Name: __________________
Class:
Date: _____________
1 x represents a real number. Find any restrictions on x.
x+8=5
2 x represents a real number. Find any restrictions on x.
5
x 6
3 x represents a real number. Find any restrictions on x.
x = 8
4 Solve the equation
3x + 2 = 20
5 Solve the equation.
3x + 13 = x + 7
6 Solve the equation.
x 4 = 1
3
7 Solve the equation
4
= 1
x 4
PAGE 1
Name: __________________
Class:
8 Solve the equation.
6 (4x + 2) 22 (x + 2) = 28
9 Solve the equation.
x(x 4) 5 = (x 1)
2
10 Solve the equation
2
9x
3x + 2 ( 6x + 3 ) =
3x + 5
3x + 5
11 Solve the equation
15 +
6
= 18 y + 4
y + 2
y + 2
12 Solve the equation
2x 2 + 2x 4 = 2 4x
x + 3
x 3
3 x
13 Solve the formula for the t.
f = 10t
14 Solve the formula for the w.
p = 7m+8w
15 Solve the formula for the x.
f = m x
v
PAGE 2
3
y
2
+ 6y + 8
Date: _____________
Name: __________________
Class:
Date: _____________
16 Solve the formula for the r.
1 = 1 + 1
r
n
j
17 Juan scored 7 points higher on his midterm and 5 points higher on his final than he did on his first exam. If his mean (average) score was 126,
what was his score on the first exam?
18 A college student earns $40 per day delivering advertising brochures door to door, plus 25 cents for each person he interviews. How many
people did he interview on a day when he earned $52?
19 The area of the triangular swimming pool shown in illustration is doubled by adding a rectangular wading pool. Find the width of the pool (x).
(The area of a triangle =
a = 25 ; b = 22
PAGE 3
1 bh , and the area of a rectangle = lw).
2
Name: __________________
Class:
Date: _____________
20 The trough in illustration has a cross sectional area of 108 square inches. Find the depth, h ,of the trough.
(Area of a trapezoid
1 h(a + b))
2
a = 18; b = 9
21 An executive invests $39000, some at 10% and some at 7% annual interest. If he receives an annual return of $3330, how much is invested at
each rate?
22 A full price ticket for a college basketball game costs $4, and a student ticket costs $2.25. If 593 tickets were sold, and the total receipts were
$1838.25 , how many tickets were student tickets?
23 Of the 649 tickets sold to a movie, 352 were full price tickets costing $5.00 each. If the gate receipts were $2799.50 , what did a student ticket
cost?
24 After being discounted 10%, a radio sells for $127.80. Find the original price.
25 A merchant increases the wholesale cost of a washing machine by 20% to determine the selling price. If the washer sells for $416.40, find the
wholesale cost.
26 A computer store has fixed costs of $8625 per month and a unit cost of $760 for every computer it sells. If the store can sell all the computers it
can get for $1335 each, how many must be sold for the store to break even? (The break even point occurs when costs equal income.)
27 An empty swimming pool can be filled in 10 hours. When full, the pool can be drained in 29 hours. How long will it take to fill the empty pool
if the drain is left open?
PAGE 4
Name: __________________
Class:
Date: _____________
28 The nurse has 0.65 liters of a solution that is 10% alcohol. How much pure alcohol must she add to bring the solution up to a 70%
concentration?
29 A swimming pool contains 38000 gallons of water. How many gallons of chlorine must be added to "shock the pool" and bring the water to a
31 % solution?
100
30 John drove to a distant city in 6 hours. When he returned, there was less traffic, and the trip took only 4 hours. If John averaged 38 mph faster
on the return trip, how fast did he drive each way?
31 Two cars leave Pima Community College traveling in opposite directions. One car travels at 88 mph and the other at 63 mph. In how many
hours will they be 1057 miles apart?
32 Some bank robbers leave town,speeding at 84 mph. 25 minutes later, the police give chase, traveling at 94 mph. How long (in hours) will it take
the police to overtake the robbers?
33 One morning, John drove 10 hours before stopping to eat. After lunch, he increased his speed by 10 mph. If he completed a 680 mile trip in 13
hours of driving time, how fast did he drive in the morning?
34 A plane can fly 410 mph in still air. If it can fly 460 miles downwind in the same amount of time it can fly 360 miles upwind, find the velocity
of the wind.
