9Dwebsite.tk
9Dwebsite.tk
9Dwebsite.tk
9Dwebsite.tk
9Dwebsite.tk
9Dwebsite.tk
9Dwebsite.tk
9Dwebsite.tk
June 2003
INTERNATIONAL GCSE
MARK SCHEME
MAXIMUM MARK: 104
SYLLABUS/COMPONENT: 0580/03, 0581/03
MATHEMATICS
Paper 3 (Core)
9Dwebsite.tk
Page 1
1
Mark Scheme
IGCSE EXAMINATIONS – JUNE 2003
(a)
7
1
(b)
42
1
Syllabus
0580/0581
Paper
3
(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 415
M1 (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)
50
SC1 for 19 (x 100) = 38%
50
(h) (i)
6
50
1
(ii) 14
1
Accept equivalent fractions,
decimals or percentages
50
(iii) 1
1
19
2
(a)
120, ……….24, 20
1, 1, 1
(b)
7 correctly plotted points f.t.
correct curve
(c)
1.6 to 1.8
1
(d)
120, ……..0
2
(e)
Straight line through 4 points
L2
(f)
(1.2 – 1.4, 92 – 96)
(4.6 – 4.8, 24 - 26)
1
1
(g)
-20
2
P3
C1
Deduct 1 for each error (61mm)
Must be a reasonable hyperbola
Accept f.t.
L1 if short or not ruled
SC1 for √ if all straight lines
Accept f.t.
SC1 for 20 or M1 for rise/run seen
(numerical attempt)
16
© University of Cambridge Local Examinations Syndicate 2003
9Dwebsite.tk
Page 2
3
Mark Scheme
IGCSE EXAMINATIONS – JUNE 2003
(a) (i) 175 cents
1
(ii) 25b cents
1
(iii) $1.75
(iv) $
(b) (i)
Syllabus
0580/0581
Paper
3
1 or √
b
25b
(allow
) (0.25b)
4
100
T
n
1 or √
If involves b
1
(ii) The cost of one bar
1
(c) (i) 4.5(0)
1
(ii) 4.2(0)
2
(iii)
y
x
1
(iv)
y-7
x -1
2
M1 for (36 – 6.60)/7
B1 for y – 7 or x – 1 seen
12
4
æ3ö æ 4 ö
2
SC1 if translated by çç ÷÷ , çç ÷÷ etc.
è 4 ø è - 3ø
(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 √ from
Q
(iv) S with vertices (7, 7), (3, 7),
(3, 9)
2
SC1 if different scale factor about A or
enlargement of triangle T s.f. 2 about B
or C
(a) (i) P with vertices (4, 11), (2, 11),
(2, 12)
(b) (i) Translation
æ3 ö
çç ÷÷
è - 4ø
1
1
(ii) Enlargement
Scale factor 1/2
centre A
1
1
1
(c) (i) 90o (anti-clockwise)
1
Accept 270o clockwise
2
B1 for 1 correct
(ii) (3, 3)
16
© University of Cambridge Local Examinations Syndicate 2003
9Dwebsite.tk
Page 3
5
Mark Scheme
IGCSE EXAMINATIONS – JUNE 2003
(a) (i) Accurate and with arcs
(ii) Accurate quarter-circle r = 5
(b)
Correct region shaded
(c) (i) 45o correct
12cm correct
Syllabus
0580/0581
Paper
3
2
B1 without arcs or inaccurate
2
SC1 for r > 4.8 or < 5.2 with compass
or correct r but freehand
1 or √
If convinced
1
1
6 2o
6 1mm
(ii) Reasonable tangent
1
Must be ruled 65o
(iii) 6.8 to 7.2
1
Accept f.t. 60.1
9
6
(a)
3 x 1 x 1.5 + 9 x 1 o.e.
2
M1 for appropriate strategy
M1 (dep.) for correct numbers used
(b)
3780
3
M1 for volume is area x length, 13.5 x
2.8 or 37.8
B1 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
Within 6 0.2cm of the centre
(d)
One vertical line drawn
1
(e)
(order) 1 or no symmetry
1
13
7
(a) (i) 84o
1
(ii) 22o
1
(b)
11
1
(c)
16o
1
(d) (i) 32, (16), 8, 4
3
(ii) Halving o.e.
1
(e)
20o
1
Accept 10.8 ® 11, 10min 48sec ®
11min
B1 for each
Allow answer >20 and <22
9
© University of Cambridge Local Examinations Syndicate 2003
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Page 4
8
(a)
Mark Scheme
IGCSE EXAMINATIONS – JUNE 2003
Syllabus
0580/0581
3 new lines from the vertex to
the 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
Paper
3
10
© University of Cambridge Local Examinations Syndicate 2003
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
Question
Number
1 a)
b)
c)
d)
e)
f)
g)
2 a) i)
ii)
iii)
b) i)
ii)
iii)
iv)
Mark Scheme
MATHEMATICS – NOVEMBER 2003
Mark Scheme
Part
Marks
1
1
1
1
1
1
1
1
1
1
2
24
25 or 52
27 or 33
23
29
26
28 cao
21 and 27
1300 or 1 pm
1030
9
4.35, 8.7(0)
Correct straight line
(through (10, 8.6 to 8.8)
9.2(0) (± 0.1)
575 (± 5)
2
2
6000
art 4400
2
3
art 10400
art 13.9
1√
3√
1
1
Syllabus
0580/0581
Notes
Paper
3
Question
Total
condone 6, 26 or 6 x 26
condone 21 x 27
8
allow 10.30, 10:30 etc
B1 for either 24 or 33 seen
or M1 for 2 correct horizontal lines
drawn or 24 and 33 marked on axis
B1 for one correct
P1 for (5, 4.2 to 4.4) or (10, 8.6 to
8.8)
no ft.
no ft.
10
18
3 a)
b) i)
ii)
iii)
4 a)
b)
c)
d)
4, 7, 6, 4, 4, 2, 3
2
1 cao
2 cao
2.5 cao
1
2
2
_
e) i)
ii)
f)
40
9
M1 for attempt at ranking list seen
M1 their
f (x ) ÷
f imp by 2.5
∑
∑
1√
seen
allow 23%
ft from their table
ft from their table
1√
ft their table x 10. Allow 40/300
1√
7
30
3
9
or
0.3 or
10 30
0.23(3....) or
M1 for 25 x 30 x 8
M2 for π x 102 x 14
or SC1 for π x 52 x 14
ft their a + bi
ft for (their bii) ÷ (25 x 30)
M2 for (their bii) ÷ (25 x 30) oe
or M1 for (their bi) ÷ (25 x 30)
SC1 for 5 or 6 correct or 7 correct
tallies
10
19
5 a)
b) i)
ii)
c) i)
ii)
d)
6
–4
Rotation
through 180°
about (2.5, 6) o.e.
Enlargement
s.f. 3
centre (1,7)
3 cao
1 : 9 cao
1
1
M1
A1
A1
B1
B1
B1
1
2
−2 −6
, –0.66 or better
'
3 9
2
Half turn M1 Al, –1 for "symmetry"
allow correct description of point
accept scale 3, x3 etc
accept'B' for (1,7)
ignore units
SC1 for 27 seen
M1 for correct answer nlt
SC1 for
2
oe or –k
3
© University of Cambridge Local Examinations Syndicate 2003
9Dwebsite.tk
13
Page 2
6 a) i)
ii)
iii)
b) i)
ii)
7 a) i)
ii)
iii)
iv)
v)
b) i)
ii)
8 a)
Mark Scheme
MATHEMATICS – NOVEMBER 2003
27
6
1
2
2
P −3
oe
6
4x + 3
10, 16 and 23
3
44
52
2
3
M1 for (39 - 3) ÷ 6
M1 for P–3 seen or
Syllabus
0580/0581
Paper
3
P 6x + 3
=
oe
6
6
seen
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
M1 for 9x + 4 = 49 oe A1 for x = 5
SC1 for 40 to 48
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.
cuboid or rectangular
1 allow rectangular cuboid but not
prism
cube or cubical
52
1 √ ft from their aii (not strict ft)
24
2 M1 for 2 x 3 x 4
2(pq + qr + pr) oe as final 2 SC1 for pq or qr or pr seen or imp.
