Download Math 155 Course Review Questions 1

Math 155 Course Review
Questions 1 - 38 can be used as a study plan for the midterm. All questions should be studied for the final exam.
Use the order of operations to find the value of the
expression.
1) 7(4 - 2)3 - 2(5 - 3)3
Use a calculator with a square root key to find a decimal
approximation for the square root. Round the number
displayed as indicated.
8) 423 to the nearest thousandth
Objective: (5.2) Use the Order of Operations
Agreement
Objective: (5.4) Simplify Square Roots
2) 52 - 25 ÷ 5 · 2 + 9
Simplify the square root.
9) 2 300
Objective: (5.2) Use the Order of Operations
Agreement
Objective: (5.4) Simplify Square Roots
Solve the problem.
3) A hill is at 500 feet above sea level, and a crater
next to it is at 254 feet below sea level. What is
the difference in height between the hill and
the crater?
Perform the indicated operation. Simplify the answer
when possible.
10) 5 · 25
Objective: (5.4) Perform Operations with Square
Roots
Objective: (5.2) Use the Order of Operations
Agreement
11)
Reduce the rational number to its lowest terms.
21
4)
35
45
5
Objective: (5.4) Perform Operations with Square
Roots
Objective: (5.3) Reduce Rational Numbers
12)
Perform the indicated operation(s). Where possible,
reduce the answer to lowest terms.
1 1
7
÷
5)
5 6
9
13)
Objective: (5.3) Use the Order of Operations
Agreement with Rational Numbers
Solve the problem.
7) Of the 648 people polled about gardening, 216
replied that they plant a garden. What
fractional part of those polled, expressed in
lowest terms, plant a garden?
Objective: (5.3) Solve Problems Involving Rational
Numbers
24
18 -
8
Objective: (5.4) Perform Operations with Square
Roots
Objective: (5.3) Add and Subtract Rational Numbers
Perform the indicated operations. If possible, reduce the
answer to its lowest terms.
2 1
4 1
6) - ÷
3 6
5 2
6+
Objective: (5.4) Perform Operations with Square
Roots
Rationalize the denominator.
7
14)
5
Objective: (5.4) Rationalize Denominators
Perform the indicated operation. Simplify the answer
when possible.
15) 2 - 5 128 - 2 72
Objective: (5.4) Perform Operations with Square
Roots
Use properties of exponents to simplify the expression.
Express answer in exponential form.
16) 33 · 3 -5
Objective: (5.6) Use Properties of Exponents
Last Revised 201130
17)
Solve and check the equation. Begin your work by
rewriting the equation without fractions.
8x
x
9
-x=
26)
7
28 4
55
53
Objective: (5.6) Use Properties of Exponents
Objective: (6.2) Solve Linear Equations Containing
Fractions
Use properties of exponents to simplify the expression.
Express answers in exponential form with positive
exponents only. Assume that any variables in
denominators are not equal to zero.
10x3y-5
18)
2x7y-11
Solve the proportion.
2 9
27) =
3 x
Objective: (6.2) Solve Proportions
Objective: (5.6) Use Properties of Exponents
28)
Perform the indicated operation and express the answer in
decimal notation.
19) (8 × 108 )(9 × 10 -6 )
Objective: (6.2) Solve Proportions
Objective: (5.6) Perform Computations Using
Scientific Notation
20)
x-6
3
=
5
10
Use a proportion to solve the problem.
29) The ratio of a basketball player's completed
free throws to attempted free throws is 4 to 5.
If she completed 8 free throws, find how many
free throws she attempted. Round to the
nearest whole number if necessary.
3 × 104
15 × 10- 2
Objective: (5.6) Perform Computations Using
Scientific Notation
Objective: (6.2) Solve Problems Using Proportions
Indicate whether the equation has no solution or is true
for all real numbers. If neither is the case, solve for the
variable.
30) 4x - 2(4 + 2x) = -8
Perform the indicated operation by first expressing each
number in scientific notation. Write answer in scientific
notation.