PAGE 5
Name: __________________
Class:
Date: _____________
35 530.14 cubic millimeters of material was removed by drilling the blind hole shown in illustration. Find the depth of the hole.
(The volume of a cylinder is given by V = r
2
h)
a=5
36 The Norman window with dimensions as shown in illustration is a rectangle topped by a semicircle. If the area of the window is 26.28 square
feet, find its height h.
a=4
PAGE 6
Name: __________________
Class:
37 Solve the equation
x
2
+ 4x 32 = 0
by factoring. Check all answers.
38 Solve the equation
x
2
+ 3x = 0
by factoring. Check all answers.
39 Solve the equation
4x
2
12x = 8
by factoring. Check all answers.
40 Use the square root property to solve the equation
( y + 16 )
2
25 = 0
You may need to factor an expression.
PAGE 7
Date: _____________
Name: __________________
Class:
41 Use the square root property to solve the equation
x
2
10x + 25 = 16
You may need to factor an expression.
42 Complete the square to make the binomial a perfect square trinomial.
2
36x
24x
43 Solve the equation
x
2
2x 63 = 0
by completing the square.
44 Solve the equation
x
2
+ 16x + 28 = 0
by completing the square.
45 Solve the equation by completing the square.
x
2
+ 2x = 11
PAGE 8
Date: _____________
Name: __________________
Class:
46 Use the quadratic formula to solve the equation.
x
2
8 = 0
47 Use the quadratic formula to solve the equation.
2x
2
12x 54 = 0
48 Use the quadratic formula to solve the equation.
7x
2
+ 63x + 126 = 0
49 Use the quadratic formula to solve each equation.
4x ( x + 5 ) = 4
50 Solve the formula
x
h
2
2
2
+ y = 1 ; y
2
f
for the indicated variable.
51 Does the equation
1.929x
2
+ 2.367x + 6.822 = 0
have any roots that are real numbers?
PAGE 9
Date: _____________
Name: __________________
Class:
Date: _____________
52 Change the equation
x + 1 = 30
x
to quadratic form and solve it by any method.
53 Change the equation
5
3x + 10 + 5x + 9 =
3x 10
3x 10
to quadratic form and solve it by any method.
54 A rectangle is 3 feet longer than it is wide. If its area is 54 square feet, find its dimensions.
55 A rectangle is 4 times as long as it is wide. If the area is 64 square feet, find its perimeter.
56 The side of a square is 5 centimeters shorter than the side of a second square. If the sum of their areas is 193 square centimeters, find the length
of one side of the larger square.
57 A piece of tin, y = 12 inches on a side, is to have four equal squares cut from its corners, as in illustration. If the edges are then to be folded up
to make a box with a floor area of 16 square inches, find the depth of the box.
PAGE 10
Name: __________________
Class:
Date: _____________
58 A piece of sheet metal, 14 inches wide, is bent to form the gutter shown in illustration. If the cross sectional area is 24 square inches, find the
depth of the gutter.
59 A cyclist rides from DeKalb to Rockford, a distance of 200 miles. His return trip takes 1 hours longer, because his speed decreases by 10 miles
per hour. How fast does he ride each way?
60 A farmer drives a tractor from one town to another, a distance of 60 kilometers. He drives 10 kilometers per hour faster on the return trip,
cutting 1 hour off the time. How fast does he drive each way?
61 If the speed were increased by 60 mph, a 70 mile trip would take 6 hour less time. How long will the trip take at the slower speed?
62 The height of a projectile fired upward with an initial velocity of 80 feet per second is given by the formula
2
h = 4t + 80t
where h is the height in feet and t is the time in seconds. Find the time required for the projectile to return to earth.
63 A bus company has 3500 passengers daily, paying a 25 cents fare. For each nickel increase in fare, the company projects that it will lose 60
passengers. What fare increase will produce $1467.00 in daily revenue?
64 A jazz group on tour has been drawing average crowds of 700 persons. It is projected that for every $1 increase in the $18 ticket price, the
average attendance will decrease by 50. At what ticket price will nightly receipts be $11550?
PAGE 11
Name: __________________
Class:
Date: _____________
65 A golden rectangle is said to be one of the most visually appealing of all geometric forms. The front of the Parthenon, built in Athens in the 5th
century B.C. and shown in illustration, is a golden rectangle. In a golden rectangle, the length l and the width w of the rectangle must satisfy the
equation
l =
h
h
l h
If a rectangular billboard is to have a height of 18 feet, how long should it be if it is to form a golden rectangle? Round to the nearest tenth of a
foot.
