© Science Exam Papers: Worked Solutions Edexcel C3 Paper L
© Science Exam Papers: Worked Solutions Edexcel C3 Paper L
© Science Exam Papers: Worked Solutions Edexcel C3 Paper L
Edexcel C3 Paper L
1.
5.
1
x
(x 3)(x + 3) (x 3)(x 1)
x(x 1) (x + 3)
(x 3)(x + 3)(x 1)
x 2 2x 3
(x 3)(x + 3)(x 1)
(a) f(0) = e3
dy
= sec2 x + 2 cos 2x
dx
at x = ,
4
2
dy
=
2 +0=2
dx
(b) at x =
x+1
(x 3)(x + 1)
=
(x 3)(x + 3)(x 1)
(x + 3)(x 1)
2.
(a)
3
ff(0) = e2e +3
,
4
y =1+1=2
equation of tangent is y 2 = 2 x
4
(6)
y = 2x + 2
(2)
6.
f 1 (x) =
1
(ln x 3)
2
3.
4.
dx
2y
y2 + 4
y2
4
dy
= 2
=
=
+
dy
dx
2y
2y
2y
y +4
(a) f(1) = ln 1 3 + 5 = 2
f(2) = ln 2 6 + 5 = 0.306
(a) R.H.S =
(3)
2 tan
sec2
(3)
(1)
=2
sin
cos2
cos
= 2 sin cos
(6)
= sin 2
(4)
change of sign root in interval
(2)
(4)
(3)
sign change
(2)
4 tan = 1 + tan2
1
sin 2 =
2
2 =
5
,
6 6
5
,
12 12
(5)
7.
(a)
8.
(a)
y
y = |xa|
(2a, a)
(0, a)
(3, 4)
y = 2a|xa|
x
(a, 0)
(5)
(b) points of intersection: (0, a) and (2a, a)
1
1
product of diagonals = (2a)(2a) = 2a 2
2
2
(5)
9.
(b)
R=
5, tan = 2
max. 5
, = 1.11
min. 5
(b)
1
+1
(0, 1)
occurs at
t
= 1.11
12
t = 4.24 (2 d.p.)
(d) t = 0. d = 15 + 1 = 16 metres
t
1.11 = 0
(e) d = 15 cos
12
asymptotes at x = 1.
maximum at (0, 1)
A(3, 0.125)
(4)
Ed
C3 paper L
(3)
2
1
5 cos + sin ;
5
5
(2)
t
1.11 =
t = 10.24
12
2
time 2230 (nearest half hour)
(4)
(2)
(4)
(1)
(4)