21) (220,000,000)(2,000,000,000)
Objective: (6.2) Identity Equations with No Solution
or Infinitely Many Solutions
Objective: (5.6) Perform Computations Using
Scientific Notation
Let x represent the number. Use the given conditions to
write an equation. Solve the equation and find the
number.
31) If 3 times a number is added to -8, the result is
equal to 11 times the number. Find the
number.
Evaluate the algebraic expression for the given value(s) of
the variable(s).
22) x3 - 3x 2 + 1 ; x = -2
Objective: (6.1) Evaluate Algebraic Expressions
Simplify the algebraic expression.
23) 6(2x - 1) - 8(x - 3)
Objective: (6.3) Use Linear Equations to Solve
Problems
Objective: (6.1) Simplify Algebraic Expressions
Solve the formula for the specified variable.
32) d = rt for t
Solve and check the equation.
24) -3y - 3 = -1 + 10y
Objective: (6.3) Solve a Formula for a Variable
Objective: (6.2) Solve Linear Equations
25) 4(2y - 2) = 7(y + 2)
Objective: (6.2) Solve Linear Equations
2
Plot the point in the rectangular coordinate system.
33) (-5, 4)
Use the x- and y-intercepts to graph the linear equation.
36) x - 2y = -10
Objective: (7.1) Plot Points in the Rectangular
Coordinate System
Graph the equation. Select integers for x, -3
34) y = -2x + 5
x
Objective: (7.2) Use Intercepts to Graph a Linear
Equation
3.
Calculate the slope of the line passing through the given
points. If the slope is undefined, so state. Then indicate
whether the line rises, falls, is horizontal, or is vertical.
37) (-19, -1), (-3, -13)
Objective: (7.2) Calculate Slope
Graph the linear function using the slope and y-intercept.
1
38) y = x + 2
3
Objective: (7.1) Graph Equations in the Rectangular
Coordinate System
35) y = x2 + 3
Objective: (7.2) Use the Slope and y-Intercept to
Graph a Line
Express the percent as a decimal.
3
%
39)
10
Objective: (8.1) Express a Percent as a Decimal
Objective: (7.1) Graph Equations in the Rectangular
Coordinate System
Solve the problem.
40) 75% of 24 is what number?
Objective: (8.1) Solve Applied Problems Involving
Sales Tax and Discounts
3
The principal represents an amount of money deposited in
a savings account subject to compound interest at the
given rate. Find how much money will be in the account
after the given number of years (Assume 360 days in a
year.), and how much interest was earned.
41) 19 is what percent of 50?
Objective: (8.1) Solve Applied Problems Involving
Sales Tax and Discounts
42) 40% of what number is 98?
Objective: (8.1) Solve Applied Problems Involving
Sales Tax and Discounts
A=P 1+
43) A dress regularly sells for $117. The sale price
is $89. Find the percent decrease of the sale
price from the regular price.
r nt
n
P=
A
r nt
1+
n
A = Pert
46) Principal: $9500
Rate: 7.5%
Compounded: monthly
Time: 4 years
Objective: (8.1) Determine Percent Increase or
Decrease
Objective: (8.3) Use Compound Interest Formulas
The graph shows the level of subsidized daycare spending
in a foreign country for the period 1995-1999. Use the
graph to answer the question.
44) Find the percent increase in daycare spending
from 1997to 1998. Round to the nearest
percent.
Solve the problem.
47) A mother invests $9000 in a bank account at
the time of her daughter's birth. The interest is
compounded quarterly at a rate of 8%. What
will be the value of the daughter's account on
her twentieth birthday, assuming no other
deposits or withdrawals are made during this
period?
Objective: (8.3) Use Compound Interest Formulas
Solve the problem.
48) How much money should be deposited today
in an account that earns 5% compounded
quarterly so that it will accumulate to $6900 in
2 years?
Objective: (8.3) Calculate Present Value
Use dimensional analysis to convert the quantity to the
indicated units. If necessary, round the answer to two
decimal places.
