MATH 1090 Algebra and Trigonometry
Final Examination - Questions
2002 Winter
Note
: Without the Symbol font, the symbol
(theta) may appear as q,
and the symbol
(pi) may appear as p.
Perform the indicated operation and simplify:
Factor:
Solve the given equation or inequality.
| 4
x
-
3 | > 9
x
(2
x
+ 3)
<
2
Find an equation of the line passing through the point
(2, 3)
and perpendicular to the line
2
x
+ 3
y
+ 1 = 0 .
Sketch the graph of each of the following equations.
Label all intercepts and also label the vertex, if appropriate.
y
= | 2
x
-
3 |
-
4
y
=
-
x
2
+ 8
x
-
12
For the functions
and
,
find
and the domain of
.
If
, find
f
-
1
(
x
) and sketch the graphs of
f
and
f
-
1
on the same set of axes.
Use the remainder theorem to find the remainder when
f
(
x
) =
x
7
+ 3
x
6
-
5
x
3
-
5
x
2
+ 7
is divided by
.
Find
c
so that
x
+ 2 is a factor of
g
(
x
) =
cx
5
+ 2
x
3
-
8
cx
-
32 .
For the polynomial
P
(
x
) = 9
x
4
-
6
x
3
+ 37
x
2
-
24
x
+ 4:
List all possible rational zeroes.
Factor
P
(
x
) completely into linear factors.
Solve for
x
:
Find all values of
q
in the interval
[0, 2
p
)
that satisfy the equation
sin 2
q
+ sin
q
= 0 .
Given that
and that
, find the exact value of:
sin
q
tan (
q
+ 2
p
)
cos 2
q
The
solutions
to this final examination will appear elsewhere on this web site.
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Created 2002 04 25 and modified 2002 04 26 by
Dr. G.H. George
.