Download QUESTIONS 1 - 46 REVIEW THE OBJECTIVES OF CHAPTER 2.

MAT 101 Course Review Questions
MIDTERM EXAM
FINAL EXAM
Valid for Fall 2014, Spring 2015 and Summer 2015
Questions 1 - 86 are covered on the Midterm.
There are 25 questions on the midterm, all multiple choice, and you are given 75 minutes for the
exam.
All questions are covered on the Final - the exam is cumulative.
There are 40 questions on the final, all multiple choice, and you are give 120 minutes for the exam.
Solve the problem.
12) Junior high classes of 25 students each met in
the cafeteria to take achievement tests. If
exactly 5 students sat at each table and 15
tables were used, how many classes took the
tests?
QUESTIONS 1 - 46 REVIEW THE
OBJECTIVES OF CHAPTER 2.
Solve the equation.
1) 7x - 4x - 2x = -12 + 14
2) -6(x + 10) = -42
Solve using the five-step problem-solving process.
13) The sum of two consecutive even integers is 62.
Find the larger number.
3) -(6y - 6) - (-5y + 9) = -4
4)
2x x
- =5
5
3
5)
x + 6 x - 2 11
+
=
3
2
6
14) The sum of the page numbers on the facing
pages of a book is 267. Find the larger page
number.
15) The sum of three consecutive odd integers is
267. Find the integers.
Solve the equation. Use words or set notation to identify
equations that have no solution, or equations that are true
for all real numbers.
6) 7(x + 5) = 7x + 35
Solve the equation.
7) -5.4m + 6 + 2.3m = -7.2 - 3.1m + 13.2
1
1
1
(10x - 15) = 6( x - ) + 4
5
3
2
Solve the equation. Use words or set notation to identify
equations that have no solution, or equations that are true
for all real numbers.
10) 4(x + 4) = 4x - 32
Use the given information to write an equation. Let x
represent the number described in the exercise. Then solve
the equation and find the number.
3
. Find the
11) Three-fourths of a number is
16
number in lowest terms.
17) The sum of two consecutive integers is -239.
Find the larger integer.
18) A rectangular Persian carpet has a perimeter of
160 inches. The length of the carpet is 18 inches
more than the width. What are the dimensions
of the carpet?
8) 8x - 9 + 7x + 5 = 9x + 6x - 7
9)
16) The sum of three consecutive integers is 426.
Find the integers.
Solve the problem.
19) The length of a rectangular storage room is 4
feet longer than its width. What are the
dimensions of the room if the area of the room
is 77 square feet?
Solve the formula for the specified variable.
1
20) V = Bh for h
3
Solve the equation for y. (You can also refer to material in
3.4 for additional examples.)
21) x = 5y + 3
Last updated Fall 2014
Solve the equation for y. (You can also refer to material in
3.4 for additional examples.)
22) 9x - 8y = 6
Set up an equation that can be used to solve the problem.
Solve the equation and answer the question asked.
33) After a 13% price reduction, a boat sold for $
30,450. What was the boat's price before the
reduction? (Round to the nearest cent, if
necessary.)
23) x - 6y = 3
Express the percent as a decimal.
24) 67.2%
25)
Solve the problem.
34) Jeans are on sale at the local department store
for 15% off. If the jeans originally cost $62, find
the sale price. (Round to the nearest cent, if
necessary.)
1
%
16
Express the decimal as a percent.
26) 8
Let x represent the number. Write the English phrase as an
algebraic expression.
35) Ten times a number, decreased by 27.
Solve the problem.
27) Due to a lack of funding, the number of
students enrolled at City College went from
6000 last year to 5000 this year. Find the
percent decrease in enrollment. (Round to the
nearest tenth of a percent, if necessary.)
36) The product of -26 and the sum of a number
and 18.
Let x represent the number. Use the given conditions to
write an equation. Solve the equation and find the
number.
37) When 2 times a number is subtracted from 7
times the number, the result is 45. Find the
number.
28) Sales at a local ice cream shop went up 60% in
5 years. If 37,000 ice cream cones were sold in
the current year, find the number of ice cream
cones sold 5 years ago. (Round to the nearest
integer, if necessary.)
