 M1 for 2×0.1×0.1 oe SC1 for fig 2

e 4.8(0) 9(.00) 14.4(0) 2.1(0) 30.3(0)

4 1√

B1 for each ft from 4 total costs

14 14

3 a 7 8 4 −1 3 B2 for 3 correct or B1 for 2 correct

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b 13 correct or ft correct points (±1/2 a square) Correct curve cao

P3√ C1

P2√ for 11 or 12 correct or P1√ for 7 to 10 correct reasonable parabola shape, no straight line segments, pointed maximum etc

c − 2.7 to −2.9 2.7 to 2.9

1 1

d −1 5

1 1

e correct line drawn −3≤x≤3

2 M1 for incomplete line or freehand line or both their (in)correct points correctly plotted

f 2 2 M1 for attempt at ∆y/∆x from their straight line graph

g −3 1

1 1

−1 if y values given as well

17 17

4 a 120 1

b 70 2 M1 for t+2t+75+75=360 oe 3t and 210 implies M1

c i 130 oe (eg 180−50) 2 M1 for angle sum of triangle(=180) used

ii

100 oe (eg 360−100−160)

2 M1 for angle sum of quadrilateral(=360) used

iii x=70 and y=30 3 √M1 for attempted elimination of one variable (be generous) A1 for each answer. no ft. correct answers reversed implies M1A1

10 10

5 a (0).2 1

b i

Tangent and radius mentioned

1 or described.

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ii 8 cao 1

iii art 1.78 3 M1 for (their) 82−7.82 oe M1(indep) for square root indicated or used 1.77 ww implies M2. 1.8 ww is zero

iv 6.9 (2 sig figs only) 3√ ft for answer correct to 2 sig figs (not strict ft) (3.9×theirbiii) or M1 for 0.5×7.8×their biii + A1 for answer to more than 2 sig figs

9

6 a i translation cao 10

2−

B1 B1 B1

or translated −1 for incorrect notation or a description SC1 for both answers correct but inverted

ii rotation or turn centre the origin oe (+) 90 (anticlockwise)

M1 A1 A1

allow quarter turn for M1A1

b i correct reflection drawn

2 SC1 for reflection in x-axis

ii correct enlargement drawn

2 SC1 for scale factor 2, wrong centre

10 19

7 a i pentagon 1

ii 540 2 M1 for 3×180, or 5×180−360 or (180−360/5)×5 or 6×90

iii 108 cao 1

b i 110 or x=70 or y=20 completion

M1 A1

may be on diagram Beware of circular arguments

ii art 50.2 2 M1 for tan(−1) and 120/100

iii 120(.2) 1√ ft for 70+their bii

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iv 300 1√ ft for 180+their biii −1 for answers reversed

10 10

8 a i 6 (±0.1) 1 ii 10 2√ √SC1 for 10n where n is an

integer. (ft 60/their ai)

iii 73 to 76 1 b both lines drawn (±0.1

cm) 2 B1 for each line. Ignore any

curves at ends, lines must be at least 5 cm long. Allow dotted etc

c mediator drawn (±0.1cm and 1o ) with two pairs of arcs

2 B1 for correct line with no arcs or correct arcs with no line

d complete circle, radius 4 (±0.1) cm drawn, centre C

2 SC1 for incomplete circle

e L marked correctly 1 be convinced

11

9 a i 12 1

ii 20 1

iii 2n+2 oe 2 M1 for 2n +k where k is an integer

b i a 20 1

b i b 25 1 ii 48 2 M1 for 12 seen (as diagram

no.)

iii 100 2 M1 for 10 seen 10

21 TOTAL MARKS 104

9Dwebsite.tk


November 2004

INTERNATIONAL GCSE

MARK SCHEME

MAXIMUM MARK: 104


MATHEMATICS

Paper 3

9Dwebsite.tk



IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 3


Question number

Mark Scheme Part Marks

Notes Question Total

1 a) i) 10 1 ii) straight line from

(11,10) to (11 30,10) 1

iii) straight line from

(11 30,10) to (12 45,16) 1√ allow +2 mm in length by

eye but must go through the correct points. f.t. from their (1130,10)

iv) a) 15 1 allow ¼ hour b) Hatab 1 v) 32 1 b) i) 450 1 ii) straight line ruled from

(1,45) to (10,450) 2 SC1 for freehand or

broken line or any straight line through the origin ± ½ small square at both points

iii) a) 306 ± 4 1 b) 10 60 to 10.80 1 allow 10.6 etc. 11

2 a) translation 1 must be single transformation

−

−

7

6

1 1

SC1 for correct vector inverted, or

−

−

14

12, or for correct row

vector, or co-ordinates. Condone missing brackets

b) rotation M1 must be single

transformation -90 or 90 clockwise o.e. A1 about (0, 0) o.e. A1

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c) (0, 0) 1 1.5 o.e. 1 not 3:2 etc.

d) i) correct triangle drawn 2 SC1 for reflection of A in

any vertical line or in y = -1

ii) correct triangle drawn 2 SC1 for 180o rotation

about any point or SC1 for rotation ± 90o about (-4,-3) 12

3 In this question alternative methods must be complete

a) 8 1 b) 6 2 M1 for 64100 − o.e.

must show square root c) art 53.1 2 M1 for sin and 8/10 seen

o.e. d) art 7.15 3 M1 for tan 40 and 6 seen

+M1 for 6/tan 40 o.e. e) 13.15 or 13.2 1√ f.t. for their b) + d) to 3 s.f.

or better 9

4 a) i) triangle drawn with three sides the correct length ± 0.1 cm

3 2 for two sides correct, with arcs 1 for two sides correct without arcs

ii) 56 ± 2 c.a.o. 1 b) in this part of the question

deduct 1 once for broken lines

i) complete locus drawn 3 1 for a line correct

distance from PQ 1 for a semicircle

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ii) correct line drawn ± 1 mm, ± 1o correct arcs, radius > 4 cm

B1 B1

iii) correct area shaded 2 SC1 for shading on left

hand side of their ‘mediator’ or inside lines drawn for their b) i) 11

5 a) i) kite 1 ii) correct line BD drawn 1 Allow broken line, one line

only iii) 70 2

M1 for 2

80140360 −−

o.e.

b) (p =) 90

(q =) 50 (r =) 50

1 1

1√

f.t. from their q, not strict f.t.

c) 128.6 c.a.o. 4 M2 for 180 -

7

360 or

7

1805× o.e.

(may be implied by art 129)

+A1 for 128.57 11

6 a) 3 0 0 1,1,1 b) 7 correct points plotted P3√ P2√ for 5 or 6 points ± ½

sm. sq.

P1√ for 4 points. not strict f.t.

smooth curve through all correct points C1 incorrectly plotted points

should be ignored for C1. Minimum curved, not pointed

c) -0.8 to -0.7 c.a.o. 1 ignore any y values 2.7 to 2.8 c.a.o. 1

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d) 4 0 1,1 e) correct line drawn through

(-4,8) and (4,0) 1 complete line

f) -1.7 to -1.4 c.a.o.

2.4 to 2.7 c.a.o.

1 1

ignore any y values

14

7 a) i) 16 1 ii) 3x + 8 o.e. 2 M1 for 3x. allow n instead

of x. deduct 1 for ‘= x’ or ‘= 0’ or = any number, but allow a different letter

b) -9a 1 +5b 1 c) 3a(2 – 3a) 2 M1 for any correct partial

factorisation d)

a

u- v o.e.

