GCE Mathematics FP3 0979-01
WJEC 2014 Online Exam Review GCE Mathematics FP3 0979-01 All Candidates' performance across questions
Question Title 1 2 3 4 5 6 7
N 222 223 223 223 220 221 221
Mean 5.9 11.4 9 5.9 3 10 8
SD 2.1 3.5 3 2.5 2.6 3.2 2.5
Max Mark 9 14 11 8 9 13 11
FF 65.4 81.4 81.6 73.2 33.6 76.7 73.2
Attempt % 99.5 100 100 100 98.7 99.1 99.1
GCE Mathematics FP3 0979-01 7
73.2
Question
6
76.7
5
33.6
4
73.2
3
81.6
2
81.4
1
65.4 0
10
20
30
40
50
60
Facility Factor %
70
80
90
100
1
5a 6a 7
2 1.
(a) Starting with the exponential definition of sinh x, show that
(
)
sinh –1 x = ln x + x 2 + 1 .
[4]
(b) Solve the equation
cosh2x = 2sinh x + 5,
(
)
giving your answers in the form ln a + b where a, b are integers.
© WJEC CBAC Ltd.
(0979-01)
[5]
Question number
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Rhify Cwestiwn
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- 2.
V
3 5.
The integral In is defined, for n x 0, by
In = (a) Show that, for n x 2,
1
∫xe 0
n – x 2 dx.
( )
–1 I n = n – 1 I n–2 – e . 2 2
© WJEC CBAC Ltd.
(0979-01)
[3]
Question number Rhify Cwestiwn
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3 6.
The curve C has polar equation
r = sinθ + cosθ, 0 X θ X π . 2 (a) Find the polar coordinates of the point at which the tangent is parallel to the initial line. [8]
© WJEC CBAC Ltd.
(0979-01)
Leave Blank Gadewch yn wag
Question number Rhify Cwestiwn
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a
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3 7.
(a) Using the substitution x = asinhθ, show that
∫
()
2 2 2 x 2 + a 2 dx = a sinh –1 x + x x 2+ a + constant . 2 a a
[5]
(b) The equation of the curve C is
y = x2, 0 X x X 1. Find the arc length of C.
© WJEC CBAC Ltd.
[6]
(0979-01)
/
Question number Rhify Cwestiwn
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x 4 )
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(4 5 = 0 - ^3
to
Question Title 1 2 3 4 5 6 7
N 222 223 223 223 220 221 221
Mean 5.9 11.4 9 5.9 3 10 8
SD 2.1 3.5 3 2.5 2.6 3.2 2.5
Max Mark 9 14 11 8 9 13 11
FF 65.4 81.4 81.6 73.2 33.6 76.7 73.2
Attempt % 99.5 100 100 100 98.7 99.1 99.1
GCE Mathematics FP3 0979-01 7
73.2
Question
6
76.7
5
33.6
4
73.2
3
81.6
2
81.4
1
65.4 0
10
20
30
40
50
60
Facility Factor %
70
80
90
100
1
5a 6a 7
2 1.
(a) Starting with the exponential definition of sinh x, show that
(
)
sinh –1 x = ln x + x 2 + 1 .
[4]
(b) Solve the equation
cosh2x = 2sinh x + 5,
(
)
giving your answers in the form ln a + b where a, b are integers.
© WJEC CBAC Ltd.
(0979-01)
[5]
Question number
Leave Blank Gadeivc/yn wag
Rhify Cwestiwn
J/L
^tr
v - / - 2. ifo -D
- 2.
V
3 5.
The integral In is defined, for n x 0, by
In = (a) Show that, for n x 2,
1
∫xe 0
n – x 2 dx.
( )
–1 I n = n – 1 I n–2 – e . 2 2
© WJEC CBAC Ltd.
(0979-01)
[3]
Question number Rhify Cwestiwn
Leave Blank Gadewctyn wag
d\j ^-— C_/fT>£
•fr—^
X
e
ci-
•i.
-i
^^TT"
O -.
3 6.
The curve C has polar equation
r = sinθ + cosθ, 0 X θ X π . 2 (a) Find the polar coordinates of the point at which the tangent is parallel to the initial line. [8]
© WJEC CBAC Ltd.
(0979-01)
Leave Blank Gadewch yn wag
Question number Rhify Cwestiwn
- o
v
a
T
t -V riv\
-V c 0
m 6
^
0
a.
0
^
-V 0011382,0
3 7.
(a) Using the substitution x = asinhθ, show that
∫
()
2 2 2 x 2 + a 2 dx = a sinh –1 x + x x 2+ a + constant . 2 a a
[5]
(b) The equation of the curve C is
y = x2, 0 X x X 1. Find the arc length of C.
© WJEC CBAC Ltd.
[6]
(0979-01)
/
Question number Rhify Cwestiwn
Leave Blank GadewcA yn wag
x 4 )
* \
(4 5 = 0 - ^3
to
