Download Math 60 Review Practice Questions

Math 60 Review Practice Questions
*Note 1: The actual Math 60 final exam may include, but is not limited to, the problems in this handout.
Study your notes,
past homework assignments, quizzes, and tests. Also, see a tutor and/or your professor if you need any additional
assistance.
*Note 2: NO NOTES OR GRAPHING CALCULATORS ARE ALLOWED ON THE FINAL EXAM.
Evaluate the expression if possible.
1.)
a) 9
b)
c) -
d)
e) none of these
d) the sum is 5
e) none of these
Solve the equation and find the SUM of the solutions.
2.)
a) the sum is -5
b) the sum is -1
c) the sum is 1
Find the SUM of the value(s) of the variable for which the rational expression is undefined.
3.)
a) the sum is 5
b) the sum is 0
c) the sum is -5
d) the sum is 8
e) none of these
c) 1
d) ∅
e) none of these
c)
d
e) none of these
Solve the equation and find the SUM of the solutions.
4.)
a) -1
b) -5
Simplify the square root.
5.)
a)
b)
Simplify the complex rational expression.
6.)
a)
b)
c)
Math 60 - 1
RETYPED BY MOLIVAS May2015 revised 5/12/2015
d)
e) none of these
Simplify.
7.)
a)
b)
c)
d)
e) none of these
Perform the indicated operation. Simplify if possible. Assume all variables are positive.
8.)
c)
d)
e) none of these
Simplify the expression. Assume all variables are positive.
9.)
a)
b)
c)
d)
e) none of these
Perform the indicated operation. Simplify if possible.
10.)
a)
b)
c)
d)
e) none of these
Solve the equation.
11.)
a)
d)
b)
c)
e) none of these
Find the distance d(
) between the points
12.) = (-5, 7) ; = (1, -7)
a) 2
b) 20
c) 160
d) 160
Math 60 - 2
RETYPED BY MOLIVAS May2015 revised 5/12/2015
.
e) none of these
Rationalize the denominator. Simplify if possible.
13.)
a)
b)
c)
d)
e) none of these
Solve the inequality. Graph the solution set. Express solution set in interval notation.
14.)
a)
(
-4
b)
)
0
)
-4
(
0
(
-4
c)
d)
(
0
)
4
)
4
e) none of these
Simplify the radical expression. Assume all variables are positive.
15.)
a)
e) none of these
b)
c)
d)
Find the domain of the function.
16.)
a)
b)
c)
d)
e) none of these
Solve the system of three linear equations containing three unknowns. The SUM of the solutions
is:
17.)
a)
b) -6
c) -4
d) 8
Math 60 - 3
RETYPED BY MOLIVAS May2015 revised 5/12/2015
e) none of these
Solve the formula for the indicated variable.
18.)
a)
solve for r.
b)
c)
d)
e) none of these
d)
e) none of these
Find the domain of the given function.
19.)
a)
b)
c)
Graph the quadratic function.
20.)
a)
b)
c)
d)
e) none of these
Solve the system of equations for the variable “x”.
21.)
a) x = -1
b) x = -5
c) infinitely many solutions
Math 60 - 4
RETYPED BY MOLIVAS May2015 revised 5/12/2015
d) no solution
e) none of these
Find the center and the radius of the circle.
22.)
a) (-3, -1), r = 7
b) (1, 3), r = 49
c) (3, 1), r = 49
d) (-1, -3), r = 7
e) none of these
Rewrite the expression with a positive rational exponent. Simplify, if possible. Assume that a
and b are greater than zero.
23.)
a)
b)
c)
d)
e) none of these
Solve the problem.
24.) Shari drove for 90 miles in the city. When she got on the highway, she increased her
speed by 20 mph and drove for 130 miles. If Shari drove a total of 4 hours, how fast did she drive
in the city?
a) 45 mph
b) 10 mph
c) 40 mph
d) 65 mph
e) none of these
Use the right triangle shown and find the missing length. If necessary, round to three decimal
places.
25.)
a
c
b
a) 8
b) 11.662
b = 6, c = 10
c) 2
d) 64
e) none of these
Solve the problem.