2 M1 for v – u seen

e) (x=) 2.5 2 M1 for correct

multiplication of LHS of one or both equations to equalise coefficients or for a recognisable attempt to eliminate one variable

(y=) -3.5 2 M1 for correct substitution of their other value or M2 correct matrix method 13

8 a) i) 22 1 ii)

77 or 2

8767 +

2 M1 for evidence of

ranking seen anywhere. e.g. 67,87

iii) 89 2

M1 for their 12

∑ x

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b) i) 72 ± 1 80 ± 1 94 ± 1

1 1 1

ii) 1080 ± 5 1200 ± 5 1410 ± 5

1√

1√

1√

strict f.t.s for their angle x 15 ± 5

iii) appropriate observation 1 12

9 a) i) 27 to 36 entered correctly 1 ii) a) square 1 b) 100 1 c) n2 c.a.o. 1 allow n x n iii) a) 43 c.a.o. 1 b) 871 2 M1 for 900 – 30 + 1 o.e. b) i) 100 1 ii) 10n c.a.o. 1 allow 10 x n iii) 91 1 vi) 10n – 9 o.e. 1 11

Total 104

9Dwebsite.tk


June 2005

IGCSE

MARK SCHEME

MAXIMUM MARK: 104


MATHEMATICS

Paper 3 (Core)

9Dwebsite.tk



IGCSE – JUNE 2005 0580/0581 3


Question Answer Marks Comments

1 (a) 2.8 1 ignore minus sign, accept 2800 g

(b) 106.5(0) 1 107 is X (but remember to look back for 106.5)

(c) (i) 10 40 1 accept 10.40, 10:40, 10.40 am

(ii) 1 (hour) 30 (mins) 1 f.t. f.t. from (c)(i) [f.t. is (c)(i) > 12 10] accept 1 ½ (hours), 1.5 (hours), 90 (mins)

(d) 13.55 1 accept 1.55 (pm) but 01 55 and 1.55 am are X

(e) 357 3 M2 for 420 – 15 x 420/100, 420 x 85/100 o.e. or M1 for 15 x 420/100 o.e. answer of 63 is M1 implied

8

2 (a) –2 1 2 –7 3 B2 for 3 correct, B1 for 1 or 2 correct

(b) 9 correct points plotted

P3 f.t. P2 f.t. for 7 or 8 correct, P1 f.t. for 5 or 6 correct limit for acurracy is ½ small square

smooth curve drawn C1 must go through the 9 correct points not dependent on P3

(c) –0.4 (± /0.1) 1 please note no f.t. on this part

2.4 (± 0.1)

1

(d) (i) correct line drawn 1 accept dotted/dashed line must be full length from (1, –14) to (1,2)

(ii) x = 1 1 f.t. f.t. from (d)(i) if x = k any reference to y is X

11

3 (a) (i) –3 9

1 1

(ii) 9 1 ignore minus sign

(b) correct max drawn correct min drawn

1 f.t. 1 f.t.

} f.t. is from (a)(i) [Sunday] } allow Sunday (only) to be 1 square out horizontally } allow freehand straight lines

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IGCSE – JUNE 2005 0580/0581 3


(c) (i) 3 1 f.t. f.t. is 3 if Sunday negative otherwise 2 allow 3 out of 7

(ii) Sunday 1 f.t. f.t. if not Sunday is Thursday

(d) 42.8 2 M1 for 9 x 6/5 + 32 or better e.g. 54/5 + 32, 10.8 + 32 answer of 43 is M1 implied

9

4 (a) (i) 3 –1

1 1

(ii) correct translation drawn

1 f.t. } f.t. where possible (i.e. still on the grid)

1 f.t. } condone inaccuracy/unruled if intention is clear } if ½ scale used then penalise first

occurence only (–1)

(b) (i) –2 2

1 1

(ii) correct translation drawn

1 f.t. } f.t. where possible (i.e. still on the grid)

1 f.t. } condone inaccuracy/unruled if intention is clear

(c) enlargement (centre) (0,0) o.e. (scale factor) 2

1 1 1

} } must be a single transformation }

(d) (i) 1 1

(ii) 1 1

(iii) correct rotation drawn

2 SC1 for 180 rotation about any other point SC1 for ± 90 rotation about O

(iv) reflection in the x-axis oe

M1 B1(dep)

} must be a single transformation } condone inaccuracy/unruled if intention is clear } enlargement, s.f. = –1, centre (0,0) is B2

17

5 (a) (i) 8 7 10 9 8 18 3 2 for 4 or 5 correct, 1 for 2 or 3 correct accept tallies if in 5’s, accept 8/60, 7/60 etc.

(ii) 6 1 c.a.o

(iii) 4 2 c.a.o M1 for evidence of ranking (cum. freq.)

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IGCSE – JUNE 2005 0580/0581 3


(iv) 3.9 3 c.a.o M1 (f.t.) for 8 x 1 + 7 x 2 + 10 x 3 or 8 +14 +30 (min 3) M1 (f.t.) dep. for /60 [both M marks may be by the table] answer of 3.93(3333) is M2 implied 39.3(33...) is M1 implied

(b) (i) 60 2 M1 for 10 + 7 + 10 + 7 + 14 + 12 (min 3)

(ii) 3.7(3333 ) 3 M1 (f.t.) for 10 x 1 + 7 x 2 + 10 x 3..... or 10 +14 + 30...... (min 3) M1 (f.t.) dep. for /(b)(i)

14

6 (a) (i) 6 2 M1 for 6x = 36 or 3x = 18 o.e.

(ii) 72 2 f.t. f.t. is 2 x (a)(i) x (a)(i) M1 (f.t.) for 6 x 12, 2 x 36, 2 x 6 x 6

(b) (i) 1.5 or 1 ½ or 3/2 2 M1 for 3y – y = 3 o.e. [unknown on one side]

(ii) 4z + 2 = 10z – 1 1 accept any equivalent equation in z if (b)(ii) is left blank may recover mark if 4z + 2 = 10z – 1 seen in (b)(iii)

(iii) 0.5 or ½ or 3/6 3 B1 for correct single z term B1 for correct single constant term

(c) (i) a – b = 3 o.e. 4a + b = 17 o.e. 5a = 20 4a + b + 3 = a – b + 17

} 1,1 }

if (c)(i) is left blank may recover mark(s) with a – b = 3, 4a + b = 17, 5a = 20 seen in (c)(ii)

(ii) (a=) 4 and (b=) 1 3 2 for either (a=) 4 or (b=) 1 or M1 (f.t.) for correctly eliminating one of the variables

15

7 (a) 050 (± 2) 2 M1 for correct angle but not 3 figures i.e. 50 ( )2±

(b) (i) correct line drawn ( ± 2)

1 length at least 3 cms long

(ii) correct position marked

1 f.t. f.t is from line drawn in (b)(i) ( 2± mm) but must be on the line AC

(c) (i) 7 ( ± 2 mm) 1

(ii) 200000 2 c.a.o. 1 for figs 2 or SC1 for figs 1.94 to 2.06

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IGCSE – JUNE 2005 0580/0581 3


(d) (i) correct locus drawn 2 f.t. f.t. is for their scale (normally 5 cm) at least over sea allow dotted/dashed locusSC1 for any other circle with centre A drawn SC1 for ¼ correct circle over sea

(ii) correct line SR drawn 5 to 6 incl.

1 f.t. 1

f.t. is for their S allow dotted/dashed line no f.t. on this part

(e) (i) 18.6 to 19.4 incl. 2 SC1 for 9.3 to 9.7 incl. seen

(ii) 27.9 to 29.1 incl. 3 M1 for conversion of minutes to hours (min of 0.66, 0.67 if dec.) M1 (indep) f.t. for their distance (e)(i)/their time taken

(iii) 15.4 2 f.t. f.t. is (e)(ii)/1.85 M1 for (e)(ii)/1.85 seen

18

8 (a) 208 3 M2 for 2(24 + 32 + 48) or 48 + 64 + 96 or 160 + 24 + 24 o.e. or M1 for 24 or 32 or 48 or 160 seen

(b) 192 2 M1 for 6 x 8 x 4

(c) (i) straight line AC

1

(ii) 12.8 3 M2 for 10 + 8 or 100 + 64 or 164 or M1 for 10 + 8 or 100 + 64 or 164 or SC1 for complete correct use of Pythagoras

(iii) 51.3 or 51.4 3 M1 for 10/8 and tan seen o.e. and M1 for tan 10/8 seen o.e. [the o.e include sin or cos with their (c)(ii)] or SC1 for complete correct use of a trig. ratio

12

104

9Dwebsite.tk


UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS

International General Certificate of Secondary Education

MARK SCHEME for the November 2005 question paper

0580/0581 MATHEMATICS 0580/03, 0581/03 Paper 3 (Core), maximum raw mark 104

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.