answer
for both parts. Other letters used
consistently MR–1
pqr as final answer
2 M1 for pqr seen
3 M1 for 7.5 x 12 oe or 80/12 oe seen
12.5
NB 4021 answer 12.5
90 − 80
+M1 for
x100 (explicit) or
working uses 75 and
80
800
7.50 − 6.66....
x100 (explicit)
10
23
13
6.66....
after M0 SC2 for figs 124 to 126
ww or SC1 for 112.5
b)
120 minutes
3
c) i)
Accurate ┴ bisector of
AB, with arcs ±1°±1mm
complete inside figure
Accurate bisector of <C
with arcs as above
correct area shaded
2
ii)
2
3
or 180 or
x 300 seen
5
5
2
+M1 for
x 300 oe or 300-180
5
B1 for
SC1 if accurate without arcs or
incomplete line. Ignore extra lines
2
SC1 if accurate without arcs or
incomplete line as above
2 √ Areas marked as diagram
ft from clear intention to draw perp.
bisector and angle bisector
12
9 a) i)
ii)
b) i)
ii)
iii)
150 (km)
15 000 000 oe (√)
1
2
1270 to 1320
2
(0)45 to (0)48 oe
245 to 248
1
2
Ml for their a)i) x 100 x 1000
or SC1 for their a)i) x 10n when n>0
M1 for their 8.6 x their 150 must
have some evidence for their 8.6
SC1 for any answer in the range
180 < x < 270
© University of Cambridge Local Examinations Syndicate 2003
9Dwebsite.tk
8
20
Page 3
10 a)
b) i)
ii)
c)
_
Mark Scheme
MATHEMATICS – NOVEMBER 2003
1 6 15 20 15 6 1
Sum 64
1 7 21 35 35 21 7 1
Sum 128
512 accept 29
2n
165 330 462
The first 6 numbers
repeated in reverse
order
_
1
1
2
1
2
2
1
1
Syllabus
0580/0581
Paper
3
SC1 if 6 or 7 correct
SC1 for 256
SC1 for 2 x 2 x 2 seen or description
11
11
TOTAL 104
© University of Cambridge Local Examinations Syndicate 2003
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
MATHEMATICS – JUNE 2004
FINAL MARK SCHEME
0580/3
Question
Answer
Number
1ai
51
Syllabus
0580/0581
Paper
3
June 2004
Marks Comments
Total
1
ii
49
2
iii
46
2
bi
20 60 160 80 40 (360)
2
ii
correct pie chart (±2°)
2
correct labels
L1
iii a
4/9 oe
1
iii b
1/3 oe
2
M1 for clear evidence of
ranking
M1 for total/10, allowing
errors in addition
M1 for evidence of ×4 oe seen
or SC1 for 3 or 4 correct
5 sectors only. Any order.
Or SC1 for 3 or 4 correct or ft
correct
4 or 5 correct or ft correct
allow (0).44…,44.….%, but
not 0.4
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
2a
9
1
6
1
18
1√
ft for 3× their bi (not strict ft)
(0).6
2
M1 for 3× 0.2
30
2√
d
(0).02
2
M1 for their bii/ci (not strict ft)
or 2×3/0.2
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
B1 for each
1√
ft from 4 total costs
bi
ii
ci
ii
14
14
3a
7 8 4 −1
3
B2 for 3 correct or
B1 for 2 correct
© University of Cambridge International Examinations 2004
9Dwebsite.tk
Page 2
b
Mark Scheme
MATHEMATICS – JUNE 2004
Syllabus
0580/0581
13 correct or ft correct
points (±1/2 a square)
P3√
P2√ for 11 or 12 correct or
P1√ for 7 to 10 correct
Correct curve cao
C1
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
f
2
2
g
−3
1
1
1
Paper
3
M1 for incomplete line or
freehand line or both their
(in)correct points correctly
plotted
M1 for attempt at ∆y/∆x from
their straight line graph
−1 if y values given as well
17
17
4a
120
1
b
70
2
M1 for t+2t+75+75=360 oe
3t and 210 implies M1
ci
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
5a
bi
(0).2
1
Tangent and radius
mentioned
1
or described.
© University of Cambridge International Examinations 2004
9Dwebsite.tk
Page 3
Mark Scheme
MATHEMATICS – JUNE 2004
Syllabus
0580/0581
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
Paper
3
9
6ai
ii
bi
ii
translation cao
B1
10
−2
B1
B1
rotation or turn
M1
centre the origin oe
A1
(+) 90 (anticlockwise)
A1
allow quarter turn for M1A1
correct reflection
drawn
2
SC1 for reflection in x-axis
correct enlargement
drawn
2
SC1 for scale factor 2, wrong
centre
or translated
−1 for incorrect notation or a
description
SC1 for both answers correct
but inverted
10
19
7ai
pentagon
1
ii
540
2
iii
108 cao
1
ii
110 or x=70 or y=20
completion
art 50.2
M1
A1
2
may be on diagram
Beware of circular arguments
M1 for tan(−1) and 120/100
iii
120(.2)
1√
ft for 70+their bii
bi
M1 for 3×180, or 5×180−360
or (180−360/5)×5 or 6×90
© University of Cambridge International Examinations 2004
9Dwebsite.tk
Page 4
iv
Mark Scheme
MATHEMATICS – JUNE 2004
300
1√
Syllabus
0580/0581
Paper
3
ft for 180+their biii
−1 for answers reversed
10
10
8ai
ii
iii
b
c
d
e
6 (±0.1)
10
1
2√
73 to 76
both lines drawn (±0.1
cm)
1
2
mediator drawn
(±0.1cm and 1o ) with
two pairs of arcs
complete circle, radius
4 (±0.1) cm drawn,
centre C
L marked correctly
2
√SC1 for 10n where n is an
integer. (ft 60/their ai)
B1 for each line. Ignore any
curves at ends, lines must be at
least 5 cm long. Allow dotted
etc
B1 for correct line with no arcs
or correct arcs with no line
2
SC1 for incomplete circle
1
be convinced
11
9ai
12
1
ii
20
1
iii
2n+2 oe
2
bia
20
1
bib
ii
25
48
1
2
iii
100
2
M1 for 2n +k where k is an
integer
M1 for 12 seen (as diagram
no.)
M1 for 10 seen
10
21
TOTAL MARKS
104
© University of Cambridge International Examinations 2004
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
IGCSE EXAMINATIONS – NOVEMBER 2004
Syllabus
0580/0581
Question
number
Mark Scheme
Part
Marks
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
Hatab
1
32
1
450
1
ii)
straight line ruled from
(1,45) to (10,450)
2
iii) a)
306 ± 4
1
10 60 to 10.80
1
allow 10.6 etc.
translation
1
must be single
transformation
 − 6


 − 7
1
SC1 for correct vector
inverted, or
1
 − 12 
 , or for correct row

 − 14 
b)
v)
b) i)
b)
2 a)
Notes
rotation
M1
-90 or 90 clockwise o.e.
A1
about (0, 0) o.e.
A1
Question
Total
SC1 for freehand or
broken line or any straight
line through the origin ±
½ small square at both
points
vector, or co-ordinates.
Condone missing
brackets
b)
Paper
3
must be single
transformation
© University of Cambridge International Examinations 2005
9Dwebsite.tk
11
Page 2
c)
Mark Scheme
IGCSE EXAMINATIONS – NOVEMBER 2004
Syllabus
0580/0581
(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)
3
Paper
3
12
In this question alternative
methods must be
complete
a)
8
1
b)
6
2
M1 for 100 − 64 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)
ii)
triangle drawn with three
sides the correct length
± 0.1 cm
3
56 ± 2 c.a.o.
1
b)
2 for two sides correct,
with arcs
1 for two sides correct
without arcs
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
© University of Cambridge International Examinations 2005
9Dwebsite.tk
Page 3
ii)
iii)
5 a) i)
b)
c)
Mark Scheme
IGCSE EXAMINATIONS – NOVEMBER 2004
correct line drawn
± 1 mm, ± 1o
correct arcs, radius > 4 cm
B1
correct area shaded
2
Syllabus
0580/0581
Paper
3
B1
kite
1
ii)
correct line BD drawn
1
iii)
70
2
(p =) 90
1
(q =) 50
1
(r =) 50
1√
128.6 c.a.o.