66 Two pipes are used to fill a water storage tank. The first pipe can fill the tank in 3 hours, and the two pipes together can fill the tank in 4 hours
less time than the second pipe alone. How long would it take for the second pipe to fill the tank?
67 A hose can fill a swimming pool in 18 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it
take the second hose to fill the pool?
68 Working together, Sarah and Heidi can milk the cows in 4 hours. If they work alone, it takes Heidi 6 hours longer than it takes Sarah. How long
would it take Heidi to milk the cows alone?
69 If two opposite sides of a square are increased by 4 meters and the other sides are decreased by 2 meters, the area of the rectangle that is formed
is 7 square meters. Find the area of the original square.
70 Maude and Matilda each have a bank CD. Maude's is $1500 larger than Matilda's, but the interest rate is 4% less. Last year Maude received
interest of $780, and Matilda received $800. Find the rate of interest for each CD.
71 Some mathematics professors would like to purchase a $200 microwave oven for the department workroom. If 1 of the professors don't
contribute, everyone's share will increase by $10. How many professors are in the department?
72
73
o
If a wagon wheel had 30 more spokes, the angle between spokes would decrease by 27 . How many spokes does the wheel have?
2
Find the dimensions of a rectangle whose area is 459 cm and whose perimeter is 88 cm.
74 Find the values of x and y.
x + 11i = y yi
PAGE 12
Name: __________________
Class:
75 Do the operation and express the answer in a + bi form.
(3 5i) + (10 + 2i)
76 Do the operation and express the answer in a + bi form.
3 + i
9 i 7
77 Do the operation and express the answer in a + bi form.
(2 25) (4i 3)
78 Do the operation and express the answer in a + bi form.
49 ) + (5 +
(52 16 )
79 Do the operation and express the answer in a + bi form.
(10 + 4i)
2
80 Do the operation and express the answer in a + bi form.
(3 +
9 )(4 4)
81 Do the operation and express the answer in a + bi form.
18
i
7
82 Do the operation and express the answer in a + bi form.
6
i
5
PAGE 13
Date: _____________
Name: __________________
Class:
83 Do the operation and express the answer in a + bi form.
12
i
32
84 Do the operation and express the answer in a + bi form.
1
3 + i
85 Simplify the expression.
i
25
86 Simplify the expression.
i
2
87 Simplify the expression.
i
38
88 Find the absolute value.
| 15 + 20i |
89 Find the absolute value.
| 9 12i |
90 Find the absolute value.
9
8 + i
91 Find the absolute value.
4 + i
4 i
PAGE 14
Date: _____________
Name: __________________
Class:
Date: _____________
92 Factor the expression over the set of complex numbers.
9a
2
+ 16
93 In electronics, the formula V = IR is called Ohm's law. It gives the relationship in a circuit between the voltage V (in volts), the current I (in
amperes), and the resistance R (in ohms).
Find V when I = 7 9i amperes and R = 3 + 8i ohms.
94 Solve the equation for real values of the variable by factoring.
x
3
8x
2
+ 7x = 0
95 Solve the equation for real values of the variable by factoring.
x
4
100x
2
+ 2304 = 0
96 Solve the equation for real values of the variable by factoring.
z
3
2
4z
1
2
= 0
97 Solve the equation for real values of the variable by factoring.
2
3
4m
44m
1
3
+ 72 = 0
98 Solve the equation for real values of the variable by factoring.
3t
1
3
15t
1
6
+ 18 = 0
99 Solve the equation for real values of the variable by factoring.
9 p 135 p
1
2
+ 504 = 0
100 Find all real solutions of the equation.
x 9 = 3
101 Find all real solutions of the equation.
x + 96 = 5 x
102 Find all real solutions of the equation.
9x + 3 =
PAGE 15
8x + 8
Name: __________________
Class:
