Download Mathematics I - Cobb Learning

Algebra Investigations Study Guide
Name ________________________Block______
Solve or simplify.
x  6  2.
1.
Solve
2.
Solve
3.
Simplify:
1._____________
x4 x4

algebraically.
x 2 x8
x2  8x  16
a. (x + 4)2
c. x + 4
3.________
b. x + 4x + 4
d. x – 4
8 x  20
.
4
4.________
5
6

x3 x3
5.________
4.
Simplify
5.
Add:
6.
Simplify the following.
a. 5 24  3 6
a.________
2 ___________
b.
50
49
b._________
c.
5
3 6
c.________
d.
45  3 20  3
d._____________
7. Simplify and state the excluded values.
8.
28 x 4  20 x 2
12 x
_________________
Use multiplication or factoring to explain your reasoning for the following
a. If x 2 + y 2 = 20 and xy = 15, find the value of (x + y) 2.
b. If x 2 – y 2 = 40 and (x + y) = 5, find the value of (x – y).
9.
For each equation, determine if the given value of x is a solution.
Be able to explain your reasoning in words.
a. Is x = 4 a solution of the equation x  2  0 ? Explain.
b. Is x = 5 a solution of the equation
10.
x2
25
? Explain.

x 5 x 5
Solve the equation showing algebraic steps. Check for extraneous roots.
3 x 5 3  6
11.
Solve the equation showing algebraic steps .
x
2

2x  5 x  3
12.
Which one of the following is not a quadratic equation?
a. x2 – 3 = 0
c. – 9 + x = 0
13.
b. x2 + x + 2 = 0
d. – 7x2 + 12 = 0
Divide (5x2 + 9x + 12) by (x + 2) using the two algebraic methods
a. long division
b. synthetic division
14.
x 2  16 12 x

4x2 4  x
Simplify.
15. Simplify
16.
x 2  5 x  36 x 2  8 x  9

5 x 2  16 x
x 1
Simplify
17. Simplify
2 x 10

x  6 4x
4
14
1  2
x4
x  x  20
18. Solve
19.
3x 3 x  12

x 3 x 3
Simplify
4x
25
12 x 2
15
20. Solve
21.
5 1

6
x 3x
Find the sum or difference.
a.
6
3

x2  6 x x
b.
3x  5 x  3

3
8x
4x2