Download Algebra 3 Unit 2 Review Name_____________________________

Algebra 3 Unit 2 Review
Sections 2.1 – 2.7
Name________________________________
Period_______Date_______
I. Determine the numerical coefficient of the following terms:
3
x
a. 4x 2 ______
b.  x ______
c. x ______
d.
______
5
3
e.  xyz ______
II. For each of the following, list terms that would be like terms and unlike terms.
Given term:
4x 2
Examples of Like Terms:
Examples of Unlike Terms:
1
xyz
3
a 2bc 3
5x
rst
xy
4
III. Simplify the following expressions.
1
a. 4 x  x 2  1
b.  x  16 
4
2
1
x  x 2  3x 2  x
5
5
e. 3  x  2  12  x 
f.
i. 3  2 x  4  7  x  1
j. 2x  4x  3  7 x  5
c. 2  x 2  3 x   5 x
d. 3  x  5
g. 4  x  3  3  x  2
h. 0.4 x  2.7 y  1.8 x
k.

 
1
1
4 x 2  2 x  8  15 x 2  9 x  3
2
3

IV. Translate the following into algebraic expressions or equations.
a. Subtract 7 x  2 from x  5 ________________________
b. The difference of a number and five, divided by seven. ________________________
c. Triple the difference of a number and two added to the sum of a number and five. _____________________
d. The sum of a number and six subtracted from two times a number decreased by one. __________________
e. Five times a number less four is the same as twice the sum of the number and three. ___________________
f. The quotient of a number and three is the same as the difference of the number and two. ________________
V. Solve for x:
a. 3x  9  18
e.
2
5
x  14  x
7
7
b. x  4x  7  x  3  8
c.   5x  1  7 x  3
d.
f. 1.72x  0.04x  0.42
g. 9 x  x  1  6( x  1)  7
h.
x 2

6 3
5  x  1
6
 2x  3
VI. Solve for x. Write the answer in interval notation and graph.
a. x  4
b. x  5
c. 2  x  3
Interval Notation:_____________
Interval Notation:_____________
Interval Notation:_____________
Graph:
Graph:
Graph:
d. 2x  5  9
e. 3x  4  x
f. 1  4x  7  15
Interval Notation:_____________
Interval Notation:_____________
Interval Notation:_____________
Graph:
Graph:
Graph:
g. 3  x  5  2  x  4
h. 4  4  x  2  12
i.
Interval Notation:_____________
Interval Notation:_____________
Interval Notation:_____________
Graph:
Graph:
Graph:
1
7
5x  2 
5
5
VII. Formulas
a. Given A  l  w ; A  56, l  8 . Find w.
b. Given d  r  t ; r  75, t  2 . Find d.
c. Solve for w: V  lwh .
9
d. Solve for C: F    C  32
5
e. Mike is trying to replace the carpet in his bedroom. His room is rectangular and has a width of 14 feet and a
length of 20 feet. How much carpet will Mike need for his bedroom?
f. The normal body temperature for a human is 98.6 degrees Fahrenheit. Express this temperature in terms of
9
degrees Celsius. F    C  32
5
g. If it takes me five hours to travel 365 miles, at what rate was I traveling? d  r  t
VIII. Solve the following word problems.
a. Greg gets paid $20 dollars an hour. If Greg’s paycheck at the end of week is $700 before taxes, how many
hours did he work?
b. The sum of three consecutive odd integers is 57. What are the three integers?
c. The sum of five consecutive numbers is 315. What are the five numbers?
d. The sum of two consecutive even numbers is 178. What are the two numbers?
e. Angela plans to invest her $25,000 inheritance into two accounts: a mutual funds account that pays 7.5%
simple interest yearly, and a certificate of deposit that pays 5.5% simple interest yearly. If the total simple
interest earned in the first year is $1645, how much did she invest into each account? Use I = PRT.
f. Caitlin plans to invest $20,000 into two accounts: a certificate of deposit that pays 6% simple interest yearly
and a mutual funds account that pays 8% simple interest yearly. If Caitlin’s accounts earn $1460 in interest in
the first year, how much did she invest in each account? Use I = PRT.
g. Megan makes $3000 month plus 15% commission on the value of the merchandise she sells. If she wants to
make at least $6000 this month, how much merchandise must Megan sell?