103 Find all real solutions of the equation.
3
2x + 52 = 4
104 Find all real solutions of the equation.
4
2t + 6 = 4
105 Find all real solutions of the equation.
x
2
+ 60 = x + 6
106 Find all real solutions of the equation.
y + 8 = 4 y
107 Find all real solutions of the equation.
x 13x 40 = 0
108 Find all real solutions of the equation.
x
2
17 = 2 2
x 4
109 Find all real solutions of the equation.
x
2
16
=
5x 16
2
110 Find all real solutions of the equation.
3
27x
3
945 = 3x 15
111 Find all real solutions of the equation.
r +
r + 11 = 11
112 Find all real solutions of the equation.
x + 16 x 35 =
3
113 Solve the inequality and write the answer in interval notation.
4x 3 < 7
114 Solve the inequality and write the answer in interval notation.
4x 3 PAGE 16
3
Date: _____________
Name: __________________
Class:
115 Solve the inequality and write the answer in interval notation.
2x 5 > 3
116 Solve the inequality and write the answer in interval notation.
1 x 5 > 15
7
117 Solve the inequality.
16 ( x 8 ) 5
8(x + 4)
4
118 Solve the inequality and write the answer in interval notation.
8 x 5
5 x 2
5 (x + 8 ) + 1
4
5
5
119 Solve the inequality and write the answer in interval notation.
x 3 > 5
2
14 120 Solve the inequality and write the answer in interval notation.
5x + 9 15x + 3 > 3x + 4
121 Solve the inequality and write the answer in interval notation.
2
10x + 7x 1
122 Solve the inequality and write the answer in interval notation.
2
x + 2x 2
x 49
0
123 Solve the inequality and write the answer in interval notation.
2
5x + 6 x + x 6
x
2
0
124 Solve the inequality and write the answer in interval notation.
10x
x
2
PAGE 17
2
+ 7x + 1 + 4x + 4
0
Date: _____________
Name: __________________
Class:
Date: _____________
125 Solve the inequality. Write the answer in interval notation.
10 x 6
2
126 Solve the inequality. Express the answer in interval notation.
3
x
2
1
1
127 A student can afford to spend up to $2172. The computer costs $1587 and the CD ROM costs $24. If she buys the computer, how many CD
ROMs can she buy?
128 The perimeter of the square is to be from 8 meters to 44 meters. Find the range of values for its area S.
129
Express the relationship 2 < C < 12 in terms of F , where F =
7C + 5 .
2
130 Write the expression | 10 | without using absolute value symbols.
131 Write the expression | 4 10 | without using absolute value symbols.
132 Write the expression without using absolute value symbols.
|6| | 4|
133 Write the expression without using absolute value symbols.
| x 5 | and x > 5
134 Solve the equation for x.
| 2x + 5 | = 9
135 Solve the equation for x.
9x 8
2
= 13
136 Solve the equation for x.
8x 2
x
= 7
137 Solve the equation for x.
|x+5|=|5 x|
138 Solve the equation for x.
| x 7 | = | 2x + 7 |
PAGE 18
Name: __________________
Class:
Date: _____________
139 Solve the equation for x.
5x 1
4
4x + 5
5
=
140 Solve the inequality. Express the solution set in interval notation.
|x+5|>9
141 Solve the inequality. Express the solution set in interval notation.
| 3x 4 | < 7
142 Solve the inequality. Express the solution set in interval notation.
| 2x 9 | 3 > 10
143 Solve the inequality. Express the solution set in interval notation.
5
5x 1
6
1
144 Solve the inequality. Express the solution set in interval notation.
0 < | 8x + 1 | < 9
145 Solve the inequality. Express the solution set in interval notation
x 8
3
3 <
< 4
146 The temperatures on a summer day satisfy the inequality below, where t is the temperature in degrees Fahrenheit. Express this range without
using absolute value symbols.
o
| t 79 | 9
o
147 A Steinway piano should be placed in an environment where the relative humidity h is between 35% and 73%. Express this range with an
inequality containing an absolute value.
PAGE 19
ANSWER KEY
Name: __________________
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
( , )
x 6
( 0, )
6
x=6
3
x= 3
7
x=7
8
x=8
2
x=2
3
x= 3
2
x= 2
5
y=5
0
x=0
t= f
10
f
10
w= ( p 7m )
8
( p 7m )
8
x=m f v
m f v
x=m vf
r= n j
( n+j)
n j
( n+j)
122
48
11
x=11
8
h=8
20000,19000
305
3.50
142.00
347.00
15
15
PAGE 1
Class:
Date: _____________
ANSWER KEY
Name: __________________
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
1.3
118.17
76,114
7
3.5
50
50
27
27.013695
7
4, 8
x=4,x= 8
3,0
x= 3,x=0
1,2
x=1,x=2
21, 11
y= 21,y= 11
9,1
x=9,x=1
42. 36x2 24x+4
43.
