Algebra and Trigonometry Review
On the first day of class in MAT 1225 or MAT 1110 you will be given an Algebra/Calculus placement exam which
will be used to determine which mathematics course is most appropriate for you based on your skills in algebra and
trigonometry. These exercises are intended as a review of many topics from algebra and trigonometry that might be
on the exam. Note that this review does not cover every possible type of problem that may be on the exam.
Do NOT use a calculator for these problems โ calculators will not be permitted on the placement exam.
1. Simplify the following as much as possible:
a. 12 18โ
b.
12 14+
c.
(
)
23 4โโ โ
d.
()
(
22 22
23uv u v u u v uv v+โ+ โ++
)
1
)
3
e.
()
(
22 22
3212xy xy x xy xy xโ++โ โ โ+
f.
(
)
(
)
234
x
yxy+โ
g.
(
)
(
32
22323xxx x
)
โ
+โ โ
h. 11
1
x
x
โ
+
i. 22
2
2( 1) (2)
1
x
xx
x
+โ
+
x
j. 332
2. Factor the following completely:
a.
252xxโโ4
2
b.
2
23xโ
c.
2
18 3 6xxโโ
3. Divide x3 โ 5x + 2 by x โ 2.
4. Solve the following: a. 2x + 1 = 3x โ 4 c. 2t + 7 โ 3(1 โ t) = 1 โ 2t
b. 3(x โ 2) < 4x โ 3 d. |3x + 1| = 5
5. Solve the following and graph the solution:
a. 31 2 9x<โ <
b. 369xโ>
6. Find the equation of the line through the point (2,-1) having slope โ3.
7. Find the intersection of the lines y = 2x โ 1 and y = -x + 8.
8. Let . Find the following:
()
2
fx x x=โ
a.
(
)
0f b.
(
)
3f c.
(
d.
)
2fโ
(
)
ft e.
(
)
2fx
+
f.
()(fx h fx
h
+โ )
9. Find a. 5
cos 4
ฯ
b. 11
tan 6
ฯ
(do not use a calculator)
10. What is the radian measure of an angle whose degree measure is 120ห?
11. Given that 1
2
cos
ฮธ
= and sin 0,
ฮธ
< find cot .
ฮธ
