ELEMENTARY ALGEBRA PRACTICE FINAL EXAM
1.
1
13w  7   2
3
Solve:
1
A. w 
13
2.
B.
4x9 y 2 z
3.
5.
6
4x 6 y 3 z 2
w 1
E. none of these
D.
4x 6 y 2 z 2
E. none of these
D.
5  z x  y 
E. none of these
11x  6
x x  3
E. none of these
D.
5x  y   zx  y 
3x  2
3x

x
x3
6 x 2  11x  6
xx  3
C.
D.
4 x  5 y  20
6
B.
5
C.
C.
 11x
x x  3
B.
Graph the equation:
A.
w5
2
5  y x  z 
B.
 11x  6
xx  3
C.
5 x  5 y  zx  zy
Subtract and simplify:
A.
3
4x 6 y 3 z
B.
5  xz  y 
4.
1
C.
5
-6
-5
-4
-3
-2
-1
6
D.
4
-1
4
3
3
-2
3
2
2
-3
2
1
1
-4
1
1
2
3
4
5
6
-1
-1
1
2
3
4
5
-5
6
-1
5x 3 y 2
7.
Simplify:
A. 3 x 
7
3
B.
 5x 3 y 2
-6
-5
-4
-3
-2
-6
Simplify (assume all variables are positive numbers):
E. none of these
5
1
4
-1
A.
3
Factor completely:
A.
1
13
 x yz  4 x y z 
Find the product:
A.
6.
w
-1
1
-1
 25 x 6 y 4
C.
 5x 3 y 2
D.  5 x y
C.
x 1
x2
D.
3
2
E. none of these
3x 2  7 x  2
x 2  3x  2
B.
3x  1
x 1
3x  1
x 1
E. none of these
8.
Divide and simplify:
A.
9.
2.3 x 10 4
t:
C.
2
x2
x
D.
x x  2 
x 1
E. none of these
7
C.
D.
5
E. none of these
7
2.3 x 10 4
0.23 x 10 2
C.
D.
2.3 x 10 3
t
E. none of these
A  P  Pr t
A P
Pr
t
m
B.
m:
Ev 2
2
B.
E
A P
P
t
t
A P
Pr
D.
C. m 
1 2
Ev
2
D. m 
C.
A P
r
E. none of these
2E
v2
E. none of these
1
mv 2
2
B. m  2Ev
B.
2
10 gallons
2
2,3 and  2,5 .
2
C.

1
2
D.
undefined
E. none of these
B.
20 gallons
C.
100 gallons
D.
150 gallons
E. none of these
A woman walked to a lake at the rate of 3 mph and returned at the rate of 4 mph.
If the return trip took one hour less time, and the round-trip distance was 10 miles, how long did the
round-trip take to complete?
A. 1 hour
16.
2
How many gallons of a 10% salt solution must be mixed with 50 gallons
of a 50% salt solution to obtain a 20% salt solution?
A.
15.
x  1
Find the slope of the line through
A.
14.
x x  2 
0.0023 in scientific notation.
Solve for
A.
13.
B.
Solve for
A.
12.
5
Express
A.
11.
B.
If a number is doubled, the result is seven less than three times the number.
What is the number?
A.
10.
1
x
x 2  3x  10 x 2  2 x

x 1
x 2  6x  5
B. 2 hours
C. 3 hours
Write, in standard form, the equation of a line with slope of
A. y 
1
7
x
2
2
B. y 
1
7
x
2
2
D. 3
1
hours
2
E. none of these
1
and passing through the point  1,3 .
2
C. x  2 y  7
D. x  2 y  7
E. none of these
17.
A.
18.