4
SC1 for shading on left
hand side of their
‘mediator’ or inside lines
drawn for their b) i)
11
Allow broken line, one line
only
M1 for
360 − 140 − 80
o.e.
2
f.t. from their q, not strict
f.t.
M2 for 180 5 × 180
o.e.
7
360
or
7
(may be implied by art
129)
+A1 for 128.57
6 a)
b)
3 0 0
1,1,1
7 correct points plotted
P3√
P2√ for 5 or 6 points ± ½
sm. sq.
P1√ for 4 points.
not strict f.t.
c)
smooth curve through
all correct points
C1
incorrectly plotted points
should be ignored for C1.
Minimum curved, not
pointed
-0.8 to -0.7 c.a.o.
1
ignore any y values
2.7 to 2.8 c.a.o.
1
© University of Cambridge International Examinations 2005
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11
Page 4
Mark Scheme
IGCSE EXAMINATIONS – NOVEMBER 2004
Syllabus
0580/0581
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.
1
ignore any y values
2.4 to 2.7 c.a.o.
1
16
1
3x + 8 o.e.
2
-9a
1
+5b
1
c)
3a(2 – 3a)
2
M1 for any correct partial
factorisation
d)
v -u
o.e.
a
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
7 a) i)
ii)
b)
8 a) i)
22
ii)
77 or
iii)
89
14
M1 for 3x. allow n instead
of x. deduct 1 for ‘= x’ or
‘= 0’ or = any number, but
allow a different letter
1
67 + 87
2
2
2
Paper
3
M1 for evidence of
ranking seen anywhere.
e.g. 67,87
M1 for their
∑x
12
© University of Cambridge International Examinations 2005
9Dwebsite.tk
13
Page 5
Mark Scheme
IGCSE EXAMINATIONS – NOVEMBER 2004
72 ± 1
1
80 ± 1
1
94 ± 1
1
1080 ± 5
1√
1200 ± 5
1√
1410 ± 5
1√
appropriate observation
1
27 to 36 entered correctly
1
square
1
b)
100
1
c)
n2 c.a.o.
1
iii) a)
43 c.a.o.
1
871
2
100
1
ii)
10n c.a.o.
1
iii)
91
1
vi)
10n – 9 o.e.
1
b) i)
ii)
iii)
9 a) i)
ii) a)
b)
b) i)
Syllabus
0580/0581
Paper
3
strict f.t.s for their angle
x 15 ± 5
12
allow n x n
M1 for 900 – 30 + 1 o.e.
allow 10 x n
11
Total 104
© University of Cambridge International Examinations 2005
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
IGCSE – JUNE 2005
Syllabus
0580/0581
Paper
3
Question
1 (a)
Answer
2.8
Marks
1
Comments
ignore minus sign, accept 2800 g
(b)
106.5(0)
1
107 is X (but remember to look back for
106.5)
(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
(c)
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
–0.4 ( ± /0.1)
1
please note no f.t. on this part
2.4 ( ± 0.1)
1
(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
(c)
(d)
11
3
(a)
(b)
(i)
–3
9
1
1
(ii)
9
1
ignore minus sign
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
© University of Cambridge International Examinations 2005
9Dwebsite.tk
Page 2
(c)
Mark Scheme
IGCSE – JUNE 2005
Syllabus
0580/0581
(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
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
(d)
Paper
3
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
enlargement
(centre) (0,0) o.e.
(scale factor) 2
1
1
1
}
} must be a single transformation
}
(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)
}
}
(c)
(d)
}
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
(ii)
6
1 c.a.o
(iii)
4
2 c.a.o
2 for 4 or 5 correct, 1 for 2 or 3 correct
accept tallies if in 5’s, accept 8/60, 7/60 etc.
M1 for evidence of ranking (cum. freq.)
© University of Cambridge International Examinations 2005
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Page 3
(b)
Mark Scheme
IGCSE – JUNE 2005
Syllabus
0580/0581
Paper
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
(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)
(b)
(c)
(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
(i)
1.5 or 1 ½ or 3/2
2
(ii)
4z + 2 = 10z – 1
1
M1 for 3y – y = 3 o.e. [unknown on one
side]
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
(i)
a – b = 3 o.e.
4a + b = 17 o.e.
5a = 20
} 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)
3
2 for either (a=) 4 or (b=) 1
or M1 (f.t.) for correctly eliminating one of
the variables
4a + b + 3 = a – b + 17
(ii)
(a=) 4 and (b=) 1
15
7
050 ( ± 2)
2
M1 for correct angle but not 3 figures i.e. 50
( ± 2)
(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
(i)
7 ( ± 2 mm)
1
(ii)
200000
2 c.a.o.
(a)
(b)
(c)
1 for figs 2
or SC1 for figs 1.94 to 2.06
© University of Cambridge International Examinations 2005
9Dwebsite.tk
Page 4
(d)
(e)
Mark Scheme
IGCSE – JUNE 2005
Syllabus
0580/0581
Paper
3
(i)
correct locus drawn
2 f.t.
f.t. is for their scale (normally 5 cm)
at least over sea allow dotted/dashed locus
SC1 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.
f.t. is for their S
1
no f.t. on this part
(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
(iii)
15.4
2 f.t.
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
f.t. is (e)(ii)/1.85
M1 for (e)(ii)/1.85 seen
allow dotted/dashed line
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
(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
(c)
12
104
© University of Cambridge International Examinations 2005
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
Question
1 (a)
(b)(i)
Mark Scheme
IGCSE – NOVEMBER 2005
Answer
Reflection drawn,
Marks
1
correctly in mirror line
1
Rotation
90° clockwise or –90
centre of rotation
marked or described
unambiguously
M1
A1
Syllabus
0580/0581
Paper
3
Comments
any recognisable reflected E in
any vertical mirror line, allow
good freehand
Total
or turn or rotated
A1
(ii) enlargement
scale factor 3
centre of enlargement
marked or described
unambiguously
M1
A1
(iii) translation
 − 7


 − 5
1
B1
B1
A1
or enlarged
SC1 for “made 3 times larger”
etc.
