Pre-calculus Review Worksheet
MATH 1500
Worksheet 1
1. Factor the following polynomials
(a) x2 + 2x
(b) x2
1
(c) x2
x
32
(d) x + 27
X
2
2
528 hint54225 65
2. Solve the equation x2 = 25
3. Solve the equation y 2 + y = 6
4. Solve the equation 2x2 + 3x + 1 = 0
5. Simplify the rational expression.
(a)
(b)
3
2
+
x+3 x 3
t
1
5t + 2
+
+ 2
t+1 t 2 t
t 2
6. Rationalize the numerator and simplify.
p
(x + h + 1)
h
p
(x + 1)
7. Solve the inequality.
(a)
(x 3)
2x(x + 1)
(b)
0
xex
<0
(x2 + 1)
(c)
x sin x
x 2 [0, 2⇡)
0,
8. Compute the following trigonometric values (If any do not exist, state so).
(a)
cos(⇡/4)
(b)
tan(3⇡/2)
9. Find all solutions in the interval [0, 2⇡) of
2 cos x + 1 = 0
10. Find an equation of the line through (0, 1) and ( 3, 4).
11. Find the slope of the line perpendicular to 2x = y
5. (Hint: slope of the perpendicular line is the
negative reciprocal of the original slope)
12. Find the domain of the function below (Write your answer in interval notation).
p
x
3
13. Find the domain of the function below (Write your answer in interval notation).
3
(x + 2)(x
14. Let f (x) =
(a) f
p
1)
x + 4 and g(x) = x2 + 4x. Find
g(x)
(b) g f (x)
(c) f
f (x)
(d) g g(x)
15.
1
1
I
f
1
16. Identify x and y intercepts, vertical asymptotes, and domain of the given functions:
a)
b)
c)
17.