26.) The width of a rectangle is 4 cm less than its length. If its area is
, what is the
perimeter?
a) 48 cm
b) 20 cm
c) 24 cm
d) 40 cm
e) none of these
27.) Shelly can cut a lawn with a riding mower in 2 hours less time than it takes William to
cut the lawn with a push mower. If they can cut the lawn in 4 hours working together find how
long to the nearest tenth of an hour it takes for William to cut the lawn alone?
a) 7.1 hrs
b) 9.1 hrs
c) 9.2 hrs
Math 60 - 5
RETYPED BY MOLIVAS May2015 revised 5/12/2015
d) 7.2 hrs
e) none of these
Find the quotient and simplify.
28.)
a)
c)
b)
d)
e) none of these
Solve the compound inequality. Express the solution in interval notation. Graph the solution
set.
29.)
a)
)
1
[
1
(
1
b) [1, 3]
c) (1, 3)
[
3
]
3
)
3
d) ∅
e) none of these
Perform the indicated operations and simplify.
30.)
a)
b)
c)
d)
e) none of these
Solve the equation.
31.)
a)
b)
c)
d)
e) none of these
Rationalize the denominator and simplify.
32.)
a) x - 7
b) x + 7
c)
d)
Math 60 - 6
RETYPED BY MOLIVAS May2015 revised 5/12/2015
e) none of these
Simplify the rational expression.
33.)
a)
b)
c)
d)
e) none of these
Divide. Write the result in the form a + bi.
34.)
a)
b)
c) 2 -
d)
e) none of these
Simplify the expression. Assume all variable represent positive real numbers.
35.)
a)
b)
c)
d)
e) none of these
d)
e) none of these
Perform the indicated operation. Simplify if possible.
36.)
a)
b)
c)
Solve the problem.
37.) If
a) C = 265
what is the value of C?
b) C = -29
c) C = 175
d) C = -257
e) none of these
Multiply, and then simplify if possible.
38.)
a)
b)
c)
d)
Math 60 - 7
RETYPED BY MOLIVAS May2015 revised 5/12/2015
e) none of these
Solve the problem.
39.) Chandra has 2 liters of a 14% solution of sodium hydroxide in a container. What is the
amount and concentration of sodium hydroxide solution she must add to this in order to end up
with 7 liters of a 34% solution?
a) 5 L of 40% solution b) 5 L of 45% solution c) 5 L of 43% solution d) 5 L of 42% solution
e) none of these
Solve the inequality. Graph the solution set and write the solution set in set-builder notation.
40.)
a)
]
-2
b)
[
]
-2
6
c)
[
6
d)
]
[
-2
6
e) none of these
Graph the linear function.
41.)
6
6
4
4
2
2
-6
-4
-2
a)
2
4
-6
6
-4
-2
2
-2
-2
-4
-4
b)
-6
4
6
-6
6
6
4
4
2
-6
c)
-4
-2
2
2
4
6
-6
-4
-2
2
-2
-2
-4
-4
-6
d)
Math 60 - 8
RETYPED BY MOLIVAS May2015 revised 5/12/2015
-6
4
6
e) none of these
Determine the discriminant of the quadratic equation. Use the value of the discriminant to
determine whether the quadratic equation has two rational solutions, two irrational solutions,
one repeated real solution, or two complex solutions that are not real.
42.)
a)
b)
c)
d)
e)
2 rational solutions
2 complex solutions that are not real
1 repeated real solution
2 irrational solutions
none of these
Solve the equation and find the SUM of the solutions.
43.)
a) 0
b) -2
c) ∅
d) - 2+
Solve the problem.
44.) The value of a $22,500 car after x years is given by the function
. What is the value of the car after 5 years?
a) $9,000
b) $17,995
Perform the indicated operation.
e) none of these
c) $0
d) $4,500
e) none of these
c)
d)
e) none of these
45.)
a)
b)
Find the domain, the range, and any intercepts.
46.)
a) domain:
range:
intercepts: (-2, 0), (0, -2), (2,0)
b) domain:
range:
intercepts: (-2, 0), (0, -2), (2,0)
c) domain:
range:
intercepts: (-2, 0), (0, -2), (2,0)
d) not a function
e) none of these
Math 60 - 9
RETYPED BY MOLIVAS May2015 revised 5/12/2015
Solve the system of equations.
47.)
a) (2, 2)
b) ∅
c)
d)
e) none of these
Find the domain of the function.
48.)
a)
b)
c)
d)
e) none of these
Solve the compound inequality. Graph the solution set. Write solution using interval notation.
49.)
a)
b)
c)
d)
e)
(
5
[
5
[
5
(
5
none of these
]
6
)
10
)
6
]
10
(5,6]
[5, 10)
[5, 6)
(5, 10]
Solve the problem.
