A2A MAT115 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 01a and 01b)
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
R.4 Factoring polynomials
Finding the GCF
Factoring a two term, three term and four term polynomial
(HW 02a and 02b)
R.5 Rational Expressions
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
1.2 Linear Inequalities in One Variable
Solving linear inequalities – single and compound
Using interval notation to display an answer
Graphing the solution to a linear inequality with interval notation
1.3 Absolute Value Equations and Inequalities
Solving absolute value equations and inequalities
(HW 03a and 03b)
A2A MAT115 Practice Exam 1 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 / 4

c.  w

2
3




3
4
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
9. Simplify completely
(2a  3) (3a 2  5a  1)
i.
ii.
iii.
x
3
 
a.
2
2 3
4 x  6 y 
2
b.
x 2
 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
10. Simplify 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
11. Factor completely
6 x 4  11x 3  10 x 2
i.
27 y 4  8 y
ii.
3 x 2  10 x  8
iii.
2 x 3  14 x 2  20 x
iv.
10a 2  3a  18
v.
16 y 4  81
vi.
x 3  2 x 2  9 x  18  0
vii.
1
12. Simplify completely
a.
1
4
x2
1 6

x x2
b.
5
2
60
 2
 3
x  2 x  2x  4 x  8
13. Solve the following equations
2 m 6
 
i.
3 9 m
ii.
2
3
( x  6)  ( x  8)
3
5
iii.
 6( x  4)  66  3x  9( x  2)
iv.
1
x3  2
2
Solve the following contextual linear equations
14. A merchant blends tea that sells for $4.05 a pound with tea that sells for $1.73 a pound to produce 76 lbs of a mixture
that sells for $2.32 a pound. The final mixture contains _________ lbs of $4.05/lbs tea and_______lbs of $1.73/lb tea.
15. Candy and Tim share a paper route. It takes Candy 60 minutes to deliver all the papers, and it takes Tim 90 minutes.
How long does it take the two when they work together?
16. A board 60 inches long is to be cut into three pieces for framing. The longest piece must be twice the length of the
middle-sized piece, and the shortest piece must be 12 inches shorter than the middle-sized piece. Write an equation to
find the length of each of the three pieces then find the length of each piece.
17. If the sum of 3 consecutive integers of the form n, n+1, n+2,..., is 99, what are the three integers. Do not use guess
and check.
18. Jamie wants to maintain an average of at least a 80% in his math class. If his first three test scores were 85, 73, and
62, what score does he need to make on his fourth exam? Assume all test grades are the same weight. The score on
the fourth exam is?
19. 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.
20. 3  3  2 x  1
21.  2 
1  2x
5
3
22. 3x  3  2x  1  7 x  9
23.  5x  5x  6
24. 4 x  6(11  2 x)  18
25. For the following:
i. write each expression as an absolute value equation or inequality and
ii. Solve the equation or inequality.
a. x is six units from the origin
b. The distance from p to -3 is five units
c. t is within three units of 6.
d. b is at least 0.5 unit from – 1