SECTION A
1. Determine the radian measure of the angle
0
135−=
α
degrees.
The formula for )sin( BA
−
is
(
)
(
)
(
)
(
)
(
)
BABABA sincoscossinsin −=−
.
Using this formula or otherwise find the exact value for )sin(
α
,
without using
tables or a calculator
. (Show all your working.)
Hence determine all the angles
θ
, in the range
[
]
00
360 ,0 satisfying
(
)
(
)
αθ
sincos =
. Your answers can be expressed in degrees or radians.
[7 marks]
2.
Sketch the graph of
(
)
xy sin=
in the range
π
π
≤
≤
−
x
. Determine
numerically the solutions of
(
)
3/1sin =x
and of
(
)
3/1sin −=x
in the same
range. You may express your answers in degrees or radians.
[7 marks]
3.
Find the domain of
x
for which both the functions )(log
3
x
and )213(log
3
−
x
are defined.
Find the only valid solution to the equation
(
)
(
)
2log213log
33
=+−
xx
.
[6 marks]
4.
You are given the values of 892789.2)24(log
3
=
and 261859.1)4(log
3
=
,
correct to six decimal places. Obtain (rounded to 4 decimal places) the values
of the following
)96(log
3
, )6(log
3
, )16(log
3
without using logarithm functions on your calculator
. (Show all your
working.)
[6 marks]
5.
Write down the first seven rows of Pascal’s triangle. Hence or otherwise find
the coefficient of
4
x
in the expansion of
(
)
6
23 x+.
[6 marks]
PAPER CODE ……M013………… PAGE 2 OF 5 CONTINUED
