Download Name__________________ _____Period_______ 2011

Name_____________________________________________Period_______
Algebra 3 Review 1 --- 1.2 – 1.8
2011-2012
1) For each of the following, list the set it best
15


represents. 4, 3 ,  2.3, 0, 6, , 7 6 
2


a. Natural numbers:________________________
b. Whole numbers:_________________________
c. Integers:_______________________________
d. Rational numbers:________________________
e. Irrational numbers:_______________________
f. Real numbers:___________________________
2) Insert >, < or = to make the statement true.
16
a. 22 _____ 11
b.  6 _____ 6
c.
_____ 8
2
e. 3 ______ 7
d. 0.52 _____ 0.55
3) Write each sentence as a mathematical statement. Use the symbols >, < , ≤ , ≥ , ≠ and =.
a. Five is greater than or equal to three___________
b. Negative two is less than zero____________
c. Six is less than or equal to nine_______________
d. One-half is equal to four-eighths__________
e. Absolute value of negative one is not equal to negative one_______________
4) Simplify the following.
a. |-2| = _________
b. |4| = _________
c. |-5.6| =__________
d. |0.25| = __________
5 ) Write each number as a product of prime factors. The factors should be stated in order from least to
greatest.
a. 81 = ____________
b. 40 = ____________
c. 70 = ___________
6) Simplify State answers as reduced fractions or mixed numbers in simplest form.
a.
15
=_____
10
b.
32
=______
44
c.
56
=______
42
d.
39
=_____
9
7) Perform the indicated operation clearly showing each step. Write your answer in lowest terms. Your
answer may be an improper fraction or mixed number.
a. 
e.
1
6
  =______
2
7
3 10
 =______
5 3
b.
16 21
 =______
9 8
c.
f.
4 1
 =______
15 15
g. 
1 5
i. 3  =_______
4 6
1
j. 4  2 =_______
5
3
m. 2 1 =_______
4
n.
2 2
 2 =_______
3 3
8) List the order of operations—be specific:
5 15

=______
11 44
7
 3
    =______
15
 10 
k. 5
o.
1
3
 2 =______
3
4
4
2
 2 =______
3
3
d. 
h.
36 9
 =______
25 10
9 2
 =_______
7 7
2
l. 6  3 =______
3
1
1
p. 1  3 =______
4
8
9) Simplify the following clearly showing each step. Write your answer in lowest terms. Your answer
may be an improper fraction or mixed number.
a. 8.3   0.62 
b. 4  8  6  2   5  3   2
d. 3  22   4   6  
e.
c. 6  2  2  25
3  6 8  5
f.
42  2
10) Find the opposite or additive inverse of the following.
1
a. 9
b. 
3
c.  
16  13  5  32
17  5
2
3
11) Find the reciprocal or multiplicative inverse of the following.
a.
1
8
b. 4
c. 
3
2
d. 5
12) Evaluate the following for x = 1, y = -4, and z = 2. FIRST STEP—SHOW THE SUBSTITUTION
BEFORE ANY CALCULATIONS!
x2  y  x  z
a. x  y
b. x  y  2
c.
z3  y
13) Write an algebraic expression or equation for each of the following.
a. The sum of three times a number,x, and two.___________________
b. The difference of four and a number,y._______________________
c. The product of five and a number,x, is 24_________________________
d. The quotient of sixteen and a number, m, is three less than a number y.______________________
e. Nine decreased by twice a number,x, is the same as four plus the number,x.________________________
f. Seven less than a number,a, equals the quotient of the number,a, and two.__________________________
g. Eight times a number,x, increased by four is three.___________________________________________
h. The ratio of two and a number, w, is the same as five less than the number, p.________________________
14) Determine if x = 3 is a solution to the following equations. Be sure to draw a conclusion supported by
calculations.
a. 7 x  6  9x
b. 2 x  5  x 2  1
c. x  4  2  2 x  5
d.
x2 x

10
9
15) For the equation x 2  2  11, determine if the following numbers are solutions.
a. 2
b. 3
c. -3