23
CHAPTER 1, FORM A
COLLEGE ALGEBRA
NAME _____
DATE
Solve each equation.
1.
5 4( 1) 2 2( 4)x x x+ − = + +
1. _______________________
2.
29
2
4 12
xx−=+
2. _____________________
3.
2
48 12 90xx+=
3. _____________________
4.
2
3 2( 1)xx=−
4. _____________________
5.
2
3 1 4
2 2 4
x
x x x
−
+=
− + −
5. _____________________
6.
3 2 3xx+ + − =
6. _____________________
7.
13xx− + =
7. _____________________
8.
42
13 36 0xx− + =
8. _____________________
9.
( )
1/ 3
2/3
( 5) 3 5 4 0xx− + − − =
9. _____________________
10.
1 8 8x− + =
10. _____________________
11.
3 2 3xx− = +
11. _____________________
12. The formula for the surface area of an open topped rectangular box is 12. _____________________
22S LW LH WH= + +
where
,,S H W
and
L
represent surface area,
height, width, and length, respectively. Solve this formula for
.W
Perform each operation. Give the answer in standard form.
13.
(1 3 )(2 5 )ii−+
13. _____________________
14.
( ) ( ) ( )
8 2 1 6 3 2i i i+ + − − −
14. _____________________
15.
2
75
i
i
+
−
15. _____________________
24
CHAPTER 1, FORM A
16. Simplify the following power of
i
:
73
i
16. _____________________
Solve each inequality. Give the answer using interval notation.
17.
245xx+
17. _____________________
18.
1
0 4 2
3x −
18. _____________________
19.
4
31
73
xx−
− +
19. _____________________
20.
2 1 3x−
20. _____________________
21.
4 2 6x−
21. _____________________
Solve each problem.
22. Bob Grey invests $22,000, some at 2% and some at 4%. 22. _____________________
annual interest. If he receives an annual return of $670,
how much is invested at each rate?
23. Jack can paint his apartment in 12 hr. His wife Cheryl 23. _____________________
requires 20 hr to do the same job. How long would it take
them to complete the job if they worked together?
24. A baseball is thrown straight upward with an initial speed 24. _____________________
of 64 ft/sec. The number of feet s above the ground after
t seconds is given by the equation
2
16 64 .x t t= − +
At what times will the baseball be 48 ft above the ground?
25. The number y of students attending Nequa Valley High School 25. _____________________
between 1988 and 1996 can be approximated by the model
2
45.28 37.6 585,y x x= − +
where
0x=
corresponds to 1988. Based on this model, in what
year did the school have about 1550 students?
25
CHAPTER 1, FORM B
COLLEGE ALGEBRA
NAME
DATE
Solve each equation.
1.
33
22
52
xx−=+
1. _____________________
2.
2 ( 3) 1xx+ = −
2. _____________________
3.
23
( 4) 4
75
x x x− − = − −
3. _____________________
4.
2
( 3) 4x− = −
4. _____________________
5.
2 3 5
5 2 1 6 3x x x
−=
+ + +
5. _____________________
6.
42
34xx−=
6. _____________________
7.
2
3
31 2 21x x x− = + −
7. _____________________
8.
4 2 2xx+ + =
8. _____________________
9.
2 3 8xx− = +
9. _____________________
10.
34xx−=
10. _____________________
11.
( ) ( )
2/3 1/3
2 2 2 8 0xx− + − − =
11. _____________________
12.
2215 0
22
xx
xx
− − =
−−
12. _____________________
Perform each operation. Give the answer in standard form.
13.
( ) ( ) ( )
7 3 4 1i i i− − + + − − +
13. _____________________
14.
( ) ( )
4 2 5 4ii+ − +
14. _____________________
26
CHAPTER 1, FORM B
15.
45
23
i
i
−
+
15. _____________________
16. Simplify the following power of
i
:
94
i
16. _____________________
Solve each inequality. Give the answer using interval notation.
17.
2
6 5 1xx− −
17. _____________________
18.
723
xx
x+ −
18. _____________________
19.