50.) The function
represents the path of a ball thrown up in the
air. Find the maximum height the ball will travel, in feet.
a) 4 ft
b) 32 ft
c) 15 ft
d) 63 ft
e) none of these
Explain how to obtain the graph of the given quadratic function from the graph of
51.)
a)
b)
c)
d)
Take the graph of
Take the graph of
Take the graph of
Take the graph of
and shift it 3 units to the left and 7 units up.
and shift it 3 units to the left and 7 units down.
and shift it 3 units to the right and 7 units up.
and shift it 3 units to the right and 7 units down.
Math 60 - 10
RETYPED BY MOLIVAS May2015 revised 5/12/2015
.
Find the center and the radius of the circle whose graph is shown. Write the standard form of
the equation of the circle.
52.)
(-3, 2)
(0, 2)
For the following function, indicate its vertex.
53.)
a) (5, -2)
b) (-3, -7)
c) (2, 42)
d) (-2, 5)
e) none of these
Solve the problem.
54.) The manufacturer of a cell phone has found that the revenue R (in dollars) is
, when the unit prices is p dollars. If the manufacturer sets the price p to
maximize revenue, what is the maximum revenue to the nearest whole dollar?
a) $26,450
b) $13,225
c) $115
d) $264,500
e) none of these
Perform the indicated operation. Write the result in the form a+bi.
55.)
a)
b)
c)
d)
e) none of these
Use the quadratic formula to solve the equation.
56.)
a)
b)
c)
d)
Math 60 - 11
RETYPED BY MOLIVAS May2015 revised 5/12/2015
e) none of these
Simplify if possible.
57.)
a)
b)
c)
d)
e) none of these
Solve the system of three linear equations. The y coordinate is:
58.)
a) 4
b) 2
c) 3
d) -5
e) none of these
Solve the problem.
59.) Bob needs to wash the windows on his house. He has a 25-foot ladder and places
the base of the ladder 10 feet from the wall on the house. How far up the wall will the ladder
reach?
a) 14 ft
b) 13 ft
c) 15 ft
d) 16 ft
e) none of these
Perform the operation. Simplify if possible.
60.)
a)
b)
c)
d)
e) none of these
Simplify the expression.
61.)
a) Not a real number
b)
c)
d)
e) none of these
Find the LCD of the following rational expressions.
62.)
a)
b)
c)
d)
e) none of these
Perform the following operation. Simplify if possible.
63.) Find the difference of
a)
b)
c)
d)
Solve the equation. Compute the sum of the solutions.
64.)
a) -14
b) 7
c) -7
d) 14
Math 60 - 12
RETYPED BY MOLIVAS May2015 revised 5/12/2015
e) none of these
e) none of these
Solve the inequality. Graph the solution set and write solution using interval notation.
65.)
a)
b)
c)
d)
(
)
-1
[
-5
(
)
10
)
[-5, 10)
(- , 1)
1
]
10
(
5
(5, 10]
e) none of these
Perform the indicated operations and simplify.
66.)
a)
b)
c)
Solve the equation.
67.)
a)
d)
b)
c)
e) none of these
d)
Write the following function in the form
68.)
a)
e) none of these
e) none of these
.
b)
c)
d)
Write the expression as a complex number in the form a + bi
69.)
a)
b)
c)
d)
e) none of these
Simplify the power of i.
70.)
a)
b)
c)
d)
e) none of these
Perform the indicated operation. Write the result in the form a+bi.
71.)
a)
b)
c)
d)
Math 60 - 13
RETYPED BY MOLIVAS May2015 revised 5/12/2015
e) none of these
Multiply, and then simplify if possible.
72.)
a)
b)
c)
d)
e) none of these
Perform the indicated operations and simplify.
73.)
a)
b)
c)
d)
e) none of these
Perform the indicated operations and simplify.
74.) Simplify
a)
by factoring out
b)
c)
d)
e) none of these
Identify the domain and the range of the relation from the graph.
75.)
(- 1, 5)
(4, 2)
(- 7, 2)
(- 1, - 1)
a) domain:
range:
b) domain:
range:
c) domain:
range:
e) none of these
Math 60 - 14
RETYPED BY MOLIVAS May2015 revised 5/12/2015
d) domain:
range:
Math 60 Review Practice Answers
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Math 60 - 15
RETYPED BY MOLIVAS May2015 revised 5/12/2015
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