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June 2003
INTERNATIONAL GCSE
MARK SCHEME
MAXIMUM MARK: 104
SYLLABUS/COMPONENT: 0580/03, 0581/03
MATHEMATICS
Paper 3 (Core)
9Dwebsite.tk
Page 1 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
9Dwebsite.tk
Page 2 Mark Scheme Syllabus Paper
IGCSE EXAMINATIONS – JUNE 2003 0580/0581 3
© University of Cambridge Local Examinations Syndicate 2003
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
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
IGCSE EXAMINATIONS – JUNE 2003 0580/0581 3
© University of Cambridge Local Examinations Syndicate 2003
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
9Dwebsite.tk
Page 4 Mark Scheme Syllabus Paper
IGCSE EXAMINATIONS – JUNE 2003 0580/0581 3
© University of Cambridge Local Examinations Syndicate 2003
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
9Dwebsite.tk
November 2003
INTERNATIONAL GCSE
MARK SCHEME
MAXIMUM MARK: 104
SYLLABUS/COMPONENT: 0580/03, 0581/03
MATHEMATICS
Paper 3 (Core)
9Dwebsite.tk
Page 1 Mark Scheme Syllabus Paper
MATHEMATICS – NOVEMBER 2003 0580/0581 3
© University of Cambridge Local Examinations Syndicate 2003
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
9Dwebsite.tk
Page 2 Mark Scheme Syllabus Paper
MATHEMATICS – NOVEMBER 2003 0580/0581 3
© University of Cambridge Local Examinations Syndicate 2003
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
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
MATHEMATICS – NOVEMBER 2003 0580/0581 3
© University of Cambridge Local Examinations Syndicate 2003
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
SYLLABUS/COMPONENT: 0580/03, 0581/03
MATHEMATICS
Paper 3 (Core)
9Dwebsite.tk
Page 1 Mark Scheme Syllabus Paper
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
9Dwebsite.tk
Page 2 Mark Scheme Syllabus Paper
MATHEMATICS – JUNE 2004 0580/0581 3
© University of Cambridge International Examinations 2004
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.
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
MATHEMATICS – JUNE 2004 0580/0581 3
© University of Cambridge International Examinations 2004
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
9Dwebsite.tk
Page 4 Mark Scheme Syllabus Paper
MATHEMATICS – JUNE 2004 0580/0581 3
© University of Cambridge International Examinations 2004
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
SYLLABUS/COMPONENT: 0580/03, 0581/03
MATHEMATICS
Paper 3
9Dwebsite.tk
Page 1 Mark Scheme Syllabus Paper
IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 3
© University of Cambridge International Examinations 2005
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
9Dwebsite.tk
Page 2 Mark Scheme Syllabus Paper
IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 3
© University of Cambridge International Examinations 2005
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
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 3
© University of Cambridge International Examinations 2005
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
9Dwebsite.tk
Page 4 Mark Scheme Syllabus Paper
IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 3
© University of Cambridge International Examinations 2005
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
9Dwebsite.tk
Page 5 Mark Scheme Syllabus Paper
IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 3
© University of Cambridge International Examinations 2005
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
SYLLABUS/COMPONENT: 0580/03, 0581/03
MATHEMATICS
Paper 3 (Core)
9Dwebsite.tk
Page 1 Mark Scheme Syllabus Paper
IGCSE – JUNE 2005 0580/0581 3
© University of Cambridge International Examinations 2005
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
9Dwebsite.tk
Page 2 Mark Scheme Syllabus Paper
IGCSE – JUNE 2005 0580/0581 3
© University of Cambridge International Examinations 2005
(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.)
