www.maxpapers.com
Mark Scheme (Results)
January 2011
O Level
GCE O Level Mathematics B (7361/02)
Edexcel Limited. Registered in England and Wales No. 4496750
Registered Office: One90 High Holborn, London WC1V 7BH
www.maxpapers.com
Edexcel is one of the leading examining and awarding bodies in the UK and
throughout the world. We provide a wide range of qualifications including
academic, vocational, occupational and specific programmes for employers.
Through a network of UK and overseas offices, Edexcel’s centres receive the
support they need to help them deliver their education and training programmes to
learners.
For further information please call our Customer Services on + 44 1204 770
696, or visit our website at www.edexcel.com.
If you have any subject specific questions about the content of this Mark
Scheme that require the help of a subject specialist, you may find our Ask
The Expert email service helpful.
Ask The Expert can be accessed online at the following link:
http://www.edexcel.com/Aboutus/contact-us/
January 2011
All the material in this publication is copyright
© Edexcel Ltd 2011
www.maxpapers.com
Mathematics B, Mark Scheme
Paper2
1.
∠AOD = 30o
∴∠OCD OR ∠ODC = 15o
∠CDE = 75o
NB: Award Bs for angles seen on diagram
B1
B1
B1
3
Total 3 marks
2.
(a)
(b)
3.
l = 62 + 2.52 (= 6.5)
π × 2.5 × "6.5"+ 2π × 2.5 × 9 + π × 2.52
(Sum of 2 correct areas)
(Sum of 3 correct areas)
3
212 cm
4.
(a)
(b)
(c)
20-x, x, 16-x, 7 shown on Venn diagram
(no slips)
“(20-x)” + x + “(16-x)” + 7 = 35
x=8
1.5 x 20000 /100
300 m
1.2 x 100 000/20000 cm
6 cm
60 000 x (100)2 x (1/20000)2
presence of one of (100)2 or (1/20 000)2
in above formula
both
1.5 cm2
GCE O Level Mathematics Syllabus B (7361) Paper 2 January 2011
B3 (-1eeoo) 3
M1
A1
2
5
Total 5 marks
M1
M1
M1 DEP
A1
4
Total 4 marks
M1
A1
M1
A1
2
2
M1
M1 DEP
A1
3
7
Total 7 marks
1
www.maxpapers.com
5.
13 ⎞
⎛ 2
B.C = ⎜
⎟
⎝ 2 y y + 3x ⎠
(
6.
15 ⎞
⎛ 5
A + B.C = ⎜
⎟
⎝ 2 y + x 2 y + 3x ⎠
B2 (-1 eeoo)
)
2y + x = 4
2y + 3x = 6
B1
B1
Elimin. x or y from 2 linear “SEs” in x and y
Subst x or y
NB: allow 1 sign slip only for both Ms
M1
M1 (DEP)
x = 1, y = 3/2
A1, A1
8
Total 8 marks
(a)
B1
(b)
(c)
(d)
1/3 , 120/360, 0.333, 33.3%
120 + 90
1/3 + 1/4
or
360
210/360, 7/12 , 0.583, 58.3%
1 1
or 60/360 x 90/360
×
6 4
1/24 , 0.0417, 4.17%
1/3 x ¼, ¼ x 1/3, 1/6 x ¼, ¼ x 1/6 (2 off)
all
1/3 x ¼ + ¼ x 1/3 + 1/6 x ¼ + ¼ x 1/6
¼
, 0.25 , 25%