3x  y  y4 x  y   4 y 2  xy
Simplify:
3 y 2  3x  y
B. y
C.
B.
-3
D.
E.
A.
20.
A.
21.
x  5
5x  32x  7
B.
x3
C.
x5
D.
x  3
E. none of these
C.
2x  35x  7
D.
2x  35x  7
E. none of these
10 x 2  x  21
5x  32x  7
A woman invests part of $10,000 at 8% annual interest and the rest at 9%. Her annual income from these
investments is $860. How much did she invest at 9%?
Divide:
B. $4,000
C. $5,000
D. $3,750
E. none of these
12
5
E. none of these
x 2  12 x  35
x5
x7
Solve:
A.
24.
B.
Factor completely:
A.
23.
None of these.
3
 3x  9  15
A. $6,000
22.
3
F.
-3
Solve:
E. none of these
C.
3
19.
D.  2 y  3 x
3x  5
2
2
Solve the inequality and graph its solution:
A.
 3 y 2  3x  y
B.
x7
C.
x  17 , remainder  50
D. x 
x 2  x  56  0
x  8 , 7
B.
x  7 , 8
C.
x  7, 8
D.
x  8 ,  7
E. none of these
A woman has some nickels, dimes and quarters; 25 coins in all. She has 3 more dimes
than nickels, and 4 more quarters than dimes. How many nickels does she have?
A. 5 nickels
B. 8 dimes
C. 8 nickels
D. 5 dimes
E. none of these
25.
2x  3y >  6
Graph the inequality:
5
A.
5
B.
4
-5
-4
-3
-2
4
27.
3
2
2
2
2
1
1
1
1
-1
1
-5
-4
-3
-2
-1
b3
a3
30.
]
(
]
(
31.
A.
3
2x
12
32.
B.
B.
Find the product:
A. 5 x  5 x  6
2
C. x  4 x  4
2
B.
-5
-8
E.
[
1
-5
-4
-3
-2
-1
1
-1
D. a b
27 18
E. none of these
D. x  4 x  4
E. none of these
2
)
-5
C
[
D.
-8
B. 4
Factor completely:
10a  14a  3
a3
b3
8
Add and simplify:
A.
-1
 5  5x  7 < 10
Solve the proportion for y :
A.
-2
-1
C.
2
5
29.
-3
 x  2 2
Graph the solution of:
D.
-4
(Write answer without using parentheses or negative exponents.)
B. x  4
2
-8
-5
3
b18
a 27
B.
A. x  4
A.
1
-1
E. none of these
4
3
Find the product:
28.
4
3
 a 4 b 3 
Simplify:  5 3 
a b 
A.
5
D.
3
-1
26.
5
C.
[
5
)
8
None of these.
-5
3y  2
y

7
28
8
C.
11
D.
11
8
E. none of these
D.
7x  1
12
E. none of these
x 1 x 1

3
4
x
6
C.
2x
7
10a 2  16a  42
5a  72a  6
C.
25a  7a  3
D.
25a  7a  3
E. none of these
2x  33x  2
B. 5 x  13 x  5
2
C. 6 x  5 x  6
2
D. 6 x  5 x  6
2
E. none of these
33.
A.
a  2ba  b
34.
If
35.
a  2ba  b
B.
B. –3
36.
2 x  52
Simplify:
A. 25x
37.
D.
a  ba  2b
E. none of these
C. –19
D. 19
E. none of these
E. none of these
4 x 2  25
Factor completely:
A.
a  2ba  b
C.
P( x)  2 x 2  6 x  1, find P (2).
A. 21
2 x  52
B.
C.
2x  52x  5
D. does not factor
C.
x2
25
D. 
(5 x) 2
2
5
x2
B.
1
25 x 2
E. none of these
The length of a rectangle is three times its width. The perimeter of the rectangle is
120 feet. Find its area.
A.
38.
A.
a 2  3ab  2b 2
Factor completely:
225 sq. ft.
B.
Factor completely:


y 2 x 2 z  2 xz  3
E. none of these
B.
675 sq. ft.
C.
15 ft.
D.
45 ft.
E. none of these
2 x 2 y 2 z  4 xy2 z  6 y 2

2 y x 2 yz  2 xyz  3 y

C.

2 x 2 y 2 z  2 xy 2 z  3 y 2

D.


2 y 2 x 2 z  2 xz  3
ELEMENTARY ALGEBRA PRACTICE FINAL
SOLUTIONS
1)
E,  1
12)
2)
C
13)
3)
D
14)
4)
A
5)
D
23)
A
34)
B
24)
A
35)
C
D
25)
D
36)
E
15)
C
26)
B
37)
B
A
16)
C
27)
C
38)
D
6)
C
17)
C
28)
B
7)
B
18)
A
29)
C
8)
A
19)
E,
30)
D
9)
D
20)
C
31)
D
10)
D
21)
A
32)
C
11)
C
22)
B
33)
B
B
2