9Dwebsite.tk



IGCSE – NOVEMBER 2005 0580/0581 3


Question Answer Marks Comments Total

1 (a) Reflection drawn, 1 any recognisable reflected E in any vertical mirror line, allow

correctly in mirror line 1 good freehand (b) (i) Rotation M1 or turn or rotated 90° clockwise or –90 A1 centre of rotation marked or described unambiguously A1 (ii) enlargement M1 or enlarged scale factor 3 A1 centre of enlargement marked or described SC1 for “made 3 times larger” unambiguously A1 etc. (iii) translation 1

−

−

5

7

B1 B1

SC1 for both values correct but inverted, or correct values with other imperfection, for example given as coordinates.

[11]

2 (a) (i) 56.3 2 M1 for tan ABC = 6/4 oe (ii) 123.7 1√

(b) 7.21 2 M1 for 62 + 42 oe (c) 17.2 m 3√ M1 for area method

12 m2 A1 for both numerically correct B1 for both units correct

[8]

3 (a) (i) 5 1 –3 1 12 1 (ii) 9 correct points plotted P3√ P2 for 7 or 8 or P1 for 5 or 6

correct, smooth curve drawn C1 (iii) –0.8 to –0.7 1 2.6 to 2.8 1 (b) (i) 8 and 2 1 (ii) points P2 P1 for 5 or 6 correct curve C1 (iii) 3.1 to 3.3 1√ ft dep on only 1 point of intersection

[14]

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IGCSE – NOVEMBER 2005 0580/0581 3



4 (a) 8.36 3 M1 for addition of at least 10 numbers M1 for divide by 14

(b) 8 www 2 M1 for ranking list seen

or SC1 for (6 + 10)/2 seen

(c) 6 1 (d) 3 4 4 3 2 1 for 2 or 3 correct (e) (i) 7/14 oe √1 ft for their (4 +3)/their 14,

correct or ft correct

(ii) 3/14 √1

(f) 12 √2 M1 for their (10 – 14) x 3

[12]

5 (a) bearing 99 to 101° B1 drawn angle BAC 109 to 111° B1 drawn

AB 4.9 to 5.1 cm B1 AC 5.9 to 6.1 cm B1 (b) (i) 37 to 40 1√

(ii) 247 to 250 1√ ft from (b)(i)

(c) 8.9 to 9.1 1√

(d) (i) Two positions found, 3 2 for two positions without arcs with appropriate arcs and labelled 1 for one position found and labelled (ii) P or Q 1 4.0 to 4.4 √1 ft for correct measurement of

their closest position to B [12]

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IGCSE – NOVEMBER 2005 0580/0581 3



6 (a) (i) 10.8 www 4 M1 for evidence of shape being broken down (or 6 by 2 rectangle – triangle) +M1 for one correct rectangular area. +M1 for evidence of triangle calculation (ii) 32400 2√ SC1 for figs 322 to 323

or M1 for (a)(i) x 3 x 1000

(iii) 36 2 M1 for 6 x 3 x 2 (b) (i) 61 hours and 30 min 2 M1 for 61.5 (ii) art 13500 1 (iii) 3.38 2 M1 for their (b)(ii) x 2.5/10000 (iv) 4 1 √ rounding up

[14]

7 (a) (i) y = 2x – 3 oe 1 (ii) 2 oe 2 SC1 for gradient of other line (–1) (iii) 3 2 1 0 –1 2 1 for two correct (iv) correct line drawn 1 (v) (x =) 1.6 1.7, or 1.8

(y =) 0.2, 0.3, or 0.4 3 2 for correct answers not to 1 dp

or 1 for 1 answer correct

(b) eliminating one of the

variables M1 working must be seen

but second M1 can imply the

eliminating the other M1 first variable (√)

1.66 or 5/3 only A1 0.3 or 1/3 only A1 SC1 for 1.67 and 0.333 [13]

8 (a) correct diagram (b) 13 16 19 2 1 for 2 correct (c) 298 2 M1 for evidence of a correct method (d) 3n + 1 2 1 for 3n + k (e) 28 2 M1 for evidence of a correct method [9]

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IGCSE – NOVEMBER 2005 0580/0581 3



9 (a) 51.4 3 2 for 51 or M1 for any complete method (b) (i) Isosceles 1 (ii) p = 50 1 q = 80 1√ ft for 180 – 2p

r = 50 1√ ft for = p

s = 50 1√ ft for = p

t = 80 1√` ft for = q or 180 – 2p

(c) 25 2 M1 for 90 – 65 oe [11]

9Dwebsite.tk




MARK SCHEME for the May/June 2006 question paper

0580 and 0581 MATHEMATICS

0580/03 and 0581/03 Paper 3, maximum raw mark 104

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.

9Dwebsite.tk



IGCSE – May/June 2006 0580 and 0581 03


9Dwebsite.tk




MARK SCHEME for the October/November 2006 question paper

0580, 0581 MATHEMATICS

0580/03, 0581/03 Paper 3 (Core), maximum raw mark 104

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 3

© UCLES 2006

Qu. Answer Marks Comments Total

1 (a) (i) √35 1

(ii) 3 1

(iii) 45 1

(iv) 2 or 3 or 37 1 accept any combination

(v) 2 1

(vi) 24 1

(b) (i) Correct arrangement of triangles drawn. 1 accept if only 1 internal line missing

(ii) 16 25 36 2 1 mark for 2 correct

(iii) 10000 or 1 x 104 1 Not 100

2

(iv) n2 or n × n 1 accept t = n

2 etc. do not accept x

2

(v) Square (numbers) 1 accept squares, squared

12

2 (a) –4 –4 –10 3 1 for each correct entry

(b) 8 correctly plotted points, within

2

1 square.

Smooth curve through 8 points

P3ft

C1

P2 for 6 or 7 correct. ft P1 for 4 or 5 correct. ft Allow small errors in the points provided shape is maintained.

(c) x = 0.5 drawn. 1 must be from (0.5, –9) to curve at least

(d) 2.2 to 2.4 1ft

(e) y = 1 drawn. 1 must touch curve as min. length

(f) (x =) –0.7 to –0.5 (x =) 1.5 to 1.7

1 1

12

3 (a) (i) 128.571…… or 128° 43 ′ (….) 2 M1 for 180 – 360/7 oe

(ii) 128.6 1 ft Follow through their (a)(i).

(b) (i) x + 3y + 80 + 95 = 360 (or better) 1

(ii) x + 3y = 185 oe 1 Both marks may be gained in (b)(i)

(iii) 40 2 ft M1 for x correctly substituted into the linear equation. Follow through their (b)(ii) provided linear in x and y.

(c) (i) 180° or angle sum of triangle mentioned 1

(ii) Angle in a semi-circle mentioned. 1

(iii) (a =) 70 (b =) 20

1 1

SC1 for a = 20 b = 70

(iv) 40 1ft 2 × their value for b provided 0 < b < 55.

12

4 (a) (i) Enlargement (Scale Factor) 3 (Centre) (2, 4)

B1 B1 B1

.

(ii) Reflection (in the line) x = 4

B1 B1

(b) (i) Correct translation drawn 2 SC1 for translation by the vector.

−

−

−

3

2

5.1

1

2

3 k

k

(ii) Correct rotation drawn 2 SC1 for any 180° rotation. SC1 for 90° or 270° rotation about (–1, –2)

9

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IGCSE - OCT/NOV 2006 0580, 0581 3

© UCLES 2006

5 (a) 90 2 M1 for 0.5 × 18 × 10

(b) 14.3 art 2 M1 for 10 × tan 55oe

(c) 18.5 to 18.6 3 M1 for 0.5 × 10 × their (b) or M1 18 – their (b)

M1 2

1 x 10 x their BX

M1 for

Their (a) – (0.5 × 10 × their (b))

(d) 20.6 art 2 M1 for √( 182 + 10

2) oe

9

6 (a) 750cao 3 M1 Figs 10 ÷ figs 20 and

figs 15 ÷ figs 10. OR M1 Figs 10 x Figs 15 and Figs 20 x Figs 10

M1 dep bricks in length × bricks in height.

