MAT 1004A
Term test #1
1 October 2009
Total marks: 30 points
Nonprogrammable calculators are permitted. This test is closed book.
Supply your answers on this sheet
, but TA’s have extra paper if you need it.
PLEASE PRINT
SOLUTION
First name
Last name
Student number
Please show your work where appropriate!
1.
[2 marks] Find the domain of
h
if:
( 29
)
2
(
3
2
3
2
+

=
+

=
x
x
x
x
x
x
x
h
2
0
2
)
3
0
)
2
3
0
3
)
1

≠
⇔
≠
+
≠
≤
⇔
≥

x
x
x
x
x
(
(
(
]
{
}
3
,
0
0
,
2
2
,
:
U
U


∞

∈
∴
x
f
dom
2.
Let
θ
be an angle in radians such that:
2
π
θ
π

<
<

a.
[1] The terminal side is in quadrant
_3___
b.
[3] Find the
exact
ratios
θ
cos
and
θ
tan
if
3
2
sin

=
θ
NB –
Show your work
(the diagram helps). By “
exact
ratios” it is meant a ratio of the form
2
3
,
etc… no decimals!
5
2
3
2
2

=


=
b
5
5
2
5
2
tan
3
5
3
5
cos
=


=

=

=
∴
θ
θ
and
3.
Let
x
x
g
x
x
f

=
=
5
)
(
and
1
)
(
2
find a rule for:
a.
[2]
))
(
(
)
(
x
g
f
x
g
f
=
o
(
29
(
29
x
x
x
g
x
g
f

=

=
=
5
1
5
1
)
(
1
))
(
(
2
2
b.
[2]
))
(
(
)
(
)
(
x
f
f
g
x
f
f
g
=
o
o
(
29
[
]
[
]
4
2
2
2
5
1
1
5
)
(
1
5
))
(
(
5
))
(
(
)
(
)
(
x
x
x
f
x
f
f
f
f
g
x
f
f
g
x

=

=

=

=
=
o
o
4.
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 Spring '11
 dewsef
 Math, Calculus, Trigonometry, Cos, 1 g

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