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ELEMENTARY ALGEBRA PRACTICE FINAL EXAM
(Revised 09/2013)
1.
Simplify: 5  2  3  2 3  2  3
2.
Evaluate:
3.
Simplify:
4.
The number of employees increased from 134 to 189. Find the percent increase to the nearest
tenth of a percent.
5.
Macy’s advertised a 20%-off sale. If a pair of boots originally sold for $119, find the decrease
in price and the sale price.
6.
242 is what percent of 550?
2
y
 z for x = 4, y = 32, and z = 1.
4x
4  3  2  5
22   5  2 
2
7 – 12. Solve.
7.
10.
13.
3  2( x  5)  3 x
8.
1
1 1
1
d   d  d
11.
18
36 6
6
5
Solve for A in B   A  11
6
4
y6  2
7
7
2

3x  4 x  2
9.
2  3x  3  5x  4  x  2  5x
12.
x3 4
17 x
  x 
2
3
6 2
14.
In an election between two candidates, 660 votes were cast. If the winner received 170 more votes
than the loser, how many votes did the loser receive?
15.
When a number is increased by 25, the result is 23. Find the number.
16.
The directions for a certain bug spray concentrate is to mix 3 ounces of concentrate with 2 gallons of water.
How many ounces of concentrate are needed to mix with 5 gallons of water?
17 – 19. Solve. Express solutions in interval notation.
17.
18.
4  7  x  2  3
8  2x 10  10
19.
4 x  3  2  x 1
20.
The length of a rectangle is 3 feet more than twice the width. Find the width if the perimeter is 30 ft.
21.
Find two consecutive odd integers whose sum is 168.
22.
Graph using the slope and y-intercept.
23 - 26. Graph
7 x  4 y  28
23.
24.
y
2
x 1
3
3x  6  0
25.
27.
What are the x - and y-intercepts of the line: 3 x  y  3 ?
28.
Give the slope of the line that contains  6,9  and  6, 6  .
y2
26.
2x  y  6
29.
What is the slope and y-intercept of the line 8 x  2 y  48 ?
30.
Determine the slope of the line graphed below.
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
1 2 3 4 5 6
-2
-3
-4
-5
-6
31.
Find the slope-intercept form of the equation of the line that passes through the points  2, 4  and  4, 7  .
32.
Write the standard form of the equation of the line with slope 0 passing through (– 4 , – 1)
33.
Find the slope-intercept form of the equation of the line that passes through the points (3, – 4) and
parallel to the line y  6 x  2.
34.
Which ordered pair(s) are solutions of the equation 5 x  y  11 ?
A.
(4, – 4)
B.
(– 4, 4)
C.
(3, – 4)
D.
(– 4,3)
35.
If f  x   3x  7 find f  2  and write as an ordered pair.
36.
Solve the system of linear equations by graphing
37.
Solve the system of linear equations by substitution
38.
Solve the system of linear equations by addition
39.
Solve the system of linear equations.
40.
The Forrest Theater can seat a total of 360 people. They take in $15,150 when every seat is sold. If
orchestra section tickets cost $45 and balcony tickets cost $35, find the number of seats in the orchestra
section and the number of seats in the balcony.
41 - 52. Simplify.
41.
40
44.
47.
 1
 
 5
8x4 y3
6 xy 3
x y 3
y  2 x  2
x  3 y  5
5 x  6 y  1
2 x  5 y  1
3 x  4 y  33
x  2 y  3
3 x  6 y  9
42.
32
43.
2 3
45.
41  32
46.
50  31
48.
 3x y  6 x y 
49.
 4a b 
2
4
2
3
5
3 4 2
3
50.
52.
 4a 3 
51.

4 
 10b 
3x 2  x 2  2 xy  y 2   5 xy  x 2  xy 
53 – 55. Multiply.
53.
 2x  7 5x  8
56 – 62. Factor Completely.
4 x 6  64 x 4
56.
59.
x 2  26 xy  48 y 2
62.
64h3  125
63 – 66. Solve.
x 2  3x  10  0
63.
 3x y 
2
4 3
18 xy 2
54.
 4 x  2   x 2  3x  2 
55.
 4x  2 y 
57.
10 x 2  17 x  6
58.
3x 3  9 x 2  7 x  21
60.
25 x 2  9 y 2
61.
25x 2  90 xy  81y 2
64.
x2  6x  0
65.
4 x2  x  5
2
66.
3x 2  7 x  4  0
67.
The length of a rectangle is 3 feet less than twice the width. If the area is 65 ft², find the dimensions.
68.
Divide:
69.
Write in standard notation.
70.
Write in scientific notation: 6,900,000
71.
A woman walked to a lake at the rate of 3 mph and returned via a different path 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?
72.
A trail mix worth $3.50 per pound is to be made by combining 20 pounds of peanuts worth $3 per pound
with raisins worth $5 per pound. How many pounds of raisins should be used?
6 x3 y 2  5 x5 y3  10 x3 y
10 x3 y
2.45 105
SOLUTIONS
1.
17
2.
1
4.
41.0%
5.
$23.80 decrease,
$95.20 sale price
7.
10.
13.
16.
x  13
1
d 
4
6 B  55
A
5
7.5 ounces
3.
6.
5
13
44%
8.
y  14
9.
No solution
11.
x  22
12.
All real numbers
14.
245 votes
15.
–2
17.
10, 1
18.
15 

 , 
7

19.
1

 , 
2

20.
22.
4 ft
21.
23.
3
2
1
-4
-3
-2
-1
1
2
3
4
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-2
-3
-4
26.
4
-3
-2
1
1
-4 -3 -2 -1
-1
1
2
3
-5
-6
-7
29.
m  4 ,  0, 24 
32.
y  1
C
35.
f  2   1 ,  2, 1
 3,  8 


 3
38.
 7, 3
Undefined
30.
3
31.
y
33.
y  6 x  22
34.
36.
 1, 4 
37.
Infinite solutions
 x, y  |  x  2 y  3
1
9
5
36
-8
40.
46.
18x 7 y 7
3x5 y10
2
3
4 x  14 x 2  14 x  4
3
x 1
2
255 orchestra tickets
105 balcony tickets
43.
1
8
2
3
53.
10 x 2  51x  56
55.
16 x 2  16 xy  4 y 2
56.
4 x4  x  4 x  4
67.
6
69.
0.0000245
70.
72.
6
x
4 x3
3
8a 9
125b12
3x 4  11x3 y  2 x 2 y 2
4
,1
3
66.
47.
25
52.
x  0,  6
x  2, 5
44.
50.
64.
63.
1
16a 6b8
61.
60.
41.
49.
 x  3  3 x 2  7 
2
5x  9 y 
10x  3 x  2
5x  3 y 5x  3 y 
2
pounds
3
-4
-6
28.
57.
-3
-5
 1, 0  , (0, 3)
54.
1 2 3 4 5 6
1 2 3 4 5 6 7 8
27.
51.
1 2 3 4 5 6
-4
-4
48.
1
-6 -5 -4 -3 -2 -1
-1
-3
-3
45.
2
-2
4
-2
42.
3
2
-1
39.
4
3
2
-1
5
4
3
-4
6
-2
-1
25.
24.
8
7
6
5
4
3
2
1
4
83, 85
58.
1
ft by 10 ft
2
6.9 106
59.
62.
65.
68.
71.
 x  24 y  x  2 y 
 4h  5 16h2  20h  25
5
4
2 2
3y x y

1
5
2
x  1,
3 hours