M1 dep. area of wall ÷ area of brick. If MO then SC1 for Figs 75

(b) (i) 756 2 M1 for 720 × 1.05 oe

(ii) 8 1ft Their (b)(i) rounded up to the number of hundreds

(c) (i) 10 4

1 1

(ii) 2 1ft Their cement buckets ÷ 3.5 and rounded up to next whole number

9

7 (a) –1 2 SC1 for 1 SC1 for

K

k−

(b) (m =) 2 (c =) 3

1 1

(c) (i) Correct line drawn. 1 must cross both axes and line A

(ii) y = 2x – 3 oe 2ft SC1 for m = 2 or c = –3. Follow through their line for 2 and SC1.

7

8 (a) (i) 3 6 8 7 6 1 1 2 3 2 for 6 or 7 correct –1 if tally marks 1 for 4 or 5 correct

(ii) 5.71 art 3 M1 for evidence of size x frequency calculated for the sizes.

M1dep for sum of at least 5 ÷ 34

(iii) 7 cao 1

(iv) 5 cao 1

(v) 5.5 2 M1 for evidence of finding the middle shoe size. (Not just an answer of 5 or 6)

(vi) 17.6 art 2ft M1 for their 6 ÷ 34 × 100 or 17.65

(vii) 54 or 53 2ft M1 for their 6 ÷ 34 × 306 or ‘53.8….’. or 53.9

(b) (i) 12 25 19 2 2 1 mark for 2 or 3 correct or all correct but not added

(ii) 5 and 6 1ft Their class with the highest frequency. –1 for tally marks

17

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IGCSE - OCT/NOV 2006 0580, 0581 3

© UCLES 2006

9 (a) Correct accurate drawing.

(lengths ± 0.2 cm, angles ± 1°)

3 M1 for angle = 90° = BAC. M1 for AB = 7.5cm and AC = 5.5 cm. A1 for completed triangle. (Dependent on at least one M)

(b) (i) 233° to 235° 2ft From their diagram. M1 for their angle BCA measured

correctly (± 1°)

(ii) 182 to 190 2ft Their BC × 20. M1 for their BC (correct is 9.1 cm to 9.5 cm)

(iii) 2 (hours) 42 (mins) 4 SC3 for 2.7(0….)

M1 for 20 × 1.85

M1 for 100 ÷ their 37 SC2 for 2 hr 7 mins with no method. B1 for their time correctly changed to hours and minutes.

(iv) 24 2 M1 for 18 ÷ 0.75 oe

(v) Correct circle drawn 2 M1 for partial circle (crossing AB and AC)

(vi) 84 to 100 2ft M1 for 4.2 to 5.0 Follow through their diagram, dependent on intersections seen on BC

17

Total marks 104

9Dwebsite.tk






0580/03 and 0581/03 Paper 3 (Core), maximum raw mark 104

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 03

© UCLES 2007

1 (a) (i)

(ii)

(iii)

(iv)

(b) (i)

(ii)

(c) (i)

(ii)

1

8 or −8 or ±8

4

6

3

Multiple of 60

9

3 and 223

B1

B1

B1

B1

B1

B1

B1

B1,B1

Not −4

[9]

2 (a) 336 3367

2×− or 336

7

5× M1

(=) 240

E1 240 must be seen for this mark

(b) 5 ÷ their(5 + 4 + 3) × 240

100

M1

A1cao

www 2

(c) 3 ÷ their(5 + 4 + 3) × 240 × 12 M1 Allow 2880 for 240 × 12 and 4

1 for

12

3.

(=) 720

E1

720 must be seen for this mark

(d) 720 × 1.062

oe

M2

Implied by 88.99(2) or 89(total interest)seen

M1 for 720 × 1.06 (implied by 763.2 seen)

808.99(2) or 809 A1 SC1 for 806.(4) (Simple Interest)

www 3 for 808.99(2) or 809

[9]

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IGCSE – May/June 2007 0580/0581 03

© UCLES 2007

3 (a) (i) 360 B2 M1 for 2

1 × 5 × 122oe

(ii) 7.5oe

B2

M1 for 225 /4 oe (implied by 56.25)

(iii) 2

2

v

E or 2

2

1vE B2 B1 for 2E or

2

1E or division by v2

(b) xy( y – x) final answer B2 B1 for x(y2 – xy) or y(xy – x2)

SC1 for xy(y + x)

(c) 3x – 15 + 28 – 6x (= 7)

13 – 3x (= 7)

x= 2

MA1

M1ft

A1cao

Independent ax + b (=7) from their expansion

www 3

(d) Equating coefficients of x or y, or

equivalent method.

5y = 5 oe or 10x = 30 oe

x = 3, y = 1

M1

A1

A1

or a correctly substituted substitution. E.g.

y = 13 – 4x ⇒ 2x + 3(13 – 4x) = 9

www 3

[14]

4 (a) (i)

(ii)

(b)

(c)

(d) (i)

(ii)

(e)

−10, −20, −60, 30, 20, 15

Their 12 points plotted correctly.

Smooth curves through all points.

2

Correct lines ruled

(2.4 to 2.5, 24 to 25)

(−2.4 to −2.5, −24 to −25)

y = 10x oe

−10

B2

P3ft

C1

B1

B1,B1

B1ft

B1ft

B1

B1

B1 for –20 (x = –3) or 20 (x = 3)

P2ft for 10 or 11 points correct.

P1ft for 8 or 9 points or 1 quadrant correct.

Two distinct curves; no part of curves between

x = –1 and x = 1

Minimum length from x = –3 to x = 3.

ft their points of intersection

ft their points of intersection

cao

cao

[13]

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IGCSE – May/June 2007 0580/0581 03

© UCLES 2007

5 (a) (i)

(ii)

(iii)

135 (green)

75 (yellow)

Ruled lines correct to 2°

3 correctly labelled sectors

B1

B1

B1ft

B1

Only if (a)(i) + (a)(ii) = 210°.

Independent of previous marks

(b) (i) 24

10 oe B1 Accept decimals, percentages

(ii) 24

15 oe B1

(iii) 24

19 oe B1

(c) (i) 0 B1 SC1 for 12

0 and

12

12 or

24

0 and

24

24

(ii) 1 B1

(d) Labelled arrows correctly

positioned by eye

B3ft 1 mark for each.

ft their probabilities from (b).

[12]

6 (a) (i)

(ii)

(iii)

(iv)

(b)(i)

(ii)

(iii)

(c)(i)

(180 – 56)/2

art 2.82

5.63 to 5.64

5.3 or art 5.30

29.8 to 29.9

art 12.5

42.3 to 42.4

21100 to 21200

B1

B2

B1ft

B2

B2ft

B2ft

B1ft

B2ft

Alt. 90 − (56 ÷ 2)

M1 for 6cos 62° (implied by 2.8)

Long method must be complete.

2 × their (a)(ii)

M1 for 6sin 62°oe

Long method must be complete.

M1 for their (a)(iii) × (a)(iv)

M1 for 0.5 × π × (their (a)(ii)2)

ft is their (b)(i) + (b)(ii)

M1 for their (b)(iii) × 500

(ii)

×1000

3600

60

500 oe M2 M1 for figs 500 ÷ figs 60

30

A1 SC2 for answer of 2

1 min

or SC1 for1km per minute seen.

www B3

[16]

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IGCSE – May/June 2007 0580/0581 03

© UCLES 2007

7 (a) Trapezium B1

(b) (i) Translation 9 across, 3 down B2 B1 for 9 across or 3 down or

−

9

3

(ii) Correct reflection B2 B1 any reflection of ABCD in a line parallel to

l.

(iii) Correct rotation B2 B1 90° clockwise rotation of ABCD about A

(iv) Correct enlargement

B3 B1 any enlargement of ABCD and

B1 any enlargement of ABCD SF 3 or

B1 any enlargement of ABCD centre O

(not penalise lack of labelling provided

intention clear)

[10]

8 (a) (i)

(ii)

(iii)

(iv)

(b) (i)

(ii)

(c)

Diameter from P through O to Q

90

P to R and Q to R ruled.

(angle in a ) semi-circle

Bisector of QR with arcs.

Bisector of PRQ with arcs.

Correct Shading

B1

B1cao

B1

B1

B2

B2

2

Angle on a diameter.

Half the angle at the centre.

SC1 if accurate without arcs. Maximum errors

2mm from mid-point and 2° from

perpendicular.

SC1 if accurate without arcs. Maximum error

2° in line from R.

If wrong line and/or angle used treat as

misread each time.