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
(ii) 123.7
M1 for tan ABC = 6/4 oe
1√
(b)
7.21
2
M1 for 62 + 42 oe
(c)
17.2 m
12 m2
3√
M1 for area method
A1 for both numerically correct
B1 for both units correct
[8]
3 (a) (i)
5
–3
12
1
1
1
(ii) 9 correct points plotted
correct, smooth curve drawn
P3√
C1
(iii) –0.8 to –0.7
2.6 to 2.8
1
1
(b)(i)
8 and 2
P2 for 7 or 8 or P1 for 5 or 6
1
(ii) points
curve
P2
C1
P1 for 5 or 6 correct
(iii) 3.1 to 3.3
1√
ft dep on only 1 point of intersection
[14]
© University of Cambridge International Examinations 2005
9Dwebsite.tk
Page 2
Question
4 (a)
Mark Scheme
IGCSE – NOVEMBER 2005
Syllabus
0580/0581
Answer
8.36
Marks
3
Comments
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)
3443
2
1 for 2 or 3 correct
(e) (i)
7/14 oe
√1
ft for their (4 +3)/their 14,
correct or ft correct
Total
√1
(ii) 3/14
(f)
Paper
3
√2
12
M1 for their (10 – 14) x 3
[12]
5 (a)
(b)(i)
bearing 99 to 101°
drawn
angle BAC 109 to 111°
drawn
AB 4.9 to 5.1 cm
AC 5.9 to 6.1 cm
B1
B1
37 to 40
1√
(ii) 247 to 250
B1
B1
1√
(c)
8.9 to 9.1
1√
(d)(i)
Two positions found,
with appropriate arcs
3
(ii) P or Q
4.0 to 4.4
ft from (b)(i)
2 for two positions without arcs
and labelled
1 for one position found and labelled
1
√1
ft for correct measurement of
their closest position to B
[12]
© University of Cambridge International Examinations 2005
9Dwebsite.tk
Page 3
Question
6 (a) (i)
Mark Scheme
IGCSE – NOVEMBER 2005
Paper
3
Marks
4
Comments
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
2
M1 for 61.5
(b)(i)
Answer
10.8 www
Syllabus
0580/0581
61 hours and 30 min
(ii) art 13500
1
(iii) 3.38
2
M1 for their (b)(ii) x 2.5/10000
(iv) 4
1√
rounding up
Total
[14]
7 (a) (i)
(b)
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
M1
M1
working must be seen
but second M1 can imply the
first
A1
A1
SC1 for 1.67 and 0.333
eliminating one of the
variables
eliminating the other
variable (√)
1.66 or 5/3 only
0.3 or 1/3 only
[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]
© University of Cambridge International Examinations 2005
9Dwebsite.tk
Page 4
Question
9 (a)
(b)(i)
Mark Scheme
IGCSE – NOVEMBER 2005
Answer
51.4
Marks
3
Isosceles
1
(ii) p = 50
q = 80
r = 50
s = 50
t = 80
(c)
25
Syllabus
0580/0581
Paper
3
Comments
2 for 51 or M1 for any complete method
1
1√
1√
1√
1√`
ft for 180 – 2p
ft for = p
ft for = p
ft for = q or 180 – 2p
2
M1 for 90 – 65 oe
Total
[11]
© University of Cambridge International Examinations 2005
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
IGCSE – May/June 2006
Syllabus
0580 and 0581
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Paper
03
Page 2
Mark Scheme
IGCSE – May/June 2006
Syllabus
0580 and 0581
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Paper
03
Page 3
Mark Scheme
IGCSE – May/June 2006
Syllabus
0580 and 0581
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Paper
03
Page 4
Mark Scheme
IGCSE – May/June 2006
Syllabus
0580 and 0581
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Paper
03
Page 5
Mark Scheme
IGCSE – May/June 2006
Syllabus
0580 and 0581
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Paper
03
Page 6
Mark Scheme
IGCSE – May/June 2006
Syllabus
0580 and 0581
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Paper
03
Page 7
Mark Scheme
IGCSE – May/June 2006
Syllabus
0580 and 0581
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Paper
03
Page 8
Mark Scheme
IGCSE – May/June 2006
Syllabus
0580 and 0581
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Paper
03
Page 9
Mark Scheme
IGCSE – May/June 2006
Syllabus
0580 and 0581
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Paper
03
Page 10
Mark Scheme
IGCSE – May/June 2006
Syllabus
0580 and 0581
© University of Cambridge International Examinations 2006
9Dwebsite.tk
Paper
03
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
Qu.
1 (a) (i)
(ii)
(iii)
(iv)
(v)
(vi)
(b) (i)
(ii)
(iii)
(iv)
(v)
Mark Scheme
IGCSE - OCT/NOV 2006
Answer
√35
3
45
2 or 3 or 37
2
24
Correct arrangement of triangles drawn.
16 25 36
10000 or 1 x 104
n2 or n × n
Square (numbers)
Marks
1
1
1
1
1
1
1
2
1
1
1
Syllabus
0580, 0581
Paper
3
Comments
Total
accept any combination
accept if only 1 internal line missing
1 mark for 2 correct
Not 1002
accept t = n2 etc. do not accept x2
accept squares, squared
12
–4
2 (a)
(b)
–4
–10
1
8 correctly plotted points, within
square.
2
Smooth curve through 8 points
3
P3ft
C1
(c)
x = 0.5 drawn.
1
(d)
(e)
(f)
2.2 to 2.4
y = 1 drawn.
(x =) –0.7 to –0.5
(x =) 1.5 to 1.7
1ft
1
1
1
1 for each correct entry
P2 for 6 or 7 correct. ft
P1 for 4 or 5 correct. ft
Allow small errors in the points
provided shape is maintained.
must be from (0.5, –9) to curve at
least
must touch curve as min. length
12
3 (a) (i)
(ii)
(b) (i)
(ii)
(iii)
(c) (i)
(ii)
(iii)
(iv)
128.571…… or 128° 34′ (….)
128.6
x + 3y + 80 + 95 = 360 (or better)
x + 3y = 185 oe
40
2
1 ft
1
1
2 ft
180° or angle sum of triangle mentioned
Angle in a semi-circle mentioned.
(a =) 70
(b =) 20
40
1
1
1
1
1ft
M1 for 180 – 360/7 oe
Follow through their (a)(i).
Both marks may be gained in (b)(i)
M1 for x correctly substituted into
the linear equation.
Follow through their (b)(ii) provided
linear in x and y.
SC1 for a = 20
b = 70
2 × their value for b provided
0 < b < 55.
12
4 (a) (i)
(ii)
(b) (i)
(ii)
Enlargement
(Scale Factor) 3
(Centre) (2, 4)
Reflection
(in the line) x = 4
Correct translation drawn
B1
B1
B1
B1
B1
2
Correct rotation drawn
2
.
SC1 for translation by the vector.
 − 3  1   2  k 
    
  
 2   − 1 .5   k   − 3 
SC1 for any 180° rotation.
SC1 for 90° or 270° rotation about
(–1, –2)
9
© UCLES 2006
9Dwebsite.tk
Page 3
5 (a)
(b)
(c)
(d)
Mark Scheme
IGCSE - OCT/NOV 2006
90
14.3 art
18.5 to 18.6
2
2
3
20.6 art
2
Syllabus
0580, 0581
Paper
3
M1 for 0.5 × 18 × 10
M1 for 10 × tan 55oe
M1 for 0.5 × 10 × their (b) or M1 18
– their (b)
1
x 10 x their BX
M1
2
M1 for
Their (a) – (0.5 × 10 × their (b))
M1 for √( 182 + 102) oe
9
6 (a)
750cao
3
(b) (i)
(ii)
756
8
2
1ft
(c) (i)
10
4
2
1
1
1ft
(ii)
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
M1 for 720 × 1.05 oe
Their (b)(i) rounded up to the
number of hundreds
Their cement buckets ÷ 3.5 and
rounded up to next whole number
9
7 (a)
(b)
(c) (i)
(ii)
–1
2
(m =) 2
(c =) 3
Correct line drawn.
y = 2x – 3 oe
1
1
1
2ft
SC1 for 1 SC1 for −
k
K
must cross both axes and line A
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
(ii)
5.71 art
3
(iii)
(iv)
(v)
7 cao
5 cao
5.5
1
1
2
(vi)
(vii)
17.6 art
54 or 53
2ft
2ft
12 25 19 2
2
5 and 6
1ft
(b) (i)
(ii)
2 for 6 or 7 correct –1 if tally marks
1 for 4 or 5 correct
M1 for evidence of
size x frequency calculated for the
sizes.
M1dep for sum of at least 5 ÷ 34
M1 for evidence of finding the
middle shoe size. (Not just an
answer of 5 or 6)
M1 for their 6 ÷ 34 × 100 or 17.65
M1 for their 6 ÷ 34 × 306 or
‘53.8….’. or 53.9
1 mark for 2 or 3 correct or all
correct but not added
Their class with the highest
frequency. –1 for tally marks
17
© UCLES 2006
9Dwebsite.tk
Page 4
9 (a)
Mark Scheme
IGCSE - OCT/NOV 2006
Correct accurate drawing.
(lengths ± 0.2 cm, angles ± 1°)
3
233° to 235°
2ft
(ii)
182 to 190
2ft
(iii)
2 (hours) 42 (mins)
4
(iv)
(v)
24
Correct circle drawn
2
2
(vi)
84 to 100
2ft
(b) (i)
Syllabus
0580, 0581
Paper
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)
From their diagram.
M1 for their angle BCA measured
correctly (± 1°)
Their BC × 20.
M1 for their BC (correct is 9.1 cm to
9.5 cm)
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.