GCE O Level Mathematics Syllabus B (7361) Paper 2 January 2011
1
M1
A1
2
M1
A1
B1
B1
M1
A1
2
9
4
Total 9 marks
2
www.maxpapers.com
7
JJJG
4
(a)(i) PA = a
5
B1
JJJG
(a)(ii) AB = b – a
OR
B1
JJJG 4
(b)(i) AQ = “(b – a)”
9
B1 ft
JJJG
4
4
(b)(ii) PQ = “ a” + “ (b – a)”
5
9
M1
JJJG
1
5
PQ = - a + b - (b – a)
5
9
(no errors)
JJJG
16
4
∴ PQ =
a + b
45
9
2
M1
A1
JJJG
4
(b)(iii) QC = b - “ (b – a)”
9
M1
OR
JJJG 5
QC = (b – a) + a
9
OR
JJJG
16
4
1
QC = -“ a + b” - a + b + a
45
9
5
(no errors)
JJJG
4
5
∴ QC =
a + b
9
9
M1
M1
A1
5
JJJG
4
(c) PC = " a” + b
5
and attempting (but NOT using vector division) to show that
JJJG
JJJG
JJJG
JJJG
PQ = nPC and QC = mPC
M1
JJJG 4 ⎛ 4
JJJ
G
4
⎞
Either PQ = ⎜ a + b ⎟ = PC
9⎝5
9
⎠
JJJG 5 ⎛ 4
5 JJJG
⎞
OR
A2
QC = ⎜ a + b ⎟ = PC
9
9⎝5
⎠
[OR
Attempting (but NOT using vector division) to show that
JJJG 4 JJJG
JJJG 5 JJJG
PQ = " QC " or QC = " PQ "
5
4
GCE O Level Mathematics Syllabus B (7361) Paper 2 January 2011
M1
3
www.maxpapers.com
JJJG 4 ⎛ 4
JJJG 5 ⎛ 16
5 ⎞
4 ⎞
PQ = ⎜ a + b ⎟ OR QC = ⎜ a + b ⎟
5⎝9
9 ⎠
4 ⎝ 45
9 ⎠
]
A2
c.c
A1
4
11
Total 11 marks
_____________________________________________________________________
8.
Penalise labelling ONCE only
(a) ∆ABC drawn and labelled
(b) (i) A1 = (3, 1), B1 = (7, 3), C1 = (8, 2)
(ii) ∆ A1B1C1 drawn and labelled
(c) A2 = (2, -2), B2 = (6, -4), C2 = (4, -6)
∆ A2B2C2 drawn and labelled
B1
1
B2 (-1 eeoo)
B1 ft 3
B2 (-1 eeoo)
B1 ft 3
(d) (i) enlargement factor 2
(ii) 270o
antclockwise
NB: Last B1 is DEP on previous B and the B in (b) (i)
(OR 90 , clockwise
o
B1, B1 (DEP)
B1
B1
B1 (DEP)
)
3
OR
d(i) enlargement factor -2
B1
o
d(ii) 270 clockwise
B1, B1 (DEP)
OR
90o anticlock.
B1, B1 (DEP)
NB: The 3rd B of (d) is DEP on the 1st and 2nd Bs of (d)
⎛ 0 2⎞
(e) ⎜
⎟
⎝ −2 0 ⎠
B2 (-1 eeoo) 2 12
Total 12 marks
GCE O Level Mathematics Syllabus B (7361) Paper 2 January 2011
4
www.maxpapers.com
9.
(a) (10 – t) (3 + t) = 0 (solving trinomial quadratic)
t = 10 secs.
(b) 38.3, 42, 41.3, 38.3
(c) curve
-1 mark for incorrect/non-uniform scale
straight line segments
each point missed
each missed segment
each point not plotted
each point incorrectly plotted
tramlines
very poor curve
(d) 3.5 secs ( ± 0.1 secs)
(1 ss = 0.1sec)
(e) Attempt to measure gradient at t = 2
Answer rounding to 3 m/ sec
(f) 2 < t < 5 ( ± 0.1 secs)
M1
A1
2
B3 (-1 eeoo) 3
B3
3
B1 ft 1
M1
A1 2
B1 ft, B1 ft 2 13
Total 13 marks
_____________________________________________________________________
10.