49) 13 yd to ft
Objective: (8.1) Determine Percent Increase or
Decrease
Objective: (9.1) Use Dimensional Analysis to Change
Units of Measurement
The principal P is borrowed at simple interest rate r for a
period of time t. Find the simple interest owed for the use
of the money. Assume 360 days in a year and round
answer to the nearest cent.
45) P = $160
r = 8%
t = 2 years
Convert the given measurement to the unit indicated.
50) 5.49 m to cm
Objective: (9.1) Convert Units Within the Metric
System
Objective: (8.2) Calculate Simple Interest
Use dimensional analysis to convert the unit indicated.
51) 7 m to yd
Objective: (9.1) Use Dimensional Analysis to Change
to and from the Metric System
4
Select the best estimate for the measure of the given
quantity.
52) the length of a bedroom wall
A) 4.2 m
B) 4.2 mm
C) 4.2 km
D) 4.2 cm
Find the measure of the complement of the angle.
59) Find the complement of 33°.
Objective: (10.1) Solve Problems Involving Angle
Measures
Find the measures of angles 1, 2, and 3.
60)
Objective: (9.1) Understand and Use Metric Prefixes
Use the fact that a solid with a volume of 1000 cubic
centimeters has a capacity of 1 liter, along with
dimensional analysis, to convert the given unit to the unit
indicated.
53) 510.6 mL to cm3
148°
Objective: (9.2) Use English and Metric Units to
Measure Capacity
Use dimensional analysis to convert the given square unit
to the square unit indicated. Where necessary, round the
answer to two decimal places.
54) 13.1 ha to acres
Objective: (10.1) Solve Problems Involving Angle
Measures
61)
Objective: (9.2) Use Dimensional Analysis to Change
Units for Area
Selecting from milligram, gram, kilogram, and tonne,
determine the best unit of measure to express the given
weight.
55) a pocket calculator
56°
Objective: (9.3) Apply Metric Prefixes to Units of
Weight
Objective: (10.1) Solve Problems Involving Angle
Measures
Convert the given unit of weight to the unit indicated.
56) 165 mg to g
Objective: (9.3) Convert Units of Weight Within the
Metric System
The figure shows two parallel lines intersected by a
transversal. One of the angle measures is given. Find the
measure of the indicated angle.
62)
Use dimensional analysis to convert the given quantity to
the units indicated. When necessary, round answers to two
decimal places.
57) 860 lb to kg
Objective: (9.3) Use Dimensional Analysis to Change
Units of Weight to and from the Metric
System
40°
Convert the given Celsius temperature to its equivalent
temperature on the Fahrenheit scale. Where appropriate,
round to the nearest tenth of a degree.
58) 62°C
Objective: (9.3) Understand Temperature Scales
Find the measure of 1.
Objective: (10.1) Solve Problems Involving Angles
Formed by Parallel Lines and Transversals
5
Find the perimeter of the figure shown. Express the
perimeter in the same unit of measure that appears on the
given side or sides.
66)
15 yd
Find the measure of angle A for the triangle shown.
63)
12°
3.5 yd
5 yd
Objective: (10.2) Solve Problems Involving Angle
Relationships in Triangles
7 yd
Use similar triangles and the fact that corresponding sides
are proportional to find the length of the side marked with
an x.
Objective: (10.3) Solve Problems Involving a
Polygon's Perimeter
64)
18 m
8 yd
1.5 yd
Use the Pythagorean Theorem to solve the problem. Use
your calculator to find square roots, rounding, if
necessary, to the nearest tenth.
67) If you drive 9 miles south, then make a left
turn and drive 12 miles east, how far are you,
in a straight line, from your starting point?
27 m
Objective: (10.2) Solve Problems Using the
Pythagorean Theorem
14 m
21 m
Use formulas to find the area of the figure.
68)
0.13 cm
28 m
Objective: (10.2) Solve Problems Involving Similar
Triangles
0.07 cm
Use the Pythagorean Theorem to find the missing length
in the right triangle. Use a calculator to find square roots,
rounding, if necessary, to the nearest tenth.