44.
45.
46.
47.
48.
49.
7,9
x= 7,x=9
2, 14
x= 2,x= 14
12 1, 12 1
8 , 8
x= 8 ,x= 8
9, 3
x=9,x= 3
6, 3
x= 6,x= 3
5+ 21 5 21
,
2
2
5 21
2
PAGE 2
Class:
Date: _____________
ANSWER KEY
Name: __________________
Class:
2 2
f
h x
h
2 2
2 2
f
h x , f
h x
h
h
x
f
1
1+ x , f
h
h
(
)
(
)
50.
(
1 x
h
y=f
)
1+ x
h
2 2
y= f h x
h
2 2
h x ,y= f y= f h
h
x
f
1
1+ x
h
h
(
(
y= f
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
)
1 x
h
,y= f
( h2 x2)
1+ x
h
5, 6
x=5,x= 6
3.56,3.00
x= 3.56,x=3.00
6,9
40
12
4
x=4
4
40,50
30,20
7
20
20
21
29.1
6
9
12
9
12,16
5
10
27,17
( 11, 11 )
13 3i
( 27 7 ) + ( 9+3 7 ) i
88
88
5 9i
PAGE 3
1 x
h
)
51. no
52.
Date: _____________
1+ x
h
1 x
h
1+ x
h
ANSWER KEY
Name: __________________
78. 57 3i
79. 84+80i
80. 18+6i
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
18i
0+18i
6i
0+6i
12
12+0i
3 i
10 10
i
1
1
25
15
9
65
1
( 3a+4i ) ( 3a 4i )
( 4+3a i ) ( 4 3a i )
93+29i
1,7,0
x=1,x=7,x=0
x=1,7,0
x=7,1,0
x=0,1,7
6, 6,8, 8
x=6, 6,8, 8
x= 6,6,8, 8
x=8, 6,6, 8
x= 8, 6,8,6
x=6,x= 6,x=8,x= 8
4,0
z=4,0
z=0,4
z=4,z=0
8,729
3 3
2 ,9
m=8,m=729
m=8,729
97. 8,m=729
3
3
m=2 ,m=9
3 3
m=2 ,9
3
3
2 ,m=9
PAGE 4
Class:
Date: _____________
ANSWER KEY
Name: __________________
64,729
6 6
2 ,3
t=64,t=729
t=64,729
98. 64,t=729
6
6
t=2 ,t=3
6 6
t=2 ,3
6
6
2 ,t=3
49,64
2 2
7 ,8
p=49,p=64
p=49,64
99. 49,p=64
2
2
p=7 ,p=8
2 2
p=7 ,8
2
2
7 ,p=8
18
100.
x=18
4
101.
x=4
5
102.
x=5
6
103.
x=6
125
104.
t=125
2
105.
x=2
1
106.
y=1
5,8
x=5,x=8
107.
x=5,8
5,x=8
5,3
x=5,x=3
108.
x=5,3
5,x=3
8
109.
x=8
3,2
x=3,x=2
110.
x=3,2
3,x=2
PAGE 5
Class:
Date: _____________
ANSWER KEY
Name: __________________
25
r=25
84
112.
x=84
113. ( , 1 )
114. 0, )
115. ( , 1 )
116. ( 70, )
117. 28, )
118. 1.023256, )
119. ( 13,31
120. ( 0.083333,0.600000
1, 1
121.
2 5
0.5, 0.2
122. ( 7, 2 0,7)
123. ( , 3 ) 3, )
124. ( , 2 ) ( 2, 0.5 0.2, )
125. ( ,6 ) 11, )
126. 2, 1 ) ( 1,2
127. 24
4 S 121
128.
4 S 121
12<F<47
129. ( 12,47)
f ( 12,47)
130. 10
131. 6
132. 2
133. x 5
134. 2, 7
34 , 2
135.
9
2 ,2
136.
15
0
137.
x=0
138. 0, 14
15 , 25
139.
41 9
140. ( , 14 ) ( 4, )
11
141. 1,
3
142. ( , 2 ) ( 11, )
1 11 ,
143. ,
25
25
10 , 1 1 ,1
144.
8 8
8
145. ( 4, 1 ) ( 17,20 )
146. 70,88
111.
PAGE 6
Class:
Date: _____________
ANSWER KEY
Name: __________________
147. h 54 19
PAGE 7
Class:
Date: _____________