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
IGCSE – JUNE 2005 0580/0581 3
© University of Cambridge International Examinations 2005
(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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Page 4 Mark Scheme Syllabus Paper
IGCSE – JUNE 2005 0580/0581 3
© University of Cambridge International Examinations 2005
(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
Page 1 Mark Scheme Syllabus Paper
IGCSE – NOVEMBER 2005 0580/0581 3
© University of Cambridge International Examinations 2005
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]
9Dwebsite.tk
Page 2 Mark Scheme Syllabus Paper
IGCSE – NOVEMBER 2005 0580/0581 3
© University of Cambridge International Examinations 2005
Question Answer Marks Comments Total
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]
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
IGCSE – NOVEMBER 2005 0580/0581 3
© University of Cambridge International Examinations 2005
Question Answer Marks Comments Total
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]
9Dwebsite.tk
Page 4 Mark Scheme Syllabus Paper
IGCSE – NOVEMBER 2005 0580/0581 3
© University of Cambridge International Examinations 2005
Question Answer Marks Comments Total
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
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
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
Page 1 Mark Scheme Syllabus Paper
IGCSE – May/June 2006 0580 and 0581 03
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Page 2 Mark Scheme Syllabus Paper
IGCSE – May/June 2006 0580 and 0581 03
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
IGCSE – May/June 2006 0580 and 0581 03
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Page 4 Mark Scheme Syllabus Paper
IGCSE – May/June 2006 0580 and 0581 03
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Page 5 Mark Scheme Syllabus Paper
IGCSE – May/June 2006 0580 and 0581 03
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Page 6 Mark Scheme Syllabus Paper
IGCSE – May/June 2006 0580 and 0581 03
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Page 7 Mark Scheme Syllabus Paper
IGCSE – May/June 2006 0580 and 0581 03
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Page 8 Mark Scheme Syllabus Paper
IGCSE – May/June 2006 0580 and 0581 03
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Page 9 Mark Scheme Syllabus Paper
IGCSE – May/June 2006 0580 and 0581 03
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Page 10 Mark Scheme Syllabus Paper
IGCSE – May/June 2006 0580 and 0581 03
© University of Cambridge International Examinations 2006
9Dwebsite.tk
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
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
Page 2 Mark Scheme Syllabus Paper
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
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
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
9Dwebsite.tk
Page 4 Mark Scheme Syllabus Paper
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
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
MARK SCHEME for the May/June 2007 question paper
0580 and 0581 MATHEMATICS
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.
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 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
Page 2 Mark Scheme Syllabus Paper
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]
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
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]
9Dwebsite.tk
Page 4 Mark Scheme Syllabus Paper
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]
9Dwebsite.tk
Page 5 Mark Scheme Syllabus Paper
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]
9Dwebsite.tk
Page 6 Mark Scheme Syllabus Paper
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]
9Dwebsite.tk
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
MARK SCHEME for the October/November 2007 question paper
0580 and 0581 MATHEMATICS
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.
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 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
Page 2 Mark Scheme Syllabus Paper
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]
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
IGCSE – October/November 2007 0580 and 0581 3
© 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]
9Dwebsite.tk
Page 4 Mark Scheme Syllabus Paper
IGCSE – October/November 2007 0580 and 0581 3
© 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]
9Dwebsite.tk
Page 5 Mark Scheme Syllabus Paper
IGCSE – October/November 2007 0580 and 0581 3
© 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]
9Dwebsite.tk
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
MARK SCHEME for the May/June 2008 question paper
0580 and 0581 MATHEMATICS
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.
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 discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the May/June 2008 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.
9Dwebsite.tk
Page 2 Mark Scheme Syllabus Paper
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]
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
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
9Dwebsite.tk
Page 4 Mark Scheme Syllabus Paper
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)
9Dwebsite.tk
Page 5 Mark Scheme Syllabus Paper
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]
9Dwebsite.tk
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
MARK SCHEME for the October/November 2008 question paper
0580 and 0581 MATHEMATICS
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.
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 discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 2008 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.
9Dwebsite.tk
Page 2 Mark Scheme Syllabus Paper
IGCSE – October/November 2008 0580 and 0581 03
© 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
9Dwebsite.tk
Page 3 Mark Scheme Syllabus Paper
IGCSE – October/November 2008 0580 and 0581 03
© UCLES 2008
Qu Answers Mark Part Marks
(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
9Dwebsite.tk
Page 4 Mark Scheme Syllabus Paper
IGCSE – October/November 2008 0580 and 0581 03
© UCLES 2008
Qu Answers Mark Part Marks
(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.
9Dwebsite.tk
Page 5 Mark Scheme Syllabus Paper
IGCSE – October/November 2008 0580 and 0581 03
© UCLES 2008
Qu Answers Mark Part Marks
(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
9Dwebsite.tk
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
MARK SCHEME for the May/June 2009 question paper
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.
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 2009 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.
9Dwebsite.tk
Page 2 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
9Dwebsite.tk
Page 3 Mark Scheme: Teachers’ version Syllabus Paper
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
Page 4 Mark Scheme: Teachers’ version Syllabus Paper
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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Page 5 Mark Scheme: Teachers’ version Syllabus Paper
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
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Page 6 Mark Scheme: Teachers’ version Syllabus Paper
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
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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
MARK SCHEME for the October/November 2009 question paper
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.
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 October/November 2009 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.
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Page 2 Mark Scheme: Teachers’ version Syllabus Paper
IGCSE – 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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Page 3 Mark Scheme: Teachers’ version Syllabus Paper
IGCSE – October/November 2009 0580 03
© 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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Page 4 Mark Scheme: Teachers’ version Syllabus Paper
IGCSE – October/November 2009 0580 03
© UCLES 2009
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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Page 5 Mark Scheme: Teachers’ version Syllabus Paper
IGCSE – October/November 2009 0580 03
© UCLES 2009
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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