Solve the problem.
38) There are 10 more sophomores than juniors in
an algebra class. If there are 80 students in this
class, find the number of sophomores and the
number of juniors in the class.
29) A IBM Proprinter printer priced at $538 is sold
for $342. What was the percent decrease of the
price? Round to the nearest tenth of a percent,
if necessary.
Use the relationship among the three angles of any
triangle to solve the problem.
39) One angle of a triangle is 2 times as large as
another. The measure of the third angle is 120°
greater than that of the smallest angle. Find the
measure of each angle.
Use the percent formula, A = PB: A is P percent of B, to
solve.
30) 21 is 2% of what number?
31) 10% of what number is 74?
Solve the problem.
32) 9% of students at a university attended a
lecture. If 2000 students are enrolled at the
university, about how many students attended
the lecture?
Find the measure of the indicated angle.
40) The angle's measure is 40° more than triple
that of its supplement.
Solve the problem.
41) Find the measure of an angle whose
supplement is 9 times the measure of its
complement.
2
Solve the problem.
52) A certain car has a weight limit for all
passengers and cargo of 1065 pounds. The four
passengers in the car weigh an average of 165
pounds. Use an inequality to find the
maximum weight of the cargo that the car can
handle.
Use both the addition and multiplication properties of
inequality to solve the inequality. Graph the solution set
on a number line.
42) 8x - 7 4x - 11
43) 5x - 6 < 6(x + 5)
53) When making a long distance call from a
certain pay phone, the first three minutes of a
call cost $2.05. After that, each additional
minute or portion of a minute of that call costs
$0.35. Use an inequality to find the maximum
number of minutes one can call long distance
for $2.75.
Solve the linear inequality. Other than , use interval
notation to express the solution set and graph the solution
set on a number line.
44) 5(4x + 4) - 4x < 4(5 + 4x) - 6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ADDITIONAL REVIEW SUGGESTIONS:
Chapter Two Review Exercises pg 204 #1 - 87
Chapter Two Test pg 207 #1 - 34
Cumulative Review Exercises pg 208 1 - 20
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
45) -4x -4(x - 6)
46) 3(x + 4)
QUESTIONS 54 - 86 COVER THE
OBJECTIVES FOR CHAPTER 3 UP TO
2(x - 3) + x
SECTION 3.4
Complete the ordered pair for the equation.
54) y = -6x - 23
( , -23)
Solve the inequality, then graph the solution.
47) 4x + 10 - 9x < 6 - 7x + 4
55) y = -3x + 21
(9, )
Find a solution to the equation using the value given for x.
56) y = -7x - 4; x = -3
Solve the inequality.
48) 7x + 13 > 7(x + 11)
49) x + 8
Graph the linear equation in two variables.
57) y = x - 1
x-5
50) -3(-3 - x) < 5x + 21 - 12 - 2x
51) 4x - 7 > 4(x - 5)
3
Find the y- and x-intercepts for the equation. Then graph
the equation.
62) 6y - 3x = -9
58) y = -2x - 4
59) y =
1
x-5
6
63) -6x - 12y = 36
Use the graph to identify the x- and y- intercepts or state
that there is no x- or y-intercept.
60)
Graph the equation.
64) -64 - 16x = 0
Find the slope of the line passing through the pair of
points or state that the slope is undefined.
65) (-6, 5), (7, -9)
Find the x-intercept and the y-intercept of the graph of the
equation. Do not graph the equation.
61) 2x + y = -6
4
Find the slope of the line that passes through the two
given points.
66) (2, 0), (0, 6)
Find the slope of the line. Interpret the slope in terms of
rise and run.
72)
Find the slope of the line passing through the pair of
points or state that the slope is undefined.
67) (-3, -2) and (-3, 6)
68) (9, -1) and (-2, -1)
Determine the slope and the y-intercept. Then graph the
equation.
69) y = 4x - 7
Determine the slope and the y-intercept. Then graph the
equation.
73) 2x - 4y = 14
Determine whether the lines through each pair of points
are parallel.