65)
12 m
0.02 cm
0.07 cm
0.13 cm
Objective: (10.4) Use Area Formulas to Compute the
Areas of Plane Regions and Solve Applied
Problems
20 m
b
69)
Objective: (10.2) Solve Problems Using the
Pythagorean Theorem
10 in.
10.5 in.
15 in.
Objective: (10.4) Use Area Formulas to Compute the
Areas of Plane Regions and Solve Applied
Problems
6
Use the given right triangle to find the trigonometric
function.
74) sin B
Solve the problem.
70) What will it cost to tile a rectangular floor
measuring 229 feet by by 27 feet if the tile costs
$10 per square foot?
Objective: (10.4) Use Area Formulas to Compute the
Areas of Plane Regions and Solve Applied
Problems
Find the circumference and area of the circle. Round the
answer to the nearest whole number.
71)
Objective: (10.6) Use the Lengths of the Sides of a
Right Triangle to Find Trigonometric
Ratios
19 ft
Find the measure of the side of the right triangle whose
length is designated by the lowercase letter. Round your
answer to the nearest whole number.
75)
Objective: (10.4) Use Formulas for a Circle's
Circumference and Area
Find the volume of the figure. If necessary, round the
answer to the nearest whole number.
72)
a
30°
b = 130 cm
10 cm
Objective: (10.6) Use Trigonometric Ratios to Find
Missing Parts of Right Triangles
20 cm
Solve the problem.
76) At a certain time of day, the angle of elevation
of the sun is 64°. To the nearest foot, find the
height of a pole whose shadow at that time is
13 feet long.
Objective: (10.5) Use Volume Formulas to Compute
the Volumes of Three-Dimensional
Figures and Solve Applied Problems
73)
3m
64°
13 ft
Objective: (10.6) Use Trigonometric Ratios to Solve
Applied Problems
13 m
77) A kite flies to a height of 35 feet when 74 feet of
string is out. If the string is in a straight line,
find the angle that it makes with the ground.
Round to the nearest tenth of a degree.
7m
Objective: (10.5) Use Volume Formulas to Compute
the Volumes of Three-Dimensional
Figures and Solve Applied Problems
Objective: (10.6) Use Trigonometric Ratios to Solve
Applied Problems
7
79) The stem-and-leaf plot below displays the
ages of 30 attorneys at a small law firm.
78) Which one of the following is true according to
the graph?
Stems
4
5
6
7
8
9
Attorneys
99
00112589
1234458
1233458
0137
12
What is the age of the oldest attorney? What is
the age of the youngest attorney?
Objective: (12.1) Organize and Present Data
Find the mean for the group of data items. Round to the
nearest hundredth, if necessary.
80) 10, 5, 7, 6, 11, 3, 1, 7
Objective: (12.2) Determine the Mean for a Data Set
Find the median for the group of data items.
81) 10, 8, 4, 0, 2, 1, 2, 0, 0
A) More people had 4 years of education
beyond high school than 3 years.
B) If the sample is truly representative, then
for a group of 50 people, we can expect
about 32 of them to have one year of
education beyond high school.
C) The graph is based on a sample of
approximately 62 thousand people.
D) The percent of people with years of
higher education greater than those
shown by any rectangular bar is equal to
the percent of people with years of
education less than those shown by that
bar.
Objective: (12.2) Determine the Median for a Data Set
Find the mode for the group of data items.If there is no
mode, so state.
82) 99, 99, 92, 39, 70, 99
Objective: (12.2) Determine the Mode for a Data Set
Find the midrange for the group of data items.
83) 10, 7, 4, 7, 2, 4, 2
Objective: (12.2) Determine the Midrange for a Data
Set
Objective: (12.1) Organize and Present Data
Find the range for the group of data items.
84) 15, 18, 15, 18, 15, 18, 15, 18
Objective: (12.3) Determine the Range for a Data Set
Find the standard deviation for the group of data items (to
the nearest hundredth).
85) 9, 9, 9, 12, 15, 15, 15
Objective: (12.3) Determine the Standard Deviation
for a Data Set
8