Dep. on B2 in (b)(i) and (b)(ii).

SC1 for ‘correct’ shading but dependent

on at least SC1 in (b)(i) and (b)(ii).

[10]

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IGCSE – May/June 2007 0580/0581 03

© UCLES 2007

9 (a)

(b)

(c) (i)

(ii)

(d)

Letter E correctly drawn

22, 29, 36

71

7n + 1 or 8 + (n – 1) × 7 oe

Their (c)(ii) = 113

Full method of solution of their

equation.

16

B1

B3

B2

B2

B1ft

M1ft

A1cao

B1 for each correct number.

B1 for 7 × 10 + 1 or 8 + 9 × 7 seen.

SC1 for 7n + k seen. (k is an integer) oe

ft any expression involving n.

ft only a linear equation.

(113 – k)/ ‘7’

www B2

[11]

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IGCSE – October/November 2007 0580 and 0581 3

© UCLES 2007

1 (a) (i) 35 B1 cao

(ii) 7 B1 cao

(iii) 8 B1 cao

(iv) 7.71 art B3 ft M1 for 1x5 + 5x6 + 10x7 + 9x8 + 7x9 + 3x10 attempted M1 for ÷ 35 (ft from (a)(i) but not for 6) SC2 for 7.7

(b) (i) 72 2 M1 for 7/35 x 360 (ft but not for 6) oe

(ii) line drawn B1 final line (ft) drawn accurately, 1° accuracy [9] 2 all within 1 mm

(a) translation B2 (–5,4), (–3,4), (–4,5) drawn SC1 for any other translation not parallel to a axis

(b) reflection B2 (1,–3), (3,–3), (2,–4) drawn SC1 for reflection in x=–1 or any y=k

(c) rotation B2 (–1,–1), (–3,–1), (–2,–2) drawn SC1 for any 180 rotation or +90, –90 about (0,0)

(d) enlargement B2 (2,2), (6,2), (4,4) drawn SC1 for any other enlargement sf=2 or centre (0,0)

(e) enlargement B1 (sf=) 1/2 B1 (centre) (0,0) B1 accept O [11]

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© UCLES 2007

3 (a) –6, –12, –36, 36, 12, 6 B3 B1 for ± 36, B1 for ± 12, B1 for ± 6 SC1 for any 3 correct

(b) 12 points plotted P3 correct points ft within 1 mm P2 for 10 or 11, P1 for 8 or 9, P1 for 1 correct branch 2 curves drawn C1 must be smooth branches of rectangular hyperbola

(c) 1.6 to 1.8 B1 ft

(d) 36, 9, 0, 9, 36 B2 B1 for 4 correct

(e) 13 points plotted P3 correct points ft within 1 mm P2 for 11 or 12 P1 for 9 or 10 curve drawn C1 must be smooth parabola

(f) 3.3, 10.9 B1ft x from 3.2 to 3.4, y from 10.0 to 12.0 [15] 4 (a) 70.7 art B2 M1 for 5 x π x 3² / 2 or better

(b) 5.05 art B3 M1 for 200 = 5 x π x r² / 2 oe M1 for (r² =) 400 / 5π oe

(c) (r =) √2A/5π B3 M1 for any correct x or ÷ of 1 term 2A = 5πr² MA1 for r² = 2A / 5π M1 for square root at end [8] 5 (a) (i) –16 B1 cao

(ii) 7 or 144 or both B1

(iii) 144 B1 cao

(iv) √7 B1 cao

(b) 2 x 2 x 2 x 5 B2 B1 for 8x5, 2x20, 4x10, 2x4x5, or list 2, 2, 2, 5

(c) 11, 29 B1 cao 17, 23 B1 cao [8]

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© UCLES 2007

6 (a) (i) 78 B1 cao

(ii) 5p + 4e B1 cao

(b) (i) 2x + 3y = 57 B1 5x + y = 58 B1 SC1 for different variables

(ii) 15x + 3y = 174 M1 oe, for useful mult. or substitution (2 terms correct) x = 9 A1 cao 18 + 3y = 57 M1 oe, for using first answer correctly and sensibly y = 13 A1 cao [8] www4

ft for M marks only for linear equations in 2 variables

7 (a) (i) 2.60 art or 2.6 B2 M1 for √(3²–1.5²) or better (√6.75) oe (ii) 3.90 art or 3.9 B2 ft M1 for 0.5 x 3 x their(a)(i) (iii) 31.2 art B2 ft M1 for 8 x their (a)(ii) (b) (i) 18 www2 M1 for 9 triangles implied, or 2 x k, or attempted sketch (ii) reasonable sketch B1 shows 3 rectangles, 2 triangles in reasonable proportion (iii) area of "rectangle" M1 for 16 x 9, 144, 3 x 9 x 16, 27 x 16, 432 height of triangle M1 for √(9²–4.5²), √60.75, 7.79, 7.8, 3 x (a)(i) ft or trig area of triangle M1 for 0.5 x height (ft but not 9) x 9, 35.1, 70.2, 70.1 OR M2 for 9 x 3.90, 9 x their (a)(ii), 35.1 , 70.2, 70.1 total area M1 3 rectangles and 2 triangles, 432 + 70.2 or 70.1 soi 502 art A2 if M<3 then add SC3 for 502 art with no wrong

working seen

(iv) 32.4(0) B2 M1 for 540 x 6 or figs 324 [17] 8 (a) (i) 10 / 12. B1 oe 2 sf for decimals and %'s (with sign) throughout (ii) 4 / 12. B1 oe (iii) 12 / 12. B1 oe (b) 10.5 B2 M1 for (10+13+10+8+ ) / 12 or 126 / 12 (c) (i) 12 points plotted B3 B2 for 11, B1 for 10

(ii) ruled line B1 reasonable, at least from 8 to 19

(iii) negative B1 cao [10]

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© UCLES 2007

9 (a) (i) arc B1 full arc, centre T, radius 4 cm, must cover whole of town (ii) locus B2 must be accurate perpendicular bisector of PQ must show 2 pairs of arcs SC1 for accurate without arcs or with 2 arcs just oor (iii) R labelled B1 ft if possible (iv) 640 to 700 m B2 ft SC1 for 3.2 to 3.5 cm (ft) (b) locus B2 must be accurate bisector of angle T must show all arcs SC1 for accurate without arcs or with all arcs just oor (c) correct shading B2 must be a quadrilateral dependent on at least SC1 in (a)(ii) and (b) [10] 10 (a) 42, 56 B1B1 cao 71, 97 B1B1 cao (b) n (n + 1) oe B2 M1 for attempt at length x width involving n or n'th (n'th + 1) or k (k + 1) where k is any variable

(c) 12 B2 M1 for 2 n² – 1 = 287 [8]

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IGCSE – May/June 2008 0580/0581 03

© UCLES 2008

1 (a) 0.68 x 450 M1

= 306 A1

2 x 450 + 306 (= 1206) M1 dep allow 900 or 450 + 450

SCM3 for 2.68 x 450 (= 1206)

(b) 2814 B3 M1 for 1206 ÷ 6 (implied by 201) or 450 ÷ 6 or 306 ÷ 6

M1 dep for x (6 + 5 + 3) implied by 14

SCM2 for 1206 + 1005 + 603

(c) 4955 B2 M1 for 500 x 9.91 implied by figs 4955

(d) 2320 or 11 20 pm B2 SC1 for 1720 or 1120 seen

SC1 for any arrival time + 6 soi

[10]

2 (a) translation B1

col.vector 2 -4 B1 B1 SC1 for col.vectors 4 -8 or -4 2 or for (2, -4)

(b) reflection B1

(in) x = 0 or y axis B1

(c) rotation B1

90º (anticlockwise) oe B1 i.e. 1/4, 270 clockwise, - 270

(about) origin oe B1 accept (0,0), O

(d) enlargement B1

(scale factor) -2 B1

(centre) origin oe B1

SC1 for enlargement, SF=2, about origin (oe) and

rotation of 180 about the origin (oe)

[11]