70) (10, -7) and (2, 7); (8, -6) and (12, 1)
By observing the vertical and horizontal change of the line
between the two points indicated, determine the slope of
the line.
71)
Determine whether the lines through each pair of points
are parallel.
74) (-3, 5) and (13, 23); (9, 10) and (17, 19)
Determine whether the lines through each pair of points
are parallel, perpendicular, or neither.
75) (-10, 9) and (-18, 7); (7, 10) and (6, 14)
5
Find the slope of the line, or state that the slope is
undefined.
76)
Graph the linear equation.
2
81) y = x - 2
5
Find the slope of the line.
77) x = 4
Put the equation in slope-intercept form by solving for y.
Use the slope and y-intercept to graph the equation.
82) 7x + 3y = 21
78) y = 2
Find the slope and the y-intercept of the line with the
given equation.
79) 8x + y = 6
Graph the linear equation using the slope and y-intercept.
1
80) y = - x
2
Interpret the linear equation.
83) The altitude above sea level of an airplane just
after taking off from an airport on a high
plateau is given by the linear function y = 600x
+ 3097, where y is in feet and x is the time in
minutes since take-off. Find and interpret the
slope and y-intercept.
Solve the problem.
84) The monthly cost of a certain long distance
service is given by the linear function
y = 0.04x + 3.95 where y is in dollars and x is
the amount of time in minutes called in a
month. Find and interpret the slope and
y-intercept of the linear equation.
6
85) When a tow truck is called, the cost of the
service is given by the linear function
y = 3x + 75, where y is in dollars and x is the
number of miles the car is towed. Find and
interpret the slope and y-intercept of the linear
equation.
Multiply the monomials.
1
1
94) - x5 x9
9
4
Find the product.
95) -10x2(-10x6 + 2x4 - 4)
Interpret the linear equation.
86) The amount of water in a leaky bucket is given
by the linear function y = 127 - 8x, where y is
in ounces and x is in minutes. Find and
interpret the slope and y-intercept of the linear
equation.
96) (9x - 1)(x2 - 2x + 1)
Use the FOIL method to find the product. Express the
product in descending powers of the variable.
97) (4x + 1)(6x + 9)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ADDITIONAL PRACTICE SUGGESTIONS:
Chapter Three Review Exercises pg 269 1 - 44
Chapter Three Test pg 272 #1 - 14 and 19
Cumulative Review Exercises pg 273 #1 = 20
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Multiply using the rule for finding the product of the sum
and difference of two terms.
98) (9x + 8)(9x - 8)
Multiply by using the rule for the square of a binomial.
99) (x3 + 5)2
STOP HERE FOR MIDTERM
100) (11 - 10x)2
QUESTIONS 87 - 122 REVIEW THE
OBJECTIVES FROM CHAPTER 5
Divide using the quotient rule.
x12y11
101)
x9 y6
Identify the polynomial as a monomial, binomial, or
trinomial. Give the degree of the polynomial.
87) -8y7 - 3
Use the zero-exponent rule to simplify the expression.
102) -3 0 + (-3)0
Add the polynomials.
88) (7x3 + 2x - 2) + (9x2 + 4x + 7)
Simplify the expression using the quotients-to-powers
rule.
2p4 v3 3
103)
s2
Subtract the polynomials.
89) (9x5 + 3x7 - 1 - 2x6 ) - (3 + 5x6 + 7x7 - 7x5 )
Perform the indicated operations.
90) Subtract -1 - 8x7 + 6x8 + 2x6 + 3x from the
sum of -9x6 + 3x + 6 and 3x8 - 3x7.
Divide the monomials.
-8x10
104)
56x6
Multiply the expression using the product rule.
91) y3 · y4 · y6
Divide the polynomial by the monomial.
6x8 + 8x6 - 6x2
105)
2x2
Simplify the expression using the power rule.
92) (-7)9 10
Divide as indicated.
p2 + 3p - 25
106)
p+7
Simplify the expression using the products-to-powers
rule.
93) (-2x4)4
7
107)
4m 3 + 6m 2 + 2m + 12
m+2
Solve the problem.