(a) L =
5x
(3x) 2 + (4 x) 2
1
(b) 2 × × 3x × 4 x + 3 x × 10 x
2
42x2
(o.e)
OR
1
× (10 x + 18 x) × 3x
2
(o.e)
(c) 2 × "42 x 2 "+ 2 × "5 x "× y + 10 xy + 18 xy = 1008
“ (10 x + 10 x + 18 x) y = 1008 − 84 x 2 ”
M1
A1
2
M1
A1
2
M1
M1 (DEP)
1008 − 84 x 2
(c.c)
A1
3
38 x
1008 − 84 x 2
2
M1
(d) V = "42 x "×
38 x
21x
V=
(1008 − 84 x 2 )
(c.c)
A1
2
19
21× 1008
3 × 21× 84 2
or (o.e)
M1
x
(e) One of
19
19
21× 1008 3 × 21× 84 2
(o.e)
A1
x
19
19
21×1008 3 × 21× 84 2
(o.e)
M1 (DEP)
“
x ”=0
19
19
1008
(o.e) (isolating x from quadratic in x2 only)
x=
252
M1 (DEP)
x = 2 cm
A1
5
14
Total 14 marks
y =
GCE O Level Mathematics Syllabus B (7361) Paper 2 January 2011
5
www.maxpapers.com
_____________________________________________________________________
11.
Penalise ncc ONCE only
EC
(a) sin 35 =
2
1.15 cm
3
(b) tan 35 =
BE
4.28 cm
M1
A1
M1
(c) BC = "4.28" + "1.15"
4.43 cm , 4.44 cm
"4.28"
(d) tan ∠BCE =
"1.15"
75o, 75.0o
2
(e)
OR
OR
OR
∆ABP :
∆CPD :
∆CEP :
∆BEP :
2
(o.e)
2
M1
A1
2
A1
∠BAP = 55 and ∠ABP = 105
∠CDP = 145 and ∠DCP = 15
∠CEP = 55 and ∠ECP=105
∠EBP = 15 and ∠BEP = 145
2
B1
B1
B1
B1
B1
2
X is a pt on AE st BX is perpendicular to AE
AX
(AX=1.721)
3
BX
(BX = 2.457)
sin 55 =
3
AND
"2.456"
tan"20" =
(PX = 6.748)
PX
AP = “AX” + “PX” = “1.721” + “6.748”
cos 55 =
OR
A1
M1
∠BPA = 20o , 20.0o
(f)
2
AX
(AX=1.721)
3
XE
cos 35 =
(XE = 3.5092)
"4.284"
AND
M1
=>
M1
M1 (DEP)
cos 55 =
M1
( DC = 2 × cos 35 = 1.6383)
M1
"1.6383"× sin15
(=1.2893)
sin"20"
AP = “AX” + “XE” + 2 + “DP” = “1.721”+”3.5092”+2+”1.2398”
M1 (DEP)
DP =
GCE O Level Mathematics Syllabus B (7361) Paper 2 January 2011
6
www.maxpapers.com
OR
OR
3
( AE = 5.2303)
AE
CD
cos 35 =
(CD = 1.6383)
2
AND
"1.6383"× sin15
DP=
(DP = 1.2398)
sin"20"
AP = “AE” + ED + “DP” = “5.2303” + 2 + “1.2398”
sin 35 =
3
( AE = 5.2303)
AE
sin"105"× "1.15"
EP =
(EP = 3.2478)
sin"20"
AP = “AE” + “EP” = “5.2303” + “3.2478”
sin 35 =
M1
M1
M1 (DEP)
M1
M1
M1 (DEP)
OR
Special Case : Sine Rule
∠ABP = 105o
AP
3
=
sin"105" sin"20"
3 × sin"105"
AP =
sin"20"
M1
M1 (DEP)
M1 (DEP)
AP = 8.46, 8.47 cm, 8.48 cm
A1
4
14
Total 14 marks
_____________________________________________________________________
TOTAL 100 MARKS
GCE O Level Mathematics Syllabus B (7361) Paper 2 January 2011
7
www.maxpapers.com
www.maxpapers.com
Further copies of this publication are available from
International Regional Offices at www.edexcel.com/international
For more information on Edexcel qualifications, please visit www.edexcel.com
Alternatively, you can contact Customer Services at www.edexcel.com/ask or on + 44 1204 770 696
Edexcel Limited. Registered in England and Wales no.4496750
Registered Office: One90 High Holborn, London, WC1V 7BH