AO Jan 2010 Paper 2
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Transcript of AO Jan 2010 Paper 2
Mark Scheme (Results) January 2010
GCE O Level
Pure Mathematics (7362/02) Paper 2
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January 2010
All the material in this publication is copyright © Edexcel Ltd 2010
AO Pure Mathematics 7362 Mark Scheme Paper 2
Q. Scheme Marks
1 2 2de sin 3 2e sin 3 3e cos3d
x xyy x x 2x xx
= = + M1A1A1
(3) 2 2 2 2
212
6.9 8.3 5(a) cos2 6.9 8.3
36.97... 37.0 (b) Area 8.3 6.9sin 17.2 cm
C
CABC C
+ −=
× ×= = °
∆ = × × =
M1A1 A1 (3)
M1A1A1 (3) (6) 3 (a) (i) (ii) 3y = 2x = B1B1 (2) (b) (i) 2 2
2 30 2 2xy x−= = = B1
(ii) 0 3 1 4x y= = + = B1 (2)
G1(2 branches) G1(asymptotes) G1(crossing pts)
(3) (7)
B2(all corr) (B1 for 2 or 3)
4 (a)
(
(
(c)
(c)
GCE AO Le
x 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
y 1 0.649 -1.28 -4.52 -8.61 -12.8 -15.9 -15.9 -9.40
(2)b) Graph drawn (see diagram overleaf)
2
2
2 2
c) (i) 4 e 8 e 4 8, 1.9 (ii) e 4 8, e 4 3, 1.3
x
x
x x
xx xx x x
= +
− = − =
= − − = − =
G1 (pts plotted) G1 (smooth curve)
(2)
M1A1
M1M1A1 (5)
(9)
vel Pure Mathematics (7362) Paper 2 January 2010
4 (b)
Diagram of graph
GCE AO Level Pure Mathematics (7362) Paper 2 January 2010
5
M1 A1A1 (3)
G1 shape G1 3 and 4
(2)
M1 M1
M1A1 (5)
(9) 6 ( )
( )( )
( )
4141 1
4 4 4 1 116 2
12
32
44 12
11
(a) 80 75
75 80 1 80 5
(b) 80 1
100 80 120
(c) 30 120 30
4
a rar rS x S x
x x r r r r
a x
a x a x x
ar x
x
−
∞ − −= = = =
= − = = =
=
⇒ = × =
= − =
×
m
>
±
6 1 4x= =
M1A1
M1A1 (4) M1
M1A1 (3) M1A1ft
A1 (3) (10)
M1
A1 M1 M1A1
B1 (6)
M1A1 (2)
7
M1
A2,1,0 ft
A1 (4) (12)
(b)
GCE AO Level Pure Mathematics (7362) Paper 2 January 2010
8
2
2
2 3
2
2
3 2
2
2125 250
d 250d
3
25034
d 500d
dd
(a) Vol 125 cm 2 2 2 *(b) 4
250 4
2.709... 2.71
(c) 4
0 0 min.
(
r rAr r
Ar r
Ar
r hA rh rrh A r
r
r
r r
r
π
π
π π
π ππ
π
π
= =
= +
= = +
= − +
=
= = =
= +
⇒ ∴> >2250
2.71d) 2 2.709... 138.3... 138A π= + × = =
B1
B1
M1A1 (4)
M1 M1 A1 (3)
M1
M1A1 (3)
M1A1 (2) (12) 9 ( ) ( )
( ) ( )
( )( )( ) ( )( )( ) ( )
2 2 3 2 2 2 2 3 3
2 2 3 2 2 2 2 3 3
3 3 2 2
2
(a)
(b) 7 3
3
7 49 9 280
(c)
3
3
α β α αβ β α α β αβ βα αβ β α β
α β α αβ β α α β αβ βα αβ β α β
α β αβ
α β α β α αβ β
α β α β αβ
α
+ − + ≡ − + + − + ≡ +
− + + ≡ + + − − + ≡ −
+ = − =
+ = + − +
= + + −
= − − = −
( ) ( )( )( ) ( ) ( )( )
( )3 3
2 2 2 2
2 2
2 2
23 3 2 2
2809
1 13
2 280 19 3
2
4 49 12 37
(d)
37 49 3 46 37
(e)
0
9 280 3 0
x x
x x
β α βαβ α α β
βααββ α
β α β αβ
α β α β α αβ β α β α β αβ
+
− = + − = − =
− = − + + = − + −
= − =
+ = = −
× = =
+ + =
+ + =
M1A1 A1 (3)
B1
M1
A1 (3)
M1A1 (2) M1M1 A1 (3) M1
B1
M1
A1 (4) (15)
GCE AO Level Pure Mathematics (7362) Paper 2 January 2010
10 ( )
sin cos cos sincos cos cos cos
sin sincos cos
sin cos cos sin(a) tancos cos sin sin
1
tan tan *1 tan tan
(b) (i) 45 30
A B A BA B A B
A BA B
A B A BA BA B A B
A BA B
A B
++ =
−+
=−
+=
−= ° = °
13
13
2
2
2
tan 45 tan 30 tan 75 1 tan 45 tan 301 3 1 ,1 3 1
1 3 1 (ii) tan15tan 75 3 1
2 tan(c) tan21 tan
2 tan(d) 22.5 11 tan
tan 2 tan
θθθ
θθθ
θ θ
+=
−+ +
= =− −
−= =
+
=−
= ° =−
+ −
( )
( )
( )2 2
45 25 204
5 21 21225
20 20 202984121 20
1 0
2 4 4 tan 1 2
2 tan 22.5 0 tan 22.5 2 1
(e) tan 21
sin 2
θ
θ
θ+
=
− ± += = −
∴ =
= = × =−
= = =
>
±
−
M1
M1A1 (3) M1
A1A1
M1A1 (5)
B1 (1)
M1
M1
A1 A1 (4)
M1A1
M1A1 (4)
(17)
GCE AO Level Pure Mathematics (7362) Paper 2 January 2010
GCE AO Level Pure Mathematics (7362) Paper 2 January 2010
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