Download Instructor: Math 181 Chris King Algebra and Trig. Review I. Factor 1

Instructor:
Chris King
I.
1.
2.
3.
4.
5.
Math 181
Algebra and Trig. Review
Factor
x2 – 6x + 9
6x2 – 9x
x3 – 6x2 + 12x – 72
x3 + 64
6x2 – 19x – 36
II.
Simplify the expression.
6
7
+
1. x x + 1
2x
7
7
−
2. x + h x
h
2z − 2y
3.
xz − xy + 3y − 3z
1
4
4
⎛ 3−1 x 2 y 4 ⎞ ⎛ x 3 y 3 ⎞
4. ⎜
⎜ 5 ⎟
⎝ z 3 ⎟⎠ ⎝ z 3 ⎠
−3
5.
4x 3 − 16x 2 + 8x − 12
8x 2
III.
1.
2.
3.
4.
5.
Graph each function.
f(x) = 2(x – 3)2 + 4
g(x) = 2sin(4x)
f(x) = 51 – x + 1
g(x) = 3 x + 2 − 1
f(x) = |x + 1| + 2
IV.
Solve each equation.
1
3 2
w− = w+2
2
4 3
2
x – 5x – 9 = 0
y2 = 18 – 7y
32n2 – 162 = 0
x+1
⎛ 1⎞
2 x−3
7
=⎜ ⎟
⎝ 49 ⎠
1.
2.
3.
4.
5.
6. log 3 ( 7 − 5z ) + 14 = 17
7. ln x + ln ( x − 4 ) = ln ( 3x − 10 )
4x
1
3x 2 + 3
−
= 2
x − 5 x + 1 x − 4x − 5
9.
m + 18 + 2 = m
10. 98t3 – 49t2 – 8t + 4 = 0
11. 2 cos ( 3x ) = 1 on the interval [0,2π )
8.
V.
Evaluate the following given the following functions.
f(x) = 2x – 5
g(x) = x2 – 1
h(x) = |x – 1|
1.
2.
3.
4.
5.
6.
7.
f(7)
f(g(2))
g(f(h(5)))
g(x + 1)
h(g(-1))
g(x + h)
g(f(x))
VI.
Evaluate each trig function.
⎛ 5π ⎞
1. sin ⎜ ⎟
⎝ 6 ⎠
(
2. cos 330!
⎛ 4π ⎞
3. tan ⎜
⎝ 3 ⎟⎠
⎛ −π ⎞
4. cot ⎜
⎝ 2 ⎟⎠
⎛π⎞
5. sec ⎜ ⎟
⎝ 4⎠
( )
6. csc 60!
)