3 (a) (i) 6,17,8,9,11,9 B2 B1 for 4 or 5 correct or for all tallies correct

(ii) correct bar chart B1ft ft from their frequency table or tallies

(iii) 2 B1ft from their table or chart

(iv) 3 B1ft from their table or chart

(v) 3.48

B3cao M1 for clear indication of 1x6 + 2x17 + 3x8 + 4x9 +

5x11 + 6x9 ft imp by 209

M1 dep for ÷ 60

(b) 66º B2ft M1 for "11" ÷ 60 x 360 or "11" x 6

[10]

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IGCSE – May/June 2008 0580/0581 03

© UCLES 2008

4 (a) (i) 3x = 14 + 4 oe M1

(x =) 6 A1cao SC2 for 6 www

(ii) y + 1 = 2 x 5 oe M1

(y =) 9 A1cao SC2 for 9 www

(iii) 6z - 21 - 2z + 6 (= -9) B1

4z = 6 B1ft ft their expansion but must be 4 terms

z = 1.5 B1cao

(b) (i) p + q = 12 B1

(ii) 25p + 40q = 375 B1

(iii) correct method M1 multiply and subtract, substitution

p = 7 A1

q = 5 A1 SC3 for p=7 and q=5 www

[12]

5 (a) (i) 43.0 art or 43 B2 M1 for π x 3.7²

(ii) 10.0 art or 10 B2ft M1 for 430 ÷ their (a)(i) ft

(b) (i) (length) = 22.2 B1 accept length and width interchanged

(width) = 14.8 B1

(height) = 20 B1ft ft is 2 x their (a)(ii)

(ii) 6570 art B2 ft ft is their L x W x H from (b)(i)

M1 for L x W x H ft (substituted)

(iii) 78.5 (%) art B3 ft ft is 5160 ÷ their (b)(ii) x 100 but only if answer < 100

B1 for 12 x 430 or 5160

M1 for 5160 ÷ their (b)(ii) x 100

[12]

6 (a) (i) 63 B1

(ii) 54

B2 cao M1 for 180 - 2 x their (a)(i) soi (may be implied by

answer)

(iii) 134 B2 cao M1 for 360 - (100 + 63 + their (a)(i)) or 197 - their (a)(i)

soi (may be implied by answer)

(b) (i) 360 ÷ 8 or 6 x 180 MA1

180 - 45 or 1080 ÷ 8 MA1 dependent

SC2 for convincing argument

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IGCSE – May/June 2008 0580/0581 03

© UCLES 2008

(ii) octagon drawn M1 closed and not re-entrant

accurate A1 angles at A and B equal to 135 +/- 2 degrees

and lines BC and AH equal to 4 +/- 0.1 cms

(iii) 4.7 to 5.0 B1

(iv) 9.6 B2ft ft is 2 x their (b)(iii)

M1 for 0.5 x 4 x their (b)(iii)

(v) 76.8 B1 ft ft is 8 x their (b)(iv)

[13]

7 (a) (i) tan (QPR) = 10.3 ÷ 7.2 M1 M1 for complete long method

55 (.0) E1

(ii) 125 B1 cao

(b) (i) 125 - 98 accept 55 + 98 + 27 = 180

or 180 - ( 98 + 55 ) E1 do not accept 180 - 153

(ii) 6.13 art B2cao M1 for 13.5 x sin27 oe (allow full correct long methods)

SCM1 for PR (pythag, sin or cos) RS (pythag) then A1

for 4.9 art or SCM1 for PR (pythag, sin or cos) RS(tan)

then A1 for 6.4 art.

(iii) 37.1 or 37.13 art B1 ft ft is 31 + their (b)(ii)

(c) 8.24 to 8.25(1….) B2 ft M1 for their (b)(iii) ÷ 4.5

[9]

8 (a) (i) x + 3 B1

(ii) x (x + 3) or x² +3x B1 ft from their (a)(i)

(iii) x² +3x = 7

x² +3x - 7 = 0 E1 both lines seen

(b) (i) -3, -9, -3 B3 B1, B1, B1

(ii) 8 points correctly plotted P3 ft P2ft or 6 or 7, P1ft for 4 or 5 (+/- 1/2 small square)

smooth curve C1 (must go below y = -9)

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IGCSE – May/June 2008 0580/0581 03

© UCLES 2008

(c) (i) 1.5 to 1.6 B1 ft

-4.5 to -4.6 B1 ft ft is their intersections with the x-axis

(ii) 4.5 to 4.6 B1 ft ft is their positive (c)(i) + 3

(d) (i) correct line L1 long enough to cross y axis (+/- 1/2 small square)

(ii) (y =) 2x - 3 B1,B1ft B1 for 2 (as coefficient of x)

B1 ft for their intersection with the y-axis

[16]

9 (a) Pentagon B1

(b) (i) 61 to 63 B1

(ii) AE = 6.3 to 6.5 cm

and DE = 5.7 to 5.9 cm B1

correct arcs seen B1 accept concave polygon

SC1 if lengths reversed and with arcs

(c) (i) perpen.bisector of BC B1 +/- 1mm and +/- 1 degree accuracy

correct arcs seen B1

(ii) bisector of angle ABC B1 +/- 1 degree accuracy

correct arcs seen B1

(d) "M" correctly marked B1 dep. on at least first B1 in each part of (c)

(e) 2 marks 0.8 (+/-0.1) apart B1

1.85 (+/-0.1) from A and B B1

[11]

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© UCLES 2008

Abbreviations

art answer rounding to cao correct answer only ft follow through after an error oe or equivalent soi seen or implied SC Special Case

Qu Answers Mark Part Marks

1 (a) (i)

(ii)

5

3 × 30 000

or 30 000 − 5

2 × 30 000

Aida $7500 Bernado $6000 Christiano $4500

M1

W3

Must see evidence of fractions

M1 for 18000345

3or4or5×

++

A1 for 1 correct answer

(b) (i) 10 500 W2 M1 for 100

35 × 30 000 or 0.35 × 30 000

(ii) 60

13 W2 W1 for 30000

6500 seen or other ‘correct’ fraction.

(iii) ($)13 000

W1ft

(c) 24 W3cao M1 for 15 500 − 12500 or 1550012500

× 100

M1 for 12500

'3000' × 100 or ‘124’− 100

2 (a) (i)

(ii)

(iii)

52.3 art 24.4 art 17.0 art

W2cao W2 ft

W2cao

M1 for 55cos18° M1 for ‘52.3’tan25°. Ft their ED

M1 for 55sin18° or √(55 2− ‘52.3’ 2 ) or ‘52.3’

tan18° Long methods, e.g. sine rule must be explicit and ‘correct’.

(b)

‘24.4’ − ‘17.0’ (= 7.4)

M1

Allow for clear attempt to find FD − AD.

(c) (i)

(ii)

14.1 art

31.7 art

W2cao

W2cao

M1 for √( 12 2 + 7.4 2 ) or correct long methods

12 ÷ cos (tan 1−

12

4.7 ) or 7.4 ÷ sin(tan 1−

12

4.7 )

M1 for tan (FBA) = 12

4.7 oe

or sin FBA = ''

4.7

FB or cos FBA =

''

12

FB

3 (a) (i)

(ii)

(iii)

(b)

12 7 8.5

10 points correctly plotted

W1 W1 W2

W3

M1 for Attempt at ordering the data. W2 for 8 or 9 points correctly plotted W1 for 6 or 7 points correctly plotted

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(c) (i)

(ii)

8.58(3…) or 8.6 Plotted (their (c)(i), 38.8)

W2

W1ft

M1 for attempt at totalling data ÷ 12 Allow method if 1 error or omission, but must see an attempt (or judge implied) to divide by 12

(d) (i)

(ii)

Line of fit Negative

W1

W1

Line must indicate understanding

4 (a)

(b)

(c)

(d)

22° Tangent (and) radius/ diameter (meet at) 90° 90° (Angle in a) semi-circle 68° (Angles in a )triangle (=)180° 68° Alternate or Z (angles)

W1cao W1

W1cao W1

W1ft W1

W1cao W1

Degree symbol not essential throughout question. Allow perpendicular for 90°

Ft is180 −( their (a) + their (b)) or alternate segment (theorem) Allow Z correctly placed on the diagram.