M1 for 18 ÷ 0.75 oe
M1 for partial circle (crossing AB
and AC)
M1 for 4.2 to 5.0
Follow through their diagram,
dependent on intersections seen on
BC
17
Total marks
© UCLES 2006
9Dwebsite.tk
104
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
1
Mark Scheme
IGCSE – May/June 2007
1
B1
(ii)
8 or −8 or ±8
B1
(iii)
4
B1
(iv)
6
B1
3
B1
Multiple of 60
B1
9
B1
(a) (i)
(b) (i)
(ii)
(c) (i)
(ii)
Syllabus
0580/0581
Paper
03
Not −4
B1,B1
3 and 223
[9]
2
(a)
(b)
(c)
2
5
336 − × 336 or × 336
7
7
(=) 240
E1
5 ÷ their(5 + 4 + 3) × 240
100
M1
A1cao
3 ÷ their(5 + 4 + 3) × 240 × 12
(=) 720
(d)
M1
M1
E1
720 × 1.06 2 oe
M2
808.99(2) or 809
A1
240 must be seen for this mark
www 2
1
3
for
.
4
12
720 must be seen for this mark
Allow 2880 for 240 × 12 and
Implied by 88.99(2) or 89(total interest)seen
M1 for 720 × 1.06 (implied by 763.2 seen)
SC1 for 806.(4) (Simple Interest)
www 3 for 808.99(2) or 809
[9]
© UCLES 2007
9Dwebsite.tk
Page 3
3
Mark Scheme
IGCSE – May/June 2007
Syllabus
0580/0581
Paper
03
1
× 5 × 122oe
2
360
B2
M1 for
(ii)
7.5oe
B2
M1 for 225 /4 oe (implied by 56.25)
(iii)
1
2E
or E v 2
2
2
v
B2
B1 for 2E or E
(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
(a) (i)
Equating coefficients of x or y, or
equivalent method.
5y = 5 oe or 10x = 30 oe
x = 3, y = 1
(d)
1
or division by v2
2
Independent ax + b (=7) from their expansion
www 3
M1
A1
A1
or a correctly substituted substitution. E.g.
y = 13 – 4x ⇒ 2x + 3(13 – 4x) = 9
www 3
[14]
4
−10, −20, −60, 30, 20, 15
B2
B1 for –20 (x = –3) or 20 (x = 3)
Their 12 points plotted correctly.
P3ft
Smooth curves through all points.
C1
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
(b)
2
B1
(c)
Correct lines ruled
(d) (i)
(2.4 to 2.5, 24 to 25)
(−2.4 to −2.5, −24 to −25)
(a) (i)
(ii)
(ii)
(e)
B1,B1
B1ft
B1ft
Minimum length from x = –3 to x = 3.
ft their points of intersection
ft their points of intersection
y = 10x oe
B1
cao
−10
B1
cao
[13]
© UCLES 2007
9Dwebsite.tk
Page 4
5
Mark Scheme
IGCSE – May/June 2007
(a) (i)
135 (green)
B1
(ii)
75 (yellow)
B1
(iii)
Ruled lines correct to 2°
3 correctly labelled sectors
B1ft
B1
Only if (a)(i) + (a)(ii) = 210°.
Independent of previous marks
Accept decimals, percentages
(b) (i)
10
oe
24
B1
(ii)
15
oe
24
B1
(iii)
19
oe
24
B1
(c) (i)
0
B1
(ii)
1
B1
Labelled arrows correctly
positioned by eye
(d)
Syllabus
0580/0581
B3ft
SC1 for
Paper
03
12
0
24
0
and
or
and
12
12
24
24
1 mark for each.
ft their probabilities from (b).
[12]
6
(180 – 56)/2
B1
Alt. 90 − (56 ÷ 2)
(ii)
art 2.82
B2
M1 for 6cos 62° (implied by 2.8)
Long method must be complete.
(iii)
5.63 to 5.64
(iv)
5.3 or art 5.30
(a) (i)
B1ft
B2
2 × their (a)(ii)
M1 for 6sin 62°oe
Long method must be complete.
29.8 to 29.9
B2ft
M1 for their (a)(iii) × (a)(iv)
(ii)
art 12.5
B2ft
M1 for 0.5 × π × (their (a)(ii)2)
(iii)
42.3 to 42.4
B1ft
ft is their (b)(i) + (b)(ii)
21100 to 21200
B2ft
M1 for their (b)(iii) × 500
 500 3600 
×

 oe
 60 1000 
M2
M1 for figs 500 ÷ figs 60
(b)(i)
(c)(i)
(ii)
30
A1
1
min
2
or SC1 for1km per minute seen.
www B3
SC2 for answer of
[16]
© UCLES 2007
9Dwebsite.tk
Page 5
7
Mark Scheme
IGCSE – May/June 2007
Syllabus
0580/0581
Paper
03
(a)
Trapezium
B1
(b) (i)
Translation 9 across, 3 down
B2
(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)
 − 3
B1 for 9 across or 3 down or  
 9 
[10]
8
(a) (i)
B1
B1cao
(ii)
90
(iii)
P to R and Q to R ruled.
B1
(iv)
(angle in a ) semi-circle
B1
Angle on a diameter.
Half the angle at the centre.
Bisector of QR with arcs.
B2
SC1 if accurate without arcs. Maximum errors
2mm from mid-point and 2° from
perpendicular.
Bisector of PRQ with arcs.
B2
SC1 if accurate without arcs. Maximum error
2° in line from R.
If wrong line and/or angle used treat as
misread each time.
(b) (i)
(ii)
(c)
Diameter from P through O to Q
Correct Shading
2
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]
© UCLES 2007
9Dwebsite.tk
Page 6
9
Mark Scheme
IGCSE – May/June 2007
Syllabus
0580/0581
Paper
03
(a)
Letter E correctly drawn
B1
(b)
22, 29, 36
B3
B1 for each correct number.
(c) (i)
71
B2
B1 for 7 × 10 + 1 or 8 + 9 × 7 seen.
7n + 1 or 8 + (n – 1) × 7 oe
B2
SC1 for 7n + k seen. (k is an integer) oe
(ii)
(d)
Their (c)(ii) = 113
Full method of solution of their
equation.
16
B1ft
M1ft
A1cao
ft any expression involving n.
ft only a linear equation.
(113 – k)/ ‘7’
www B2
[11]
© UCLES 2007
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
1
(a) (i) 35
Mark Scheme
IGCSE – October/November 2007
Syllabus
0580 and 0581
Paper
3
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
2
M1 for 7/35 x 360 (ft but not for 6) oe
B1
final line (ft) drawn accurately, 1° accuracy
(b) (i) 72
(ii) line drawn
[9]
all within 1 mm
2
(a) translation
drawn
B2
(–5,4), (–3,4), (–4,5)
SC1 for any other translation not parallel to a axis
(b) reflection
drawn
B2
(1,–3), (3,–3), (2,–4)
SC1 for reflection in x=–1 or any y=k
(c) rotation
drawn
B2
(–1,–1), (–3,–1), (–2,–2)
SC1 for any 180 rotation or +90, –90 about (0,0)
(d) enlargement
drawn
B2
(2,2), (6,2), (4,4)
SC1 for any other enlargement sf=2 or centre (0,0)
(e) enlargement
(sf=) 1/2
(centre) (0,0)
B1
B1
B1
accept O
© UCLES 2007
9Dwebsite.tk
[11]
Page 3
3
Mark Scheme
IGCSE – October/November 2007
5
Paper
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
C1
correct points ft within 1 mm
P2 for 10 or 11, P1 for 8 or 9, P1 for 1 correct branch
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
curve drawn
C1
correct points ft within 1 mm
P2 for 11 or 12 P1 for 9 or 10
must be smooth parabola
(f) 3.3, 10.9
B1ft
x from 3.2 to 3.4, y from 10.0 to 12.0
(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
2 curves drawn
4
Syllabus
0580 and 0581
(a) (i) –16
B1
[15]
[8]
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
17, 23
B1
B1
cao
cao
© UCLES 2007
9Dwebsite.tk
[8]
Page 4
6
7
Mark Scheme
IGCSE – October/November 2007
(a) (i) 78
B1
cao
(ii) 5p + 4e
B1
cao
(b) (i) 2x + 3y = 57
5x + y = 58
B1
B1
SC1 for different variables
Paper
3
(ii) 15x + 3y = 174
x=9
18 + 3y = 57
y = 13
M1
A1
M1
A1
oe, for useful mult. or substitution (2 terms correct)
cao
oe, for using first answer correctly and sensibly
cao
www4
ft for M marks only for linear equations in 2 variables
(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)
