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Math 119 - 01 — Practice Test 1
Summer 2007
Circle your answers. Partial credit will be based on work shown. There should be sufficient work
shown to support your answers. NO CALCULATORS!
1.
2.
3.
4.
Identify the verbal description of the interval.
 2, 2
[A] All real numbers greater than -2 and less than or equal to 2.
[B] All real numbers greater than or equal to -2 and less than or equal to 2.
[C] All real numbers greater than -2 and less than 2.
[D] All real numbers greater than or equal to -2 and less than 2.
Answer: A
3
Evaluate  2 
[B]
Answer: C
 2
1
8
[D] -8
[E] none of these
3
3
1
 1
    
8
 2
[E] none of these
Write the inequality using interval notation and sketch the subset of real numbers on the real
number line.
x  2
--------[------------>
-2
Evaluate the expression.
[A] 4
[B] -4
Answer:
6.
[C] 
Identify the expression that is equivalent to 10  x  5 .
[A]  10,5 [B]  10,5 [C]  10,5 [D] 10,5
Answer: A
Answer: [2, )
5.
1
6
[A] 6
B
8
2
3
2
8 3
[C] 2
[D] not a real number
 
 3 82   3 8
2
   2
  3 23
2
2
 4
Identify which of the following is an example of the Associative Property of Multiplication.
[A] 3   4  5   3  4  5
[B] 3   4  5   3  4  5
[C] 3  4  5  3  4  3  5
[D] 3  4  4  3
Answer: B
7.
[E] none of these
Rewrite using rational exponents.
[A] x
6
5
[B] x
5
6
[C] x 30
6
x5
[D] none of these
[E] none of these
8.
Answer: B
Evaluate 4 16
[A] -4
[B] 4
[C] -2
[D] 2
[E] not a real number
Answer: E ( because there is a negative sign under the radical and the index is even).
9.
Circle the numbers that are irrational.

-5.7
10.
11.
27.88888
7
9
5
0
15
Answer:  , 7
Rewrite the expression using only positive exponents.
5 x 4 5 x 4
25
Answer: 5 x  4 5 x  4  511 x  4 ( 4 )  5 2 x 8  8
x
a. Evaluate the expression for x  2 . 2 x 4  3x3  2 x
Answer:  2(2) 4  3(2) 3  2(2)  2(16)  3(8)  4  32  24  4  12
b. Evaluate the expression for x  6 . 3 | 4  x | 2 x  5
Answer: 3 | 4  6 | 2(6)  5  3 | 2 | 12  3  2  12  5  6
12.
Perform the operation. Put the answer in simplest form.
2
a.
1 9 3
   
2 10  5 

1 9
9
1 9 25
1 1 25
1 5 4
 
  
  
   2
2 10 25
2 10 9
2 10 1
2 2 2
2
1 3
1
b. 2     9
4 2
 3
2 2
2 6 2 1 4 9 13
1 1 2
 2     3    3  
   

9 12
9 12 9 2 18 18 18
9 4 3
13.
Simplify the expression. Leave your answer with only positive exponents.
2
2
 2 x 3 
 2 x 3  x 4
 5x4 


 

=
 3 
 5x 4 
1
 2x 


5
14.
2

 2 x 7
   

5 1
Simplify the expression. (Hint: 54  27  2 )
2

2
   
5

2
 x 7

 1
2

4 x 14
4
 


25 1
25 x14

5  3 16  3  3 54 = 5  3 23  2  3  3 27  2  5  2  3 2  3  3  3 2  10  3 2  9  3 2  3 2
15.
Perform the operation and simplify. Leave your answer with only positive exponents.
6 5
11
 

2  1
2
1
1
5 3
15 15
15
5
3
a. x  x
x
x
 x  11
x 15
1
b. y  y
c.
d.
16.
3
2
6
=y
x 4 / 5 y 1/ 7
x
1/ 5
y 1/ 7

6
1 2

3 6
=
y
x
4
5
6
1 1

3 3
y
x 5y
1
6
7
 y0  1
x
4 6
 
5 5
y
1 6
 
7 7
x

10
5
y

7
7
 x 2  y 1 
7
32  5 5
1 1
1 1
1
 321  5 5( 3)  33  5 2  3  2 


3
27 25 675
5 3
3 5
Consider the following polynomial: 5  3 x3  7 x  x 2
A) Put the polynomial in standard form.
3x 3  x 2  7 x  5
B) What is the leading coefficient?
3
C) What is the degree?
3
D) What is the constant term?
5
17.
18.
Perform the operations and write the result in standard form.
a.
(5b5  7b3  6)  (2b5  4b3  11)
 5b 5  7b 3  6  2b 5  4b 3  11  3b 5  11b 3  5
b.
( x  2)( x  3)  7 x( x 2  5)
 x 2  3x  2 x  6  7 x 3  35 x  7 x 3  x 2  40 x  6
Multiply.
a. ( x  5) 2 = x 2  2  5  x  25  x 2  10 x  25
1
x2 y
b. 3x  2 y   9 x 2  2  3x  2 y  4 y 2  9 x 2  12 xy  4 y 2
Factor completely.
2
19.
2
a.
1 2
 x
x
 x

2
x  36 y 2     6 y     6 y   6 y 
4
2
2
 2

b.
2 x  3x 4  2 x 3  x 3 2 x 2  3x  2  x 3 2 x 2  4 x  x  2  x 3 2 xx  2  x  2  x 3 x  22 x  1

5
20.





c.
x 3  5x 2  4 x  20  x 2 x  5  4x  5  x 2  4 x  5  x  2x  2x  5
d.
2 x 6  4 x 4  3x 2  6 = 2 x 4 ( x 2  2)  3( x 2  2)  ( x 2  2)( 2 x 4  3)  x  2 x  2 2 x 4  3


Find the domain. Write your answers in interval notation.
7 x2  8x  5
a.
Domain: All real numbers,  , .
b.
3x  9
3x  9  0  3x  9  x  
Domain: [3, )
21.
9
 x  3
3
Perform the operation and simplify. State the domain
 y  4 8 ( y  5)
4
y 2  8 y  16 ( y  4)3 ( y  4)( y  4) 8 y  40
a.
=





3
3
2( y  5)
2 y  10
8 y  40
 y  4
 y  4  2 ( y  5)  y  4
Domain: y  4, y  5
2
b.
4
5  x  2
5 x  10 3 x
3x
15

=


2
2
x  x x  4 x  x  1  x  2  ( x  2)  x  1 x  2 
Domain: x  1, x  2, x  2, x  0
22.
Does the following contain an error? If so, describe and correct the error.
5  x  2  4
 5 4  9
x2
Yes there is an error. You cannot simplify (x+2).
5( x  2)  4 5 x  10  4 5 x  14


x2
x2
x2


23.
Write the fraction as the sum of two or more terms. Then write each term so that it has no
denominator (other than 1). Exponents may be negative.
5 x8  4 x 4  3 x 3  2 5 x 8 4 x 4 3 x 3 2
 3  3  3  3  5 x 8  3  4 x 4  3  3 x 3 3  2 x  3  5 x 5  4 x  3  2 x  3
3
x
x
x
x
x
24.
Insert the missing factor. (Simplify the missing factor before you insert it.)
5x  3
3
2
 10x  3
1
2
 5x  3
1
2
x  3  2  5x  3 12 x  1