5 (a)

(b) (i)

(ii)

(c) (i)

(ii)

(d) (i)

(ii)

6 10 30 Line from 09 30 to 0945 Line to (‘10 30’, 18) 20 Line (11 15, 0) to ( their 11 35, 18) Line (12 00,18) to (12 45,0)

24

W1

W2

W1 W1ft

W1

W1ft

W1

W2

M1 for 20

15

SC1 for 10 15

accuracy ± 1mm

ft their time in (c)(i) provided in minutes and Y 45 Line (11 15, 0) to (11 [15 + ‘20’], 18)

M1 for 18 ÷ 0.75

Allow 18 ÷ 45 × 60 for method

6 (a) (i)

(ii)

(b)

( y =)13 ( x =) 9

7

275 y−

or 2y−75

−7

W2

W2

W2

M1 for (2y =) 75 − 7 × 7

M1 for 7x = 75 − 12 or −7x = 12 − 75

M1 for 7x + 2y = 75.

7x = 75 − 2y or −7x = 2y − 75 or −7x − 2y = −75

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(c) (x =) 11, (y =) −1

W3 M1 for multiply and correct add/subtract or correct substitution.

A1 for x = 11 or y = −1

7 (a)

(b)

(c)

(d) (i)

(ii)

3, −3, 3 8 correctly plotted points Smooth curve

( −0.5, −3.25)

Line x = −0.5 drawn

x = −0.5 oe

W3

W3ft W1

W2ft

W1cao

W1ft

W1 for each correct value W2 for 6 or 7 points, W1 for 4 or 5 points Half square accuracy

must go below line y = −3 W1 for one coordinate correct

Ft their graph but −1 < x < 0 and y < −3 Allow calculated if exact values (W2 or W1) Half square accuracy Ft any vertical line only

8 (a) (i)

(ii)

(b)

(−3, −2)

(AB =)

2

4, (BC =)

−

2

3

(1, −5), (5, −3), (2, −1)

W1

W1, W1

W2

SC1 for 2

4

and

2

−3

W1 for 2 correct points plotted Must join points, with straight lines, for both marks.

(c) (i)

(ii)

(d)

P( 5, 2), Q( −1, 6) Enlargement (Scale factor) 2

(Centre ) A or (−3, −2)

( 0, −4) marked Joined to A and B

W1, W1

W1 W1

W1ft

W1 W1ft

Ft their (a)(i) Zero if not a single transformation Their image of C joined to A and B.

9 (a) (i)

(ii)

(b) (i)

(ii)

99 to 101 (metres) 103° to 105° Bisector of angle ABC

(45 ± 1 to BC) with arcs Bisector of AD with arcs

±1mm from centre of AD

and 89° to 91° to AD. Closed region T indicated

W1 W1

W2

W2

W1

W1 correct bisector without arcs W1 correct bisector without arcs. Bisector about 89° to 91° to AD by eye and centre within 2mm by eye. Dependent on at least W1 for each bisector. Allow T omitted if region is clear.

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(c) Lines parallel to and 3cm

(±0.1cm) from AB and BC. Lines joined by arc, centre B.

radius 3cm (±0.1cm)

W1

W1

10 (a)

(b)

(c) (i)

(ii)

(d)

(Lines) 10 and 13 (Dots) 8 and 10 (Lines) 31, (Dots) 22 3n + 1 oe 2n + 2 oe

n − 1 or 1 − n

W1 W1

W1, W1

W2cao

W2cao

W2ft

SC1 for jn + 1 or 3n + k

where j and k are integers. j ≠ 0 SC1 for jn + 2 or 2n + k

where j and k are integers. j ≠ 0

M1 for ‘(3n + 1)’ − ‘(2n + 2)’ or reversed Ft and M1 dependent on two linear algebraic expressions

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for the guidance of teachers

0580, 0581 MATHEMATICS

0580/03, 0581/03 Paper 3 (Core), maximum raw mark 104

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 03

© UCLES 2009

Abbreviations

cao correct answer only ft follow through after an error oe or equivalent SC Special Case www without wrong working

Qu Answers Mark Part marks

1 (a) (i)

(ii)

(b) (i)

(ii)

(c)

(d)

6000 ÷ (7 + 5 + 3) Multiply by 7 (Stephano) 2000 www (Tania) 1200 www ($)47040

($)28224

($)1200 ($) 14292

1

1

1 1

2

2ft

2

4

M1 6000 ÷ clear attempt at total M1 Dependent on first mark. Must be clearly Stephano. Must be clearly Tania.

M1 1.40 × 12 × 2800

M1 5

3 × ‘47040’ or 0.6 × ‘47040’

M1 5000 × 8 × 3 ÷ 100 SC1 for final answer 6200

M2 12000 × (1.06)3

Or M1(12000+12000 × 0.06) × 0.06 M1 dep. Correct method for the next 2 years A1cao ($)14292(.19(2)) W1ft Their answer rounded to the nearest dollar. If M0 then maximum SC2 for ($) 2292 or SC1 for ($) 2292.2 or ($) 2292.19(2) or ($) 2300

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IGCSE – May/June 2009 0580, 0581 03

© UCLES 2009

2 (a)

(b) (i)

(ii)

(iii)

(c) (i)

(ii)

(d)

One-third of 360 oe 30 90 60 26(.0) or 25.98(……) (c) (i)sin (b) (iii) oe 22.5 48.36 to 48.4

1

1

1

1ft

2ft

1 1

2

90 − their (b) (i)

M1 30cos (b) (i) or 30sin(90 − (b) (i))

or equivalent full method M1 for correct full method for AD W1 dependent on M1

M1 tan (AED) = 20

5.22

or cos (AED) = 2

5.222

20

20

+

or

sin(AED) = 2

5.222

20

5.22

+

3 (a)

(b) (i)

(ii)

(c)

Horizontal line from (08 30, 30) to (09 30, 30) Line from (their 09 30, 30) to (10 15, 380) Horizontal line from their (10 15, 380) to (10 50, their 380) Line from their (10 50, 380) to (11 30, 420)

0.75 or 4

3 hour

466 to 467 35

W1

W1ft W1ft

W1ft

1

2cao

3cao

Only ft from their 09 30 Ft incorrect 10 15 and 380 Ft incorrect 10 50 and 380

M1 for 350 ÷ their (b) (i) W1ft (air) 3 h 30 mins oe 210 min W1(train) 2 h 55 mins oe 175 min

9Dwebsite.tk



IGCSE – May/June 2009 0580, 0581 03

© UCLES 2009

4 (a) (i)

(ii)

(iii)

(iv)

(b)

x − 4 2x + 5

‘2x + 5’ = 3 × ‘(x − 4)’ oe (x =) 17 www (x =) 2, (y =) 1.5

1

1

1ft

3cao

3

Allow x + x + 5 Only ft linear expressions in x.

M1 ‘3x − 12’ M1 indep px = q

Reducing their equation to a single term in x and a single constant. M1 for complete correct method A1 for 1 correct answer ww both correct W3 ww one correct W0 Multiply and add/subtract. 2 terms correct. Eliminate x: subtract + 2 terms right Eliminate y: add + 2 terms right. Substitution

M1 for 3(8 − 4y) − 2y = 3 or

x + 4 ( )2

33 −x = 8 or 3x − 2 ( )4

8 x− = 3 or

( )3

23 y− + 4y = 8 or ( )3

23 y+ = 8 − 4y or

( )2

33 ±x = ( )4

8 x± or better.

5 (a)

(b)

(c)

(d)

(e)

Reflection in y axis or x = 0

Translation

0

8 or 8 right (only)

Correct reflected pentagon Correct rotated pentagon Rotation, 180, (About) origin oe Correct enlarged pentagon

2

2

2

2

3

2

W1 transformation W1 Line W1 transformation W1 vector or description SC1 A reflected in a horizontal line, not the x axis

SC1 B rotated anti-clockwise 90° about the

origin or 90° clockwise about any other point.

W1 rotation, W1 180, W1 origin SC3 Enlargement (SF) –1 origin Accept (0, 0) for origin. W1 for any enlargement of A with a scale factor

of 2

1 .