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"
height of triangle
area of triangle
M1
M1
M1
for 16 x 9, 144, 3 x 9 x 16, 27 x 16, 432
for √(9²–4.5²), √60.75, 7.79, 7.8, 3 x (a)(i) ft or trig
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
3 rectangles and 2 triangles, 432 + 70.2 or 70.1 soi
if M<3 then add SC3 for 502 art with no wrong
working seen
(b) (i) 18
total area
502 art
8
Syllabus
0580 and 0581
M1
A2
(iv) 32.4(0)
B2
M1 for 540 x 6 or figs 324
(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
© UCLES 2007
9Dwebsite.tk
[8]
[17]
[10]
Page 5
9
(a) (i) arc
Mark Scheme
IGCSE – October/November 2007
Syllabus
0580 and 0581
Paper
3
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 (a) 42, 56
71, 97
B1B1
B1B1
cao
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
© UCLES 2007
9Dwebsite.tk
[10]
[8]
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
IGCSE – May/June 2008
Syllabus
0580/0581
Paper
03
0.68 x 450
= 306
2 x 450 + 306 (= 1206)
M1
A1
M1
(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
1 (a)
dep allow 900 or 450 + 450
SCM3 for 2.68 x 450 (= 1206)
[10]
translation
col.vector 2 -4
2 (a)
B1
B1 B1
SC1 for col.vectors 4 -8 or -4 2 or for (2, -4)
(b)
reflection
(in) x = 0 or y axis
B1
B1
(c)
rotation
90º (anticlockwise) oe
(about) origin oe
B1
B1
B1
enlargement
(scale factor) -2
B1
B1
(centre) origin oe
B1
SC1 for enlargement, SF=2, about origin (oe) and
rotation of 180 about the origin (oe)
[11]
6,17,8,9,11,9
B2
B1 for 4 or 5 correct or for all tallies correct
(d)
3 (a) (i)
(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
(b)
i.e. 1/4, 270 clockwise, - 270
accept (0,0), O
66º
B2ft
M1 for clear indication of 1x6 + 2x17 + 3x8 + 4x9 +
5x11 + 6x9 ft imp by 209
M1 dep for ÷ 60
M1 for "11" ÷ 60 x 360 or "11" x 6
[10]
© UCLES 2008
9Dwebsite.tk
Page 3
4 (a)
(i)
(ii)
(iii)
(b)
Mark Scheme
IGCSE – May/June 2008
3x = 14 + 4 oe
(x =) 6
M1
A1cao
SC2 for 6 www
y + 1 = 2 x 5 oe
(y =) 9
M1
A1cao
SC2 for 9 www
6z - 21 - 2z + 6 (= -9)
4z = 6
z = 1.5
B1
B1ft
B1cao
(i)
p + q = 12
B1
(ii)
25p + 40q = 375
B1
(iii)
correct method
p=7
q=5
M1
A1
A1
Syllabus
0580/0581
Paper
03
ft their expansion but must be 4 terms
multiply and subtract, substitution
SC3 for p=7 and q=5 www
[12]
5 (a)
(b)
6 (a)
(b)
(i)
43.0 art or 43
B2
(ii)
10.0 art or 10
B2ft
M1 for 430 ÷ their (a)(i) ft
(i)
(length) = 22.2
(width) = 14.8
(height) = 20
B1
B1
B1ft
accept length and width interchanged
(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]
(i)
63
(ii)
54
(iii)
134
(i)
360 ÷ 8 or 6 x 180
180 - 45 or 1080 ÷ 8
M1 for π x 3.7²
ft is 2 x their (a)(ii)
B1
B2 cao
M1 for 180 - 2 x their (a)(i) soi (may be implied by
answer)
B2 cao
M1 for 360 - (100 + 63 + their (a)(i)) or 197 - their (a)(i)
soi (may be implied by answer)
MA1
MA1
dependent
SC2 for convincing argument
© UCLES 2008
9Dwebsite.tk
Page 4
Mark Scheme
IGCSE – May/June 2008
Syllabus
0580/0581
(ii)
octagon drawn
accurate
M1
A1
(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)
Paper
03
closed and not re-entrant
angles at A and B equal to 135 +/- 2 degrees
and lines BC and AH equal to 4 +/- 0.1 cms
[13]
7 (a)
(b)
(i)
tan (QPR) = 10.3 ÷ 7.2
55 (.0)
M1
E1
M1 for complete long method
(ii)
125
B1
cao
(i)
125 - 98
or 180 - ( 98 + 55 )
E1
accept 55 + 98 + 27 = 180
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)
8.24 to 8.25(1….)
B2 ft
M1 for their (b)(iii) ÷ 4.5
(c)
[9]
8 (a)
(b)
(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
(i)
-3, -9, -3
B3
B1, B1, B1
(ii)
8 points correctly plotted
smooth curve
P3 ft
C1
P2ft or 6 or 7, P1ft for 4 or 5 (+/- 1/2 small square)
(must go below y = -9)
© UCLES 2008
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Page 5
(c)
(d)
Mark Scheme
IGCSE – May/June 2008
Syllabus
0580/0581
(i)
1.5 to 1.6
-4.5 to -4.6
B1 ft
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
(i)
correct line
(ii)
(y =) 2x - 3
L1
Paper
03
long enough to cross y axis (+/- 1/2 small square)
B1,B1ft B1 for 2 (as coefficient of x)
B1 ft for their intersection with the y-axis
[16]
Pentagon
B1
(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
(i)
perpen.bisector of BC
correct arcs seen
B1
B1
+/- 1mm and +/- 1 degree accuracy
(ii)
bisector of angle ABC
correct arcs seen
B1
B1
+/- 1 degree accuracy
(d)
"M" correctly marked
B1
dep. on at least first B1 in each part of (c)
(e)
2 marks 0.8 (+/-0.1) apart
1.85 (+/-0.1) from A and B
B1
B1
9 (a)
(b)
(c)
[11]
© UCLES 2008
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
IGCSE – October/November 2008
Syllabus
0580 and 0581
Paper
03
Abbreviations
art
cao
ft
oe
soi
SC
answer rounding to
correct answer only
follow through after an error
or equivalent
seen or implied
Special Case
Qu
1 (a) (i)
Answers
3
5
× 30 000
or 30 000 −
(ii)
(b) (i)
(ii)
(iii)
2
5
Part Marks
Must see evidence of fractions
× 30 000
Aida
$7500
Bernado $6000
Christiano $4500
W3
M1 for 5 or5+44+or3 3 × 18000
A1 for 1 correct answer
10 500
W2
M1 for
W2
W1ft
W1 for
13
60
($)13 000
2 (a) (i)
(ii)
52.3 art
24.4 art
(iii)
17.0 art
× 30 000 or 0.35 × 30 000
35
100
6500
30000
seen or other ‘correct’ fraction.
W3cao M1 for 15 500 − 12500 or 15500
12500 × 100
'3000 '
M1 for 12500 × 100
or ‘124’− 100
W2cao M1 for 55cos18°
W2 ft M1 for ‘52.3’tan25°. Ft their ED
24
(c)
3
Mark
M1
W2cao 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)
(c) (i)
14.1 art
W2cao M1 for √( 12 2 + 7.4 2 ) or correct long methods
12 ÷ cos (tan −1 712.4 ) or 7.4 ÷ sin(tan −1 712.4 )
(ii)
31.7 art
W2cao M1 for tan (FBA) = 712.4 oe
or sin FBA = ' 7FB.4 ' or cos FBA =
M1
W1
W1
W2
(a) (i) 12
(ii) 7
(iii) 8.5
(b)
10 points correctly plotted
W3
Allow for clear attempt to find FD − AD.
12
' FB '
M1 for Attempt at ordering the data.
W2 for 8 or 9 points correctly plotted
W1 for 6 or 7 points correctly plotted
© UCLES 2008
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Page 3
Mark Scheme
IGCSE – October/November 2008
Qu
Answers
(c) (i) 8.58(3…) or 8.6
Mark
W2
W1
(d) (i) Line of fit
5
90°
(Angle in a) semi-circle
(c)
68°
(Angles in a )triangle
(=)180°
(d)
68°
Alternate or Z (angles)
(a)
6
W1ft
W1
Line must indicate understanding
Ft is180 −( their (a) + their (b))
or alternate segment (theorem)
W1cao
W1
Allow Z correctly placed on the diagram.
