Math 150, Calculus for BM&SS
Topics from College Algebra I
name:
date:
Here are some practice problems from College Algebra. This is by no means a comprehensive list.
Please complete these, showing your best algebra presentation, and have them ready for turn-in on the first
day of class, February 11, 2014.
Problems
Solving Equations I
4y 14
y
−
=
5
15
3
2. Solve for p: 4 (p + 3) = 3 (p − 2) + 5p + 18
1. Solve for y:
3. Solve for r: d = rt
x−µ
4. Solve for x: Z =
σ
Factoring
1. Factor completely: −45x2 + 66x + 27
2. Factor completely: 81x2 − 100
3. Factor out x1/2 : x5/2 − 9x1/2
4. Factor out x−2 : 1 + 6x−1 + 8x−2
Solving Inequalities
Solve each inequality, sketch the graph of the solution set on a number line, and then write the solution set
in interval notation.
3x + 1
4 + 2x
≥
1.
3
2
2. 2x2 + 5x − 3 > 0
4
3
≤
3.
x−2
x+5
Solving Equations II
1. Solve for x: 5x2 = 6x + 4
2w − 3
w−4
2. Solve for w:
=
2w + 1
w−5
3. Solve for t: 24,000 = 8,000 (1 + 0.0124)
√
√
4. Solve for x: x − 3 + 4 = 2x + 1 + 2
t
Functions I
f (x + h) − f (x)
.
h
1
g(x + h) − g(x)
2. If g(x) =
, find and simplify
.
x−3
h
1. If f (x) = 3x2 − x, find and simplify
3. If f (x) = x2 + x and g(x) = 3x − 7, find and simplify f (g(x)).
4. Find the zeros of the function p(x) = 3x3 − 15x2 − 42x.
Math 150, Topics from College Algebra I
Solutions
Solving Equations I
1. y = 2
2. p = 0
d
t
4. x = Zσ + µ
3. r =
Factoring
1. −3 (3x + 1) (5x − 9)
2. (9x − 10) (9x + 10)
3. x1/2 (x − 3) (x + 3)
4. x−2 (x + 4) (x + 2)
Solving Inequalities
1. (−∞, 1]
2. (−∞, −3] ∪
1
,∞
2
3. (−5,2) ∪ [23, ∞)
Solving Equations II
1. x =
3±
√
29
5
19
2. w =
6
ln (3)
3. t =
≈ 89.1459
ln (1.0124)
4. x = 4 or x = 12
Functions I
1. 6x + 3h − 1
−1
2.
(x + h − 3) (x − 3)
3. 9x2 − 39x + 42
4. x = −2, x = 0, and x = 7
2