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IGCSE – May/June 2009 0580, 0581 03

© UCLES 2009

6 (a)

(b)

(c) (i)

(ii)

(iii)

(d)

(e) (i)

(ii)

Octagon 135 Angle OAB = their (b)/2 or

angle AOM = 90 − their (b)/2

4 × tan ‘67.5’ or 4 ÷ tan ‘22.5’ 9.656… or 9.66 38.6 to 38.64 308.8 to 309.12 3705.6 to 3709.44 or 3710 2400 35.2(3…) to 35.3(0…)

1

2

W1ft

M1 A1cao

2

1ft

1ft

2cao

3cao

M1 for 180 − (360 ÷ 8) oe 67.5 or 22.5 correct values, Dep on W1 and M1

M1 for 0.5 × 8 × 9.66

Their (c) (ii) × 8

Their (c) (iii) × 12

M1 for 3 × 2 × 2 × 200

M1 for their ((d) − (e) (i)) soi.

M1 for (d)

(e)(i)(d)− × 100

Or M2 for ( )(d)

(e)(i)1 × 100

SC1 for Answer 64.7 to 64.77

7 (a)

(b)

(c)

(d) (i)

(ii)

x 0 1 2 3 4 5 6 7 8 9 y 0 8 14 18 20 20 18 14 8 0 Their 10 points correctly plotted, within half a square. Smooth curve through the 10 correct points (x =) 4.4 to 4.6 (y =) 20.1 to 20.5 Ruled line y = 6 8.1 to 8.5 Must be to 1 decimal place 0.5 to 0.9 Must be to 1 decimal place

3

P3ft

C1

1cao 1cao

1

1cao 1cao

W2 for 4 correct W1 for 3 correct P2ft for 8 or 9 correct P1ft for 6 or 7 correct Shape must be correct and the curve goes above y = 20. SC1 for both correct but not to 1dp e.g. 8.27 and 0.73

9Dwebsite.tk



IGCSE – May/June 2009 0580, 0581 03

© UCLES 2009

8 (a)

(b) (i)

(ii)

(c) (i)

(ii)

(iii)

5, 126, 90 3, 5, 6, 4, 2 Blocks ‘correct’ heights No gaps. 10 points plotted correctly Zero oe

20

3 oe or 0.15 or 15%

1 1, 1

2

2ft

3

1

2ft

SC1 for both angles incorrect but totalling 216°. W1 for 3 or 4 correct or left as tallies and all correct. W1 for only 1 incorrect SC1 All correct but small gaps between or full horizontal lines only W2 for 8 or 9 correct W1 for 6 or 7 correct

On vertical age line (±1 mm) and between (or on) correct horizontal lines. (allow weak (slight) negative) Ft numerator only

W1 for k

their3 k ≥ 3

9 (a) (i)

(ii)

(iii)

(b)

(c)

−8,

−13 Subtract 5 oe

−5n + 17

5n − 8 9 www

1cao 1ft

1

2

2

1ft

Ft sixth term 5 less than the fifth W1 for jn + 17 or –5n + k where j and k are

integers, j ≠ 0

W1 for jn − 8 or 5n – k where j and k are

integers, j ≠ 0 Ft two linear expressions only

9Dwebsite.tk





for the guidance of teachers

0580 MATHEMATICS

0580/03 Paper 3 (Core), maximum raw mark 104

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.



9Dwebsite.tk



IGCSE – October/November 2009 0580 03

© UCLES 2009

Qn Answers Mark Notes

1 (a) (i)

(ii)

(iii)

(b) (i)

(ii)

(iii)

(iv)

1/5

2/5

0

6

1

2.6 (0) www

heights 8, 4, 5, , 2

6 or ft height for their (b) (i)

1

1

1

1

1

3

2

1 ft

Accept 0.2 or 20%

Accept 0.4 or 40%

Accept 0/5 or 0%

cao

cao

M1 for 1 × 8 + 2 × 4 + 3 × 5 + 4 × their

(b) (i) + 5 × 2

M1 dep for ÷ 25 or their 25

SC1 for one error, or small gaps

2 (a) (i)

(ii)

(iii)

(b)

(c)

15.7 art

19.6 art

14.6 art

Within range 7840 to 7860

31

2

2

2

2 ft

3 ft

M1 for 2 × π × 2.5

M1 for π × 2.52

M1 for π × (2.5 + 0.8)2

M1 for their (a) (ii) × 0.4 × 1000

M1 for their (b) ÷ 250 soi

A1 ft for 31.4 art

W1 for their answer correctly rounded

3 (a) (i)

(ii)

(b) (i)

(ii)

(iii)

(iv)

4.5

3

8.14

32.56

46.25

8.75(6…) or 8.76

2

1 ft

3

1 ft

1

3

M1 for 15 × 3 / (7+3)

Their (a) (i) ÷ 2 and rounded up

M1 for 100 – 12 soi

M1 for 9.25 × their 88 / 100

4 × their (b) (i)

cao

M1 for (their (ii) + their (iii)) soi

2nd M1 dep for ÷ (4 + 5) soi

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© UCLES 2009

4 (a) (i)

(ii)

(iii)

(b) (i)

(ii)

(c)

(d)

Isosceles

DNC

70°

49.4° or 49°24′ art

9.22 art

12.2 art

42.8(4….) or 42.85

1

1

1

2

2

3

2 ft

Condone spelling

Condone order of letters

cao

M1for inv tan (7/6)

M1 for √(62 + 72 ) soi (e.g. √85)

M2 for 7/sin35

M1 for 2 × [their (b) (ii) + their (c)] oe

5 (a)

(b)

(c) (i)

(ii)

(d) (i)

(ii)

(iii)

(iv)

2 –6 2

seven points correctly plotted

smooth correct curve through 7 correct

points

(–2, –7)

–4.6 to –4.75

and 0.6 to 0.75

correct point marked

ruled line from their A to their (0, –3)

–4 / 2 oe

y = –2x – 3 oe

1, 1, 1

P3ft

C1

1

1

1

1

1

2

2

5 or 6 P2ft, 3 or 4 P1ft

cao

cao

cao

Condone lack of label

Continuous line of this minimum length

M1 for attempt at gradient

or

SC1 for 2 oe or –1 oe from correct line

SC1 for y = kx – 3 oe or y = –2x + k oe

or y = their (d) (iii)x + k oe

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6 (a)

(b)

(c) (i)

(ii)

(iii)

(d)

(e)

x + 4

3x

x + x + 4 + 3x

5x + 4

Their c (i) ÷ 3 = 28 or their c (i) = 28 × 3

(x = ) 16

48 or 3 × their x

84%

1

1

M1 ft

A1 cao

1

2

1 ft

2

soi ft is x + (a) + (b)

5x + 4 www scores both marks

M1 for 5x = 84 – 4 or 5x = 80 or x = 80/5

Ft is 3 x (c) (iii)

M1 for 63 / 75 × 100

7 (a)

(b)

(c)

(d)

(e)

4

4 correct lines drawn, accept reasonable

freehand

2600

3100.40

5962.32

1

2

3

2

3

cao

SC1 for 2 correct lines

M1 for 2800 × 1.75 or 4900

M1 for their 4900 – 2300

M1 for 2300 × 1.348

M2 for 5000 × (1.092)2

SC1 for 5000 × (1.92)² or full equiv.

or 18432

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8 (a) (i)

(ii)

(b) (i)

(ii)

(iii)

Correct X

Correct Y

Correct Z1

Correct Z2

Translation ,

4

8

OR Rotation , through 180 about (4, 0)

2

2

2

2 ft

1 , 1

SC1 for translation of

− 7

2

SC1 for rotation through 90 clockwise

Or 90 anticlockwise about any point

SC1 for reflection in y axis

Or in any horizontal line

strict ft reflection of their Z1 if possible

SC1 for reflection in y = 4 or any vertical

line

W1 transformation, W1 full description

SC2 for Enlargement sf = –1 coe (4, 0)

9 (a)

(b)

(c) (i)

(ii)

(d)

13 21

10 15

43

28

½ × 5 × 6

= 15 seen

½ × 20 × 21

= 210

(k =) –1

1 1

1 1

1

1

1

1dep

1

1

2

cao

cao

cao

cao

accept ½ × 5 × (5 + 1)

accept ½ × 20 × (20 + 1)

accept 210 www for both marks

M1 for 7 = 3² + k × 3 + 1 oe

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0580+0581 s02 ms 1+2+3+4 - weebly9dwebsite.weebly.com/uploads/3/0/7/8/3078174/paper_3.pdfpage 1 mark...

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