GCE Mathematics FP1 0977-01
WJEC 2014 Online Exam Review GCE Mathematics FP1 0977-01 All Candidates' performance across questions
Question Title 1 2 3 4 5 6 7 8 9
N 326 323 324 327 320 324 317 319 317
Mean 7.7 4.8 6.4 5.2 7.2 7.5 6.4 4.7 6.2
SD 2.6 1.9 2.1 1.2 2.8 2.2 2.9 2.2 2.7
Max Mark 10 7 8 6 10 9 9 7 9
FF 77.3 68 79.8 87.2 72.1 83.1 70.8 67.1 69.2
Attempt % 99.7 98.8 99.1 100 97.9 99.1 96.9 97.5 96.9
Question
GCE Mathematics FP1 0977-01 9 8 7 6 5 4 3 2 1
69.2 67.1 70.8 83.1 72.1 87.2 79.8 68 77.3 0
10
20
30
40
50
60
Facility Factor %
70
80
90
100
4 5b 7 8
2 4.
The complex number z is given by
z = 1 + 2i . 1– i Find the modulus and the argument of z.
© WJEC CBAC Ltd.
[6]
(0977-01)
W
"7 -~ Z_ -=-
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t
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2 5.
The roots of the cubic equation
x3 + 2x2 + 2x + 3 = 0 are denoted by α, β, γ. (a) Find the cubic equation whose roots are β γ, γα, αβ. (b)
[6]
Show that
α 2 + β 2 + γ 2 = 0. Deduce the number of real roots of the cubic equation
x3 + 2x2 + 2x + 3 = 0, justifying your answer.
© WJEC CBAC Ltd.
[4]
(0977-01)
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3 7.
The transformation T in the plane consists of a clockwise rotation through 90° about the origin, followed by a translation in which the point (x, y) is transformed to the point (x + 1, y + 2), followed by a reflection in the y-axis. (a) Show that the matrix representing T is
0 –1 –1 –1 0 2 0 0 1
.
(b) Find the equation of the image under T of the line y = 2x + 1.
© WJEC CBAC Ltd.
(0977-01)
[5]
[4]
Leave Blank Gadewch yn wag
Question number Rhify Cwestiwn
7 T= O
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0 O
i
0 ( Z D
0
6
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3 8.
Using mathematical induction, prove that n
∑ ( r × 2r – 1 ) = 1 + 2 n ( n – 1),
for all positive integers n.
r =1
© WJEC CBAC Ltd.
[7]
(0977-01)
Leave Blank GactewcA yn wag
Question number Rhify Cwestiwn
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1
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Question Title 1 2 3 4 5 6 7 8 9
N 326 323 324 327 320 324 317 319 317
Mean 7.7 4.8 6.4 5.2 7.2 7.5 6.4 4.7 6.2
SD 2.6 1.9 2.1 1.2 2.8 2.2 2.9 2.2 2.7
Max Mark 10 7 8 6 10 9 9 7 9
FF 77.3 68 79.8 87.2 72.1 83.1 70.8 67.1 69.2
Attempt % 99.7 98.8 99.1 100 97.9 99.1 96.9 97.5 96.9
Question
GCE Mathematics FP1 0977-01 9 8 7 6 5 4 3 2 1
69.2 67.1 70.8 83.1 72.1 87.2 79.8 68 77.3 0
10
20
30
40
50
60
Facility Factor %
70
80
90
100
4 5b 7 8
2 4.
The complex number z is given by
z = 1 + 2i . 1– i Find the modulus and the argument of z.
© WJEC CBAC Ltd.
[6]
(0977-01)
W
"7 -~ Z_ -=-
\O \ - V / - \ v-
\ v-7 < i— -\
\7 >'
t
-V \
~~ «
2 5.
The roots of the cubic equation
x3 + 2x2 + 2x + 3 = 0 are denoted by α, β, γ. (a) Find the cubic equation whose roots are β γ, γα, αβ. (b)
[6]
Show that
α 2 + β 2 + γ 2 = 0. Deduce the number of real roots of the cubic equation
x3 + 2x2 + 2x + 3 = 0, justifying your answer.
© WJEC CBAC Ltd.
[4]
(0977-01)
WHW^T WTf^H
c -T J^ A-y
'
UMI}Si
3 7.
The transformation T in the plane consists of a clockwise rotation through 90° about the origin, followed by a translation in which the point (x, y) is transformed to the point (x + 1, y + 2), followed by a reflection in the y-axis. (a) Show that the matrix representing T is
0 –1 –1 –1 0 2 0 0 1
.
(b) Find the equation of the image under T of the line y = 2x + 1.
© WJEC CBAC Ltd.
(0977-01)
[5]
[4]
Leave Blank Gadewch yn wag
Question number Rhify Cwestiwn
7 T= O
(
0 O
i
0 ( Z D
0
6
/
0
0
o | ,
O
0
0 6) O
\
o
o
~\
u
0
\
O
0 v
-
i- x >
0
2
°
0
b
0
j
/ o
o
2.
\\\O
X -
*
-t
nzz 2
M
- }c
3 8.
Using mathematical induction, prove that n
∑ ( r × 2r – 1 ) = 1 + 2 n ( n – 1),
for all positive integers n.
r =1
© WJEC CBAC Ltd.
[7]
(0977-01)
Leave Blank GactewcA yn wag
Question number Rhify Cwestiwn
g.
1
ft
I -t
- 2.
foh
n
n