30
2x
−
−
19. _____________________
20.
2 5 4x+
20. _____________________
21.
2 1 3x−
21. _____________________
Solve each problem.
22. What weight of an alloy containing 10% silver must be melted with an 22. _____________________
alloy containing 60% silver to obtain 10 lb of an alloy containing 40%
silver?
23. The cost of installing insulation in a particular two bedroom home 23. _____________________
is $2400. Present monthly heating costs average $200, but the
insulation is expected to reduce heating costs by 10%. How many
months will it take to recover the cost of the insulation?
24. The population y of Stevensville between 1986 and 1995 can 24. _____________________
be approximated by the model
2
326.5 780.3 5670,y x x= − +
where
0x=
corresponds to 1986. Based on this model, in what
year was the population about 6250?
25. A ball is thrown upward from ground level with an initial 25. _____________________
velocity of 108 ft per sec. Its height h in feet after t seconds
is given by the equation
2
16 108 .h t t= − +
At what times will the ball be 180 ft above the ground?
27
CHAPTER 1, FORM C
COLLEGE ALGEBRA
NAME
DATE
Solve each equation.
1.
4 3 5 6xx− = − +
1. _____________________
2.
2 4 7
5 10 5 2 1xx
+=
++
2. _____________________
3.
( )
2
4 1 9 0x− + =
3. _____________________
4.
( )
2
2 48 1x+ − =
4. _____________________
5.
4 1 4 2 2
4 6 5
x x x+−
− = −
5. _____________________
6.
2 3 2xx+ − =
6. _____________________
7.
2
312x−=
7. _____________________
8.
42
6 7 2xx− = −
8. _____________________
9.
( ) ( )
2
3 2 1 11 2 1 10 0zz− − − + =
9. _____________________
10.
4 3 8xx+ = −
10. _____________________
11.
7 3 11x+=
11. _____________________
12. Solve the following equation for x:
2 2 5ax by az bx+=−
12. _____________________
Perform each operation. Give the answer in standard form.
13.
( ) ( ) ( )
4 2 16 8 13 2i i i− + − + + −
13. _____________________
14.
( ) ( )
3 5 2 7ii+−
14. _____________________
15.
42
5
i
i
−
−
15. _____________________
16. Simplify the following power of
i
:
68
i
16. _____________________
28
CHAPTER 1, FORM C
Solve each inequality. Give the answer using interval notation.
17.
25 4 0xx− +
17. _____________________
18.
( )
3 4 5 51
2
xx
−+
18. _____________________
19.
4
21
x
x−
+
19. _____________________
20.
7 3 2x−
20. _____________________
21.
25
1
3
x+
21. _____________________
Solve each problem.
22. How many pounds of extra-lean hamburger that is 7% fat 22. _____________________
must be mixed with 30 pounds of hamburger that is 15% fat
to obtain a mixture that is 10% fat?
23. A workman’s basic hourly wage is $24, but he receives one 23. _____________________
and a half times his hourly rate for any hours worked in
excess of 40 hours per week. If his paycheck for the week
is $1392, how many hours of overtime did he work?
24. A ball is thrown upward from ground level with an initial 24. _____________________
velocity of 108 ft per sec. Its height h in feet after t seconds
is given by the equation
2
16 108 .h t t= − +
At what time will the ball hit the ground?
25. The number y of visitors to Dragon Lake State park between 25. _____________________
1984 and 1992 can be approximated by the model
2
172.35 303.4 6972,y x x= − +
where
0x=
corresponds to 1984. Based on this model, in what
year did the park have about 8500 visitors?
29
CHAPTER 1, FORM D
COLLEGE ALGEBRA
NAME
DATE
Solve each equation.
1.
( ) ( )
52
8 6 2 10
63
x x x+ − + = +
1. _____________________
2.
( ) ( ) ( ) ( )
2 3 3 4x x x x− − = + +
2. _____________________
3.
( )
2
5 3 49x− = −
3. _____________________
4.
1
53
5
xx
+=
4. _____________________
5.
2
7 6 3
2 4 2 4x x x
−=
− − +
5. _____________________
6.