W1
W2
W1
W1ft
(ii) Line from 09 30 to 0945
Line to (‘10 30’, 18)
M1 for 15
20
SC1 for 10 15
accuracy ± 1mm
W1
(i) 20
W1ft
(ii) Line (11 15, 0) to
( their 11 35, 18)
6
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
W1cao
W1
(b) (i) 10 30
(c)
Part Marks
W1
W1cao Degree symbol not essential throughout question.
Allow perpendicular for 90°
W1
(ii) Negative
22°
(a)
Tangent (and) radius/
diameter (meet at) 90°
(b)
Paper
03
W1ft
(ii) Plotted (their (c)(i), 38.8)
4
Syllabus
0580 and 0581
ft their time in (c)(i) provided in minutes and Y 45
Line (11 15, 0) to (11 [15 + ‘20’], 18)
(d) (i) Line (12 00,18) to (12 45,0)
(ii) 24
W1
W2
(a) (i) ( y =)13
W2
M1 for (2y =) 75 − 7 × 7
(ii) ( x =) 9
W2
M1 for 7x = 75 − 12 or −7x = 12 − 75
W2
M1 for 7x + 2y = 75.
7x = 75 − 2y or −7x = 2y − 75 or −7x − 2y = −75
(b)
75 − 2 y
7
or
2y−75
−7
M1 for 18 ÷ 0.75
Allow 18 ÷ 45 × 60 for method
© UCLES 2008
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Page 4
7
Mark Scheme
IGCSE – October/November 2008
Answers
Mark
W3
(x =) 11, (y =) −1
(a)
3, −3, 3
(b)
8 correctly plotted points
Smooth curve
W3ft
W1
W2 for 6 or 7 points, W1 for 4 or 5 points
Half square accuracy
must go below line y = −3
(c)
( −0.5, −3.25)
W2ft
W1 for one coordinate correct
Ft their graph but −1 < x < 0 and y < −3
Allow calculated if exact values (W2 or W1)
W3
(b)
(c)
(d)
 4
(AB =)   , (BC =)
 2
Part Marks
M1 for multiply and correct add/subtract or correct
substitution.
A1 for x = 11 or y = −1
W1 for each correct value
W1cao Half square accuracy
W1ft Ft any vertical line only
(a) (i) (−3, −2)
(ii)
9
Paper
03
Qu
(c)
(d) (i) Line x = −0.5 drawn
(ii) x = −0.5 oe
8
Syllabus
0580 and 0581
W1
 − 3
 
 2 
(1, −5), (5, −3), (2, −1)
W1,
W1
W2
(i) P( 5, 2), Q( −1, 6)
W1,
W1
(ii) Enlargement
(Scale factor) 2
(Centre ) A or (−3, −2)
W1
W1
W1ft
( 0, −4) marked
Joined to A and B
W1
W1ft
 2
SC1 for   and
 4
2
 
−3
W1 for 2 correct points plotted
Must join points, with straight lines, for both
marks.
Ft their (a)(i)
Zero if not a single transformation
Their image of C joined to A and B.
(a) (i) 99 to 101 (metres)
(ii) 103° to 105°
W1
W1
(b) (i) 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.
W2
W1 correct bisector without arcs
W2
W1 correct bisector without arcs. Bisector about
89° to 91° to AD by eye and centre within 2mm by
eye.
(ii) Closed region T indicated
W1
Dependent on at least W1 for each bisector.
Allow T omitted if region is clear.
© UCLES 2008
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Page 5
Qu
(c)
10 (a)
(b)
(c)
(d)
Mark Scheme
IGCSE – October/November 2008
Answers
Lines parallel to and 3cm
(±0.1cm) from AB and BC.
Lines joined by arc, centre B.
radius 3cm (±0.1cm)
Mark
W1
Syllabus
0580 and 0581
Paper
03
Part Marks
W1
(Lines) 10 and 13
(Dots) 8 and 10
W1
W1
(Lines) 31, (Dots) 22
W1,
W1
(i) 3n + 1 oe
SC1 for jn + 1 or 3n + k
W2cao where j and k are integers. j ≠ 0
(ii) 2n + 2 oe
SC1 for jn + 2 or 2n + k
W2cao where j and k are integers. j ≠ 0
n − 1 or 1 − n
W2ft
M1 for ‘(3n + 1)’ − ‘(2n + 2)’ or reversed
Ft and M1 dependent on two linear algebraic
expressions
© UCLES 2008
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
IGCSE – May/June 2009
Syllabus
0580, 0581
Paper
03
Abbreviations
cao
ft
oe
SC
www
correct answer only
follow through after an error
or equivalent
Special Case
without wrong working
Qu
1
Answers
(a) (i) 6000 ÷ (7 + 5 + 3)
Multiply by 7
(ii) (Stephano) 2000 www
(Tania) 1200 www
(b) (i) ($)47040
(ii) ($)28224
Mark
Part marks
1
M1 6000 ÷ clear attempt at total
1
M1 Dependent on first mark.
1
1
Must be clearly Stephano.
Must be clearly Tania.
2
M1 1.40 × 12 × 2800
2ft
M1
3
5
× ‘47040’ or 0.6 × ‘47040’
(c)
($)1200
2
M1 5000 × 8 × 3 ÷ 100
SC1 for final answer 6200
(d)
($) 14292
4
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
© UCLES 2009
9Dwebsite.tk
Page 3
2
(a)
Mark Scheme: Teachers’ version
IGCSE – May/June 2009
Syllabus
0580, 0581
1
One-third of 360 oe
(b) (i) 30
1
(ii) 90
1
(iii) 60
1ft
90 − their (b) (i)
2ft
M1 30cos (b) (i) or 30sin(90 − (b) (i))
or equivalent full method
(c) (i) 26(.0) or 25.98(……)
(d)
(ii) (c) (i)sin (b) (iii) oe
22.5
1
1
M1 for correct full method for AD
W1 dependent on M1
48.36 to 48.4
2
M1 tan (AED) =
or cos (AED) =
sin(AED) =
3
Paper
03
(a)
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)
(b) (i) 0.75 or
3
4
hour
(ii) 466 to 467
(c)
35
22.5
20
20
20 2 + 22.5 2
or
22.5
20 2 + 22.5 2
W1
W1ft
W1ft
Only ft from their 09 30
Ft incorrect 10 15 and 380
W1ft
Ft incorrect 10 50 and 380
1
2cao
M1 for 350 ÷ their (b) (i)
3cao
W1ft (air) 3 h 30 mins oe 210 min
W1(train) 2 h 55 mins oe 175 min
© UCLES 2009
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Page 4
4
Mark Scheme: Teachers’ version
IGCSE – May/June 2009
(a) (i) x − 4
Syllabus
0580, 0581
Paper
03
1
1
(ii) 2x + 5
(iii) ‘2x + 5’ = 3 × ‘(x − 4)’ oe
1ft
3cao
(iv) (x =) 17 www
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.
(b)
3
(x =) 2, (y =) 1.5
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 3 x −3 = 8 or 3x − 2 8− x = 3 or
( )
( )
2
4
( ) + 4y = 8 or ( ) = 8 − 4y or
( ) = ( ) or better.
3− 2 y
3
3 x ±3
2
5
3+ 2 y
3
8± x
4
Reflection in y axis or x = 0
2
W1 transformation W1 Line
8
Translation   or 8 right (only)
0
2
W1 transformation
W1 vector or description
(b)
Correct reflected pentagon
2
SC1 A reflected in a horizontal line, not the x
axis
(c)
Correct rotated pentagon
2
SC1 B rotated anti-clockwise 90° about the
origin or 90° clockwise about any other point.
(d)
Rotation, 180, (About) origin oe
3
W1 rotation, W1 180, W1 origin
SC3 Enlargement (SF) –1 origin
Accept (0, 0) for origin.
(e)
Correct enlarged pentagon
2
W1 for any enlargement of A with a scale factor
of 12 .
