Exam 1 Outline of content (Chpts follow the Coleman Book - Second Edition)
R.3 Exponents, scientific notation, and review of polynomials
Simplifying integer exponents using the properties of exponents
Scientific notation
Add/subtract and multiplying polynomials
Conjugates of binomials
(HW set 01)
R.6 Radicals and Rational Exponents
Simplifying radicals of multiple degrees
Simplify rational exponents using the same properties as integer exponents
Converting radicals to rational exponents and visa versa
Adding, subtracting, multiplying and dividing radical expressions
Rationalizing the denominator of a radical expression
(HW set 02 begins here)
R.4 Factoring polynomials
Finding the GCF
Factoring a two term, three term and four term polynomial
R.5 Rational Expressions
(HW set 03 begins here)
Simplify, multiply, divide, add and subtract rational (fraction) expressions
1.1 Linear equations, formulas and problem solving
Solving a linear equations (with integer and rational coefficients)
Solve a variable expression for a specific variable
Linear modeling using contextual word problems and geometric shapes
Solving linear inequalities – single and compound
Using interval notation to display an answer
Graphing the solution to a linear inequality with interval notation
Solving absolute value equations and inequalities
(HW set 04 begins here)
Practice Exam problems
1. Simplify completely. Write your final answer in exponential form. The final answer should have positive
exponent only.

2
a. x yz
  2x
3 2
2
4


 2a 3 b 3
c.  1 3 2
 3 2 a  2 b  3






2
3
y z
 2 a 2 b 4
b.  1 3  2
3 a b

4 2



2
2
3
2. Simplify completely and write the answer in radical form
12m 7 n 4
3. Write the radical expressions using rational exponents only.
a.
6
8n 4
b.
1
6
4. Write the exponential expressions using radicals only.
 4x 
b.  
 3 
a. 15 3 / 5
3
3 / 4
 23  4
c.  w 
 
5. Simplify completely and write the answer in radical form Be sure to rationalize the denominator if necessary
a.
d.
x2/7
1/ 2 4 / 5
b. (3 x) y
54a 5 b 4
25c 2
 3 50n 2  18n 2
c.
2
2
3
3
e. 5 48x  4 750 x
2 27 - 3 12 + 2 75
6. Multiply (3  2 x ) by its conjugate and simplify
7. Simplify completely and write the answer in radical form
8. Rationalize the denominator of the expression
a.
2
2 3

c.
 
4 x  6 y 
b.
x 2
9. Simplify completely
a. (2a  3) (3a 2  5a  1)
b. x 3  3x 2 y  4 xy 2  y 3  7 x 3  yx 2  9 xy 2  y 3

x 5 4 x 7
10
3
9

c.
2 5
6

2
10. Simplify completely
11. Factor completely
a.
2 x 2  5 x  12
x 2  16

4 x 2  8x  3 2 x 2  7 x  3
b.
6x 2  x  1
15
 2
6x  3
9x  1
a.
b.
c.
d.
e.
f.
g.
6 x 4  11x 3  10 x 2
27 y 4  8 y
3 x 2  10 x  8
2 x 3  14 x 2  20 x
10a 2  3a  18
16 y 4  81
x 3  2 x 2  9 x  18  0
12. Simplify completely
a.
2 x 2  5 x  12
x 2  16

4 x 2  8x  3 2 x 2  7 x  3
1
13. Simplify completely
a.
1
4
x2
1 6

x x2
b.
b.
6x 2  x  1
15
 2
6x  3
9x  1
5
2
60
 2
 3
x  2 x  2x  4 x  8
14. Solve the following equations
2 m 6
 
a.
3 9 m
b.
2
3
( x  6)  ( x  8)
3
5
c.  6( x  4)  66  3x  9( x  2)
d.
1
x3  2
2
15. Rework the contextual problems in HW 04 (Make sure students rework the word problems from WHS)
A train travels 150 km at a speed of 40 km per hour. Write an equation in terms of t describing the distance the train
travels in t time. How long will it take the train to travel 300 km? If the train travels 240 km in 3 hours how fast was
the train traveling in km per hour.
16. Solve:
a. R 
3  4A
 T for A
M
b. sr 
3  4s
for s
p
Solve and graph the following inequalities and express the answer in interval notation.
17. 3  3  2 x  1
18.  2 
1  2x
5
3
19. 3x  3  2x  1  7 x  9
20.  5x  5x  6
21. 4 x  6(11  2 x)  18