7 2 6xx+ = −
6. _____________________
7.
3
371xx− + =
7. _____________________
8.
4256x=
8. _____________________
9.
()()
2
22
4 36 9 4x x x x− − = −
9. _____________________
10.
7 5 12x− = −
10. _____________________
11.
2 3 3 5xx− = −
11. _____________________
12. Solve the following equation for C:
2C
PN C
+
+=
12. _____________________
Perform each operation. Give the answer in standard form.
13.
( ) ( )
3 4 2 7ii++
13. _____________________
14.
( ) ( ) ( )
5 3 2 4 3 8i i i+ + − − −
14. _____________________
15.
2 16
31
−−
+−
15. _____________________
30
CHAPTER 1, FORM D
16. Simplify the following power of
i
:
55
i=
16. _____________________
Solve each inequality. Give the answer using interval notation.
17.
256xx− −
17. _____________________
18.
( ) ( )
3 2 2 5xx− +
18. _____________________
19.
41
1x
+
19. _____________________
20.
1 2 4x −
20. _____________________
21.
3 9 10x−
21. _____________________
Solve each problem.
22. How many gallons of a cream that is 22% butterfat must be 22. _____________________
mixed with milk that is 2% butterfat to get 20 gallons
of milk containing 4% butterfat?
23. Jay invested $28,500 in two accounts, one paying 23. _____________________
2.5% simple interest, and the other paying 3.5%. She
received $877.50 in interest for 1 yr. How much did she
invest each time?
24. An arrow is shot upward from a platform 40 ft high with an 24. _____________________
initial velocity of 224 ft per sec. Its height h in feet after
t seconds is given by the equation
2
16 224 40.h t t= − + +
At what times will the arrow be 424 ft above the ground?
25. The number y of students enrolled in Fox Grove Community 25. _____________________
College between 1983 and 1990 can be approximated by the
model
2
36.28 98.61 8605,y x x= − +
where
0x=
corresponds to 1983. Based on this model, in
what year did the college have about 8800 students?
31
CHAPTER 1, FORM E
COLLEGE ALGEBRA
NAME
DATE
Choose the best answer.
Solve each equation.
1.
( ) ( ) ( ) ( )
2 1 1 3 4 5 1 2 6 1x x x x− + = − + − + +
1. _____________________
a.
b.
0
c.
1
d.
2
2.
( )
3 2 6 1 5 3x x x− − + + = − −
2. _____________________
a.
7
3
b.
11
8
−
c.
7
8
−
d.
11
3
3.
1
53
5
xx
+=
3. _____________________
a.
4 10
12
−
b.
4 10
6
−
c.
4 22
6
−
d.
8 10
6
−
4.
24 5 0xx+ − =
4. _____________________
a.
5, 5−
b.
5,1−
c.
1,5−
d.
5,0−
5.
97
4 8 2
xx
x− = −
5. _____________________
a.
28
11
b.
28
9
c.
28
11
−
d.
28
9
−
6.
22
33
3 3 2x x x− = −
6. _____________________
a.
2−
b.
3
c.
1
2, 2
−
d.
7.
14 7 3xx− = +
7. _____________________
a.
2
b.
4−
c.
4
d.
3−
32
CHAPTER 1, FORM E
8.
42
34xx+=
8. _____________________
a.
3, i
b.
1, 3i
c.
1, 3
d.
1, 3
9.
2/ 3 1/3 60xx− − =
9. _____________________
a.
8, 27−
b.
8, 27−
c.
8, 27
d.
8, 27−−
10.
3 3 18x− − =
10. _____________________
a.
3,9−
b.
3
c.
9,3−
d.
11.
3 1 2xx− = −
11. _____________________
a.
b.
2−
c.
1
3, 2
d.
4
2, 3
−
12. Solve the following equation for x:
4 2 2 5ax by cx− = +
12. _____________________
a.
25
42
c
xa by
+
=−
b.
25
42
by
xac
+
=−
c.
42
25
ac
xby
−
=+
d.
25
42
c
xa by
+
=−
Perform each operation. Give the answer in standard form.