(a)
© UCLES 2009
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Page 5
6
Mark Scheme: Teachers’ version
IGCSE – May/June 2009
Syllabus
0580, 0581
(a)
Octagon
1
(b)
135
2
M1 for 180 − (360 ÷ 8) oe
W1ft
67.5 or 22.5 correct values,
(c) (i) 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
M1
A1cao Dep on W1 and M1
2
(ii) 38.6 to 38.64
(iii) 308.8 to 309.12
(d)
Paper
03
3705.6 to 3709.44 or 3710
(e) (i) 2400
(ii) 35.2(3…) to 35.3(0…)
M1 for 0.5 × 8 × 9.66
1ft
Their (c) (ii) × 8
1ft
Their (c) (iii) × 12
2cao
M1 for 3 × 2 × 2 × 200
3cao
M1 for their ((d) − (e) (i)) soi.
M1 for (d)−(d)(e)(i) × 100
Or M2 for
( ) × 100
1
(e)(i)
(d)
SC1 for Answer 64.7 to 64.77
7
(a)
x 0 1 2 3 4 5 6 7 8
y 0 8 14 18 20 20 18 14 8
(b)
Their 10 points correctly plotted, within
half a square.
Smooth curve through the 10 correct
points
P3ft
(x =) 4.4 to 4.6
(y =) 20.1 to 20.5
1cao
1cao
(c)
9
0
(d) (i) Ruled line y = 6
3
C1
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.
1
(ii) 8.1 to 8.5 Must be to 1 decimal place
0.5 to 0.9 Must be to 1 decimal place
1cao
1cao
SC1 for both correct but not to 1dp e.g. 8.27 and
0.73
© UCLES 2009
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Page 6
8
Mark Scheme: Teachers’ version
IGCSE – May/June 2009
5,
126,
(a)
(b) (i) 3,
90
5,
6,
4,
2
(ii) Blocks ‘correct’ heights
No gaps.
(c) (i) 10 points plotted correctly
Syllabus
0580, 0581
Paper
03
1
1, 1
SC1 for both angles incorrect but totalling 216°.
2
W1 for 3 or 4 correct or left as tallies and all
correct.
2ft
W1 for only 1 incorrect
SC1 All correct but small gaps between or full
horizontal lines only
3
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.
(ii) Zero oe
1
(allow weak (slight) negative)
3
20
2ft
(iii)
oe or 0.15 or 15%
Ft numerator only
W1 for their3 k ≥ 3
k
9
(a) (i) −8,
−13
1cao
1ft
Ft sixth term 5 less than the fifth
(ii) Subtract 5 oe
1
(iii) −5n + 17
2
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
(b)
5n − 8
2
(c)
9 www
1ft
Ft two linear expressions only
© UCLES 2009
9Dwebsite.tk
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.
9Dwebsite.tk
Page 2
Qn
1
2
3
Mark Scheme: Teachers’ version
IGCSE – October/November 2009
Syllabus
0580
Paper
03
Answers
Mark
Notes
(a) (i)
1/5
1
Accept 0.2 or 20%
(ii)
2/5
1
Accept 0.4 or 40%
(iii)
0
1
Accept 0/5 or 0%
(b) (i)
6
1
cao
(ii)
1
1
cao
(iii)
2.6 (0) www
3
M1 for 1 × 8 + 2 × 4 + 3 × 5 + 4 × their
(b) (i) + 5 × 2
M1 dep for ÷ 25 or their 25
(iv)
heights 8, 4, 5, , 2
6 or ft height for their (b) (i)
2
1 ft
SC1 for one error, or small gaps
(a) (i)
15.7 art
2
M1 for 2 × π × 2.5
(ii)
19.6 art
2
M1 for π × 2.52
(iii)
14.6 art
2
M1 for π × (2.5 + 0.8)2
(b)
Within range 7840 to 7860
2 ft
M1 for their (a) (ii) × 0.4 × 1000
(c)
31
3 ft
M1 for their (b) ÷ 250 soi
A1 ft for 31.4 art
W1 for their answer correctly rounded
(a) (i)
4.5
2
M1 for 15 × 3 / (7+3)
3
1 ft
Their (a) (i) ÷ 2 and rounded up
8.14
3
M1 for 100 – 12 soi
M1 for 9.25 × their 88 / 100
(ii)
32.56
1 ft
4 × their (b) (i)
(iii)
46.25
1
cao
(iv)
8.75(6…) or 8.76
3
M1 for (their (ii) + their (iii)) soi
2nd M1 dep for ÷ (4 + 5) soi
(ii)
(b) (i)
© UCLES 2009
9Dwebsite.tk
Page 3
4
Syllabus
0580
Paper
03
Isosceles
1
Condone spelling
(ii)
DNC
1
Condone order of letters
(iii)
70°
1
cao
49.4° or 49°24′ art
2
M1for inv tan (7/6)
9.22 art
2
M1 for √(62 + 72 ) soi (e.g. √85)
(c)
12.2 art
3
M2 for 7/sin35
(d)
42.8(4….) or 42.85
2 ft
M1 for 2 × [their (b) (ii) + their (c)] oe
(a)
2
1, 1, 1
(b)
seven points correctly plotted
smooth correct curve through 7 correct
points
P3ft
C1
5 or 6 P2ft, 3 or 4 P1ft
(c) (i)
(–2, –7)
1
cao
–4.6 to –4.75
and 0.6 to 0.75
1
1
cao
cao
correct point marked
1
Condone lack of label
(ii)
ruled line from their A to their (0, –3)
1
Continuous line of this minimum length
(iii)
–4 / 2 oe
2
M1 for attempt at gradient
or
SC1 for 2 oe or –1 oe from correct line
(iv)
y = –2x – 3 oe
2
SC1 for y = kx – 3 oe or y = –2x + k oe
or y = their (d) (iii)x + k oe
(a) (i)
(b) (i)
(ii)
5
Mark Scheme: Teachers’ version
IGCSE – October/November 2009
(ii)
(d) (i)
–6
2
© UCLES 2009
9Dwebsite.tk
Page 4
6
7
Mark Scheme: Teachers’ version
IGCSE – October/November 2009
Syllabus
0580
Paper
03
(a)
x+4
1
(b)
3x
1
(c) (i)
x + x + 4 + 3x
5x + 4
M1 ft
A1 cao
(ii)
Their c (i) ÷ 3 = 28 or their c (i) = 28 × 3
1
(iii)
(x = ) 16
2
M1 for 5x = 84 – 4 or 5x = 80 or x = 80/5
(d)
48 or 3 × their x
1 ft
Ft is 3 x (c) (iii)
(e)
84%
2
M1 for 63 / 75 × 100
1
cao
soi ft is x + (a) + (b)
5x + 4 www scores both marks
(a)
4
(b)
4 correct lines drawn, accept reasonable 2
freehand
(c)
2600
3
M1 for 2800 × 1.75 or 4900
M1 for their 4900 – 2300
(d)
3100.40
2
M1 for 2300 × 1.348
(e)
5962.32
3
M2 for 5000 × (1.092)2
SC1 for 5000 × (1.92)² or full equiv.
or 18432
© UCLES 2009
9Dwebsite.tk
SC1 for 2 correct lines
Page 5
8
Syllabus
0580
Paper
03
(a) (i)
Correct X
2
 2 
SC1 for translation of  
− 7
(ii)
Correct Y
2
SC1 for rotation through 90 clockwise
Or 90 anticlockwise about any point
(b) (i)
Correct Z1
2
SC1 for reflection in y axis
Or in any horizontal line
(ii)
Correct Z2
2 ft
strict ft reflection of their Z1 if possible
SC1 for reflection in y = 4 or any vertical
line
1,1
W1 transformation, W1 full description
SC2 for Enlargement sf = –1 coe (4, 0)
(iii)
9
Mark Scheme: Teachers’ version
IGCSE – October/November 2009
8
Translation ,  
 4
OR Rotation , through 180 about (4, 0)
(a)
13 21
10 15
1 1
1 1
cao
cao
(b)
43
28
1
1
cao
cao
(c) (i)
½×5×6
= 15 seen
1
1dep
accept ½ × 5 × (5 + 1)
½ × 20 × 21
= 210
1
1
accept ½ × 20 × (20 + 1)
accept 210 www for both marks
(k =) –1
2
M1 for 7 = 3² + k × 3 + 1 oe
(ii)
(d)
© UCLES 2009
9Dwebsite.tk