College Algebra Final Exam Review
Critical Thinking:
1.
Perform the indicated operations and simplify: (Chapter 0)
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2.
Find the equation of the line which passes through the point (-7 , 5) and is perpendicular
to the line -3x + 3y = 7. Express your answer in slope-intercept form. (Chapter 2)
3.
Use synthetic division or polynomial division to find all solutions in the real numbers of
the equation (Chapter 4)
- 16= -4 + + 12.
4.
and g() = (Chapter 3)
a. Find a formula for the composition (f ◦ g)(). Express the composition in simplified
form, i.e. not as a complex fraction.
b. Find the domain of the composite function (f ◦ g)().
Quantitative Literacy:
1. How many cups of grapefruit juice must be added to 30 cups of a punch that contains
8% grapefruit juice to obtain a punch that is 10% grapefruit Juice? (Chapter 1)
2. The length of a rectangle is 4 centimeters more than its width. If the width is increased
by 2 centimeters and the length is increased by 3 centimeters, a new rectangle is formed
that has an area of 44 square centimeters more than the area of the original rectangle.
Find the dimensions of the original rectangle. (Chapter 1)
3. The formula A = P1 is used to determine how much money will be present if P
dollars are invested in an account bearing compound interest n times per year for t
years. r is the interest rate expressed as a decimal number. For example, r = 0.25 if the
interest rate is 25%. Find the amount of money present after 40 years if $2000 is
invested into an account bearing 1.2% interest compounded monthly. (Chapter 1)
4. Three points A,B,C, in the xy-plane have coordinates A(8 , -3), B(-6 , 2), C(-8 , -3).
Determine whether triangle ABC is a right triangle. (Chapter 2)
Ethics:
1. In the year 2000, Anna bought a new car for $28,000. In 2005,
she was told that the value of her car was $18,000 due to
depreciation. She is told that the value of her car depreciates
linearly.
a. Find a function V(t) which gives the value of the car t years after the year 2000.
b.In 2008, Anna is told that she will be given $6000 for her car if she decides to trade it in
for a new car. Use the function from part (a) above to determine the value of her car
in 2008.
c. Is the $6000 value fair based on what she was told about linear depreciation? Explain
your answer. (Chapter 2)
2. Two cities are located in the xy-plane at the points A(8 , 9) and B(1 , 7). A company
wishes to place a factory on a road between the cities at A and B. It is determined that
the company can make the most money if it places the factory exactly halfway between
A and B. However, due to environmental hazards produced by the factory, it is safe for
the people living in A and B only if the factory is located exactly ⅓ of the distance from
A going toward B. Find the coordinates of the point where the factory should be placed
to ensure the most ethical outcome. Explain your decision. (Chapter 2)
3. An insurance company states in its automobile insurance policy that in case of an
accident, it uses the formula
P = ( - )(
)
to determine how much to reimburse a policyholder, where is the value of the car at
the time of the accident and is the age of the person driving. The policyholder must
sign a document indicating agreement with this procedure for determining
reimbursement amounts. Joe, a 35 year old policyholder, was driving his car when he
had an accident. The car was valued at $2500 at the time of the accident. The insurance
company sends him a check for $50.84. Use the formula above to find the amount he
should have been reimbursed. Should Joe contact the insurance company and report this
mistake? (Chapter 2)
4. Safety regulations state that it is not safe for a nuclear power plant to be located within
10 miles of any living space. In a certain town, houses are located at A(14 , 5), B(1 ,
13), and C(13 , 0) in the xy-plane. A company places a power plant at the point P(1 , 7).
Use the distance formula to determine if the company was ethical in its choice of
location for the power plant. (Chapter 2)
Written communication:
1. Write a paragraph explaining how to find the equation of a line if you know two points that
are on that line.
2. Write a paragraph explaining how the Pythagorean Theorem, the distance formula, and the
equation of a circle are related in finding distances.
3. Explain the method of completing the square.
4. Explain the exponent rules.