13.
( ) ( ) ( )
4 2 6 8 13 2i i i− + + + − −
13. _____________________
a.
11 8i−+
b.
11 12i−+
c.
15 8i−+
d.
15 12i−+
14.
( ) ( )
8 5 9 8ii−+
14. _____________________
a.
2
40 19 72ii− + −
b.
112 19i+
c.
112 19i−
d.
32 109i−
15.
63
58
i
i
−
+
15. _____________________
a.
54 33
89 89 i−
b.
18 21
13 13 i−−
c.
6 63
89 89 i−
d.
2 21
13 13 i−−
33
CHAPTER 1, FORM E
16. Simplify the following power of i:
37
i
16. _____________________
a.
i
b.
1−
c.
i−
d.
1
Solve each inequality. Give the answer using interval notation.
17.
3
2( 2) 1
4
xx+ −
17. _____________________
a.
(
,4−• −
b.
()
4,−•
c.
)
4,−•
d.
(
,4−•
18.
14 3 5 23x +
18. _____________________
a.
6, 3−−
b.
()
6, 3−−
c.
()
3,6
d.
3,6
19.
2 1 5
33
x−
19. _____________________
a.
()
2,3−
b.
()
3, 2−−
c.
()
3, 2−
d.
2,3−
20.
5
2
x
x
−
20. _____________________
a.
5
2, 2
b.
5
2, 2
c.
5
2, 2
d.
5
2, 2
21.
5 3 7x−
21. _____________________
a.
4,2
5
−
b.
()
2,
c.
)
4
, 2,
5
− −
d.
()
)
, 2 7,− −
Solve each problem.
22. A 60% alcohol solution is to be mixed with a 42% alcohol solution. 22. _____________________
How many liters of the 60% solution should be used to make 30 liters
of a 54% alcohol solution?
a.
15
b.
18
c.
20
d.
10
23. Two cars leave at the same point at the same time traveling in opposite 23. _____________________
directions. One travels 8 mph slower than the other. After 4 hr, they
are 368 mi apart. Find the speed of the faster car.
a.
42 mph
b.
50 mph
c.
60 mph
d.
68 mph
34
CHAPTER 1, FORM E
24. The number y of people attending the Ozark Mountain Bluegrass 24. _____________________
Festival between 1989 and 1996 can be approximated by the model
2
69.75 328.7 1283,y x x= − +
where
0x=
corresponds to 1989. Based
on this model, in what year was the festival attendance about 1800?
a.
1999
b.
1991
c.
1995
d.
1993
25. The height in feet of an object thrown upward is given by the equation 25. _____________________
2
80 16 ,h t t=−
where h is the height of the object after t seconds. After
how many seconds will the object reach a height of 100 feet?
a.
1
12
sec b.
2
sec c.
1
22
sec d. sec
35
CHAPTER 1, FORM F
COLLEGE ALGEBRA
NAME
DATE
Choose the best answer.
Solve each equation.
1.
( ) ( ) ( )
2 2 3 2 5 4 5 7 2 1x x x+ + + = + −
1. _____________________
a.
b.
3
4
−
c.
3
2
−
d.
5
4
2.
( )
2 3 1 3
27
3 2 2 4
x x x+ − = −
2. _____________________
a.
2−
b.
1
c.
5
4
d.
0
3.
( )
3 4 2 9x x x− = −
3. _____________________
a.
5 2 2
3
b.
522
33
i
c.
7 22
3
d.
7122
33
i
4.
2
2 1 1
36 6 6x x x
−=
− − +
4. _____________________
a.
1−
b.
12
5
−
c.
1
d.
3
2
5.
2
15 8xx=
5. _____________________
a.
0
b.
88
,
15 15
−
c.
8
0, 15
d.
8,0
15
−
6.
3 2 4xx− − =
6. _____________________
a.
2,9
b.
9
c.
1−
d.
1, 2
7.
22
33
4 3 10x x x+ = +
7. _____________________
a.
0, 10−
b.
1,3
3
−−
c.
13
2i
d.