119) NEW
The national debt of a small country is $
6,780,000,000 and the population is 2,236,000.
What is the amount of debt per person?
Simplify the expression. Write the result using positive
exponents only.
y-9
108)
y4
120) The sun radiates energy into space at the rate
of 3.9 × 1026 joules per second. How many
joules are emitted in three weeks?
109) (-4x4y-5 )(2x-1 y)
Solve the problem. Express the answer in scientific
notation to two decimals.
121) A light-year is the distance that light travels in
one year. Find the number of miles in a
light-year if light travels 1.86 × 105
110) -4z -3
111) m -4 · m3 · m-8 · m
miles/second.
Write the expression with positive exponents only. Then
simplify, if possible.
1
112)
4x-4
Solve.
122) Approximately 7 × 103 employees of a certain
company average $30,000 each year in salary.
What is the total amount earned by all the
employees of this company per year? Write
your answer in scientific notation.
Simplify the exponential expression.
113) (3x3 )3 x-15
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ADDITIONAL PRACTICE SUGGESTIONS:
Chapter Five Review Exercises pg 421
#1 - 73, 77 - 103
Chapter Five Test pg 423 #1 - 18, 20 - 32
Cumulative Review pg 424 #1 - 12, 17 - 20
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Write the number in decimal notation without the use of
exponents.
114) 2.212 x 10-5
Write the number in scientific notation.
115) 13,000,000
QUESTIONS 123 - 148 REVIEW THE
OBJECTIVES FROM CHAPTER 6
Perform the indicated computations. Write the answer in
scientific notation.
116) (3 × 109 )(6 × 10-7)
Factor out the GCF from the polynomial.
123) 120x6y9 - 36x4 y6 - 60x2 y4
Perform the indicated operation by first converting the
numbers to scientific notation. Write the answer in
scientific notation.
(0.00016)(0.0004)
117)
0.0008
Factor by grouping.
124) 6x6 - 15x3 + 10x3 - 25
Factor completely.
125) x7 - 11x6 + 24x5
Solve.
118) A particle is observed moving at 3.57 × 10-3
meters per second. Find the distance the
particle would travel in 9.45 × 10-6 seconds.
Factor completely using the trial and error method to
factor trinomials. If unfactorable, indicate that the
polynomial is prime.
126) 8z 2 + 6z - 9
8
Factor completely using the grouping method to factor
trinomials. If unfactorable, indicate that the polynomial is
prime.
127) 12z 2 - 7z - 12
142) 3x2 - 27x + 60 = 0
143) 36x2 = 25
144) 16x2 - 5x = 0
Factor completely. If unfactorable, indicate that the
polynomial is prime.
128) 25k2 - 81m 2
145) x2 = -16x - 64
146) x(x - 24) = -144
129) z2 + 14z + 49
147) (x + 2)(x2 + 2x - 24) = 0
Factor completely, or state that the polynomial is prime.
130) 25x2 + 16
Solve the problem.
148) The width of a rectangle is 6 kilometers less
than twice its length. If its area is 176 square
kilometers, find the dimensions of the
rectangle.
Factor the polynomial completely. If the polynomial
cannot be factored, write "prime."
131) x4 - 81
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ADDITIONAL PRACTICE SUGGESTIONS:
Chapter Six Review Exercises pg 485 #1 - 95
Chapter Six Test pg 487 #1 - 30
Cumulative Review pg 488 #1 - 8, 12 - 20
Factor completely. If the polynomial is prime, say so.
132) x2 + 59x + 60
Factor the polynomial completely. If the polynomial
cannot be factored, write "prime."
133) 12(a + 5) - y(a + 5)
134) x2 + 36
Factor completely. If prime, so state.
135) w4 - s4
136) 2x2 - 20x + 50
137) 17x2 + 17xy + y2
Factor the polynomial completely. If the polynomial
cannot be factored, write "prime."
138) 256 - 4x2
Factor.
139) t3 + 729
Factor completely.
140) 64 - t3
Solve the equation.
141) (9x + 23)(3x + 22) = 0
9