James Madison University Algebra Property of Root Questions

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Algebra 2 Midterm Exam
Algebra II Midterm Exam
Name: _________________________
Score: ______ / ______
Answer the questions below. Make sure to show your work and justify all of your answers
1.
Simplify:
Show your work.
2. For the given quadratic equation convert into vertex form, find the vertex, and find
the value for x = 6. Show your work.
y = -2×2 + 2x +2
3. A manufacturer of shipping boxes has a box shaped like a cube. The side length is
(5a + 4b). What is the volume of the box in terms of a and b? Show your work.
Algebra 2 Midterm Exam
4. If a function, f(x) is shifted to the left four units, what will the transformed function look
like?
5. Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a
fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an
equation to find how many T-shirts the club needs to make and sell in order to profit at
least $100. Show your work.
6. The velocity of sound in air is given by the equation
, where v is the
velocity in meters per second and t is the temperature in degrees Celsius. Find the
temperature when the velocity is 329 meters per second by graphing the equation. Round
the answer to the nearest degree. Show your work.
7. The volume in cubic feet of a box can be expressed as
, or as the
product of three linear factors with integer coefficients. The width of the box is x-2.
Factor the polynomial to find linear expressions for the height and the length. Show your
work.
8. What is the solution to the equation
. Show your work.
Algebra 2 Midterm Exam
9. Solve the equation. Check for extraneous solutions. Type your answers in the blanks.
Show your work.
x = _____ or _____
10. Write an expression for the volume of a cylinder with a height 7in. greater than the
radius.
11. What is the value of log81 3? Show your work.
12. In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures
and then warmed again.
Time (hours)
0
1
2
3
4
5
6
Population (1000s)
5.1 3.03 1.72 1.17 1.38 2.35 4.08
Find a quadratic model for the data in the table. Type your answer below. Show your work.
13. Use the model from problem 12 to estimate the population of bacteria at 9 hours.
Type your answer below. Show your work.
Algebra 2 Midterm Exam
14. Evaluate the expression for the given value of the variable(s). Show your work.
15. Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your
work.
16. Simplify the expression. Type your answer in the blank.
–
17. Suppose you cut a small square from a square of fabric as shown in the diagram. Write
an expression for the remaining shaded area. Factor the expression. Type your answer
below.
Algebra 2 Midterm Exam
18. Is the relation {(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)} a function? Explain. Type your
answer below.
19. Evaluate
Show your work.
20. Consider the leading term of the polynomial function. What is the end behavior of the
graph? Describe the end behavior and provide the leading term.
-3×5 + 9×4 + 5×3 + 3
Name:
Algebra 2 Part 2 Final Exam
Directions: Answer the questions below. Make sure to show your work and justify all your
answers.
1. Bradley dropped a ball from a roof 16 feet high. Each time the ball hits the ground, it bounces
the
previous height. Find the height the ball will bounce after hitting the ground the fourth time.
(SHOW WORK)
2. The 2002 Denali earthquake in Alaska had a Richter scale magnitude of 6.7. The 2003 Rat Islands
earthquake in Alaska had a Richter scale magnitude of 7.8.
(SHOW WORK)
Suppose an architect has designed a building strong enough to withstand an earthquake 70 times as
intense as the Denali quake and 30 times as intense as the Rat Islands quake. Find which structure is
strongest. Explain your finding.
(SHOW WORK)
3. Assume that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The
growth in the sale of motorcycles is 16% every year and that of cars is 25% every year. Find when the
sale of cars will be more then the sale of motorcycles.
(SHOW WORK)
In a survey in 2010, the population of two plant species were found to be growing exponentially. Their
growth is given by these equations: species A,
and species B,
, where t = 0 in
the year 2010.
4. After how many years will the population of species A be equal to the population of species B in the
forest?
(SHOW WORK)
Name:
Algebra 2 Part 2 Final Exam
Directions: Answer the questions below. Make sure to show your work and justify all your
answers.
5. A raffle prize of
dollars is to be divided among 7x people. Write an expression for the amount of
money that each person will receive.
(SHOW WORK)
6. The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to
the temperature of the gas. If the pressure is 6 pounds per square inch when the temperature is
find
the pressure exerted when the temperature of the gas is
(SHOW WORK)
7. Blake and Ned work for a home remodeling business. They are putting the final touches on a home
they renovated. Working alone, Blake can paint one room in 9 hours. Ned can paint the same room in 6
hours. How long will it take them to paint the room if they work together?
(SHOW WORK)
8. A tourist boat is used for sightseeing in a nearby river. The boat travels 2.4 miles downstream and in
the same amount of time, it travels 1.8 miles upstream. If the boat travels at an average speed of 21 miles
per hour in the still water, find the current of the river.
(SHOW WORK)
Sandra swims the 100-meter freestyle for her school’s swim team. Her state’s ranking system awards 3
points for first place, 2 points for second, 1 point for third, and 0 points if she does not place. Her coach
used her statistics from last season to design a simulation using a random number generator to predict
how many points she would receive in her first race this season.
Integer Value
1-8
Points Awarded
3
Frequency
20
Name:
Algebra 2 Part 2 Final Exam
Directions: Answer the questions below. Make sure to show your work and justify all your
answers.
9 – 15
16 – 19
20
2
1
0
12
6
2
9. What is Sandra’s expected value of points awarded for a race?
(SHOW WORK)
A carnival game has the possibility of scoring 50 points, 75 points, or 150 points per turn. The probability
of scoring 50 points is 60%, 75 points is 30%, and 150 points is 10%. The game operator designed a
simulation using a random number generator to predict how many points would be earned for a turn.
Integer Value
0-5
6-8
9
Points
50
75
150
Frequency
55
32
13
10. What is game’s expected value of points earned for a turn?
(SHOW WORK)
11. A research company wants to test the claim that a new multivitamin helps to improve short term
memory. State the objective of the experiment, suggest a population, determine the experimental and
control groups, and describe a sample procedure.
(SHOW WORK)
Name:
Algebra 2 Part 2 Final Exam
Directions: Answer the questions below. Make sure to show your work and justify all your
answers.
A medical team sent surveys to randomly selected households to determine the various health problems.
The result of the survey is shown below.
Health Problems
Obesity
Diabetes
Heart problems
Eye problems
Dental problems
Number of Patients
32
54
78
112
96
Note: The survey result for each health problem is mutually exclusive.
12. Based on the survey, what is the probability that a person chosen at random is a diabetic patient or an
eye patient?
(SHOW WORK)
For a short time after a wave is created by wind, the height of the wave can be modeled using y = a sin
, where a is the amplitude and T is the period of the wave in seconds.
13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.
amplitude: 4, period
4
phase shift =
–
vertical shift = 2
14. Write an equation for the given function given the period, phase shift, and vertical shift.
cotangent function, period
phase shift
vertical shift
Name:
Algebra 2 Part 2 Final Exam
Directions: Answer the questions below. Make sure to show your work and justify all your
answers.
15. Use the unit circle to find the value of
and
.
16. Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and
Find the exact values of the five remaining trigonometric functions of θ.
(SHOW WORK)
17. Verify
is an identity.
18. Find all solutions of each equation on the interval
.
.
Name:
Algebra 2 Part 2 Final Exam
Directions: Answer the questions below. Make sure to show your work and justify all your
answers.
19. Solve
20. Verify
on the interval
.
.