1,3
3
36
CHAPTER 1, FORM F
8.
42
45xx+=
8. _____________________
a.
1, 2
b.
1, 2
c.
,2ii
d.
1, 2i
9.
( ) ( )
2
3 1 3 1 72xx− + − =
9. _____________________
a.
9, 8−
b.
9,8−
c.
7 10
,
33
−
d.
8,3
3
−
10.
3 9 0x+=
10. _____________________
a.
3,3−
b.
c.
3−
d.
3
11.
3 1 4 7x+ − = −
11. _____________________
a.
4
3
−
b.
24
,
33
c.
42
,
33
−−
d.
12. Solve the following equation for x:
4 3 4 2ax by cx dz− + = +
12. _____________________
a.
2
4 3 4
c dz
xa by
+
=−+
b.
42
34
ac
xby dz
−
=+−
c.
4 3 4
2
a by
xc dz
−+
=+
d.
34
42
by dz
xac
+−
=−
Perform each operation. Give the answer in standard form.
13.
( ) ( ) ( )
5 3 2 4 3 8i i i+ − − − −
13. _____________________
a.
9i
b.
67i+
c.
15i
d.
6 15i+
14.
( ) ( )
10 2 10 2ii+−
14. _____________________
a.
10 4i−
b.
10 4i+
c.
14
d.
8
15.
62
47
i
i
+
+
15. _____________________
a.
10 34
33 33 i−+
b.
38 34
33 33 i−+
c.
38 34
65 65 i−
d.
2 10
13 13 i−
37
CHAPTER 1, FORM F
16. Simplify the following power of i:
65
i
16. _____________________
a.
i
b.
1−
c.
i−
d.
1
Solve each inequality. Give the answer using interval notation.
17.
9 8 64
89
x+
17. _____________________
a.
440 ,
81
b.
64 ,
9
c.
440
,81
−
d.
64
,9
−
18.
34
0
21
x
x
+
−
18. _____________________
a.
41
,,
32
− −
b.
41
,
32
−
c.
41
,
32
−
d.
41
,
32
−
19.
2
4 20 11xx+
19. _____________________
a.
()
5
, 4,
4
− −
b.
5,4
4
−
c.
5
4, 4
−
d.
()
5
, 4 ,
4
− −
20.
6 9 12x+ −
20. _____________________
a.
()()
, 23 7,− − −
b.
()()
, 27 15,− −
c.
()()
, 7 23,− −
d.
()
23,11−
21.
3 2 19x−
21. _____________________
a.
8,11−
b.
()
8,11−
c.
( )
,8− −
d.
( )
11,
Solve each problem.
22. Two runners, Alma and Kim, leave home at the same time and jog 22. _____________________
in different directions. Alma travels east at a uniform rate that is 2 mph
faster than Kim, who is traveling west. After 2 hr, they are 28 mi apart.
Find Alma’s rate.
a. 4 mph b. 6 mph c. 8 mph d. 10 mph
38
CHAPTER 1, FORM F
23. Mona can process 100 requests in 4 hr, and Jane can process 100 23. _____________________
requests in twice the time. How long will it take both Mona and
Jane, working together, to process 200 requests?
a.
2
23
hr b. 6 hr c.
2
33
hr d.
1
53
hr
24. The number y of fish in Silver Lake between 2000 and 2015 can be 24. _____________________
approximated by the model
2
( ) 1000(30 17 )f x x x= + −
where x corresponds to the year 2000. Based on this model, in what
year was the fish population about 100,000?
a. 2005 b. 2007 c. 2010 d. 2012
25. The height in feet of an object thrown upward is given by the equation 25. _____________________
where h is the height of the object after t seconds. After
how many seconds will the object reach a height of 36 feet?
a.
1
12
sec b.
1
22
sec c. 2 sec d. 5 sec
39
CHAPTER 1, FORM A
40
CHAPTER 1, FORM B
41
CHAPTER 1, FORM C
42
43
CHAPTER 1, FORM D
44
CHAPTER 1, FORM E
45
CHAPTER 1, FORM F