Name: ________________________
Algebra III / Functions Practice Final
1.) What is the supplement of a 51° angle?
2.) The measure of the angle is 10° more than four times its complement. Find the measure of both angles
described.
3.) The bottom of a 30 foot ladder is 8 feet from the base of a building. If the top of the ladder is resting
against the top of the building, how tall is the building?
Use the following diagram to answer questions 4-7.
2
142°
3
1
4
4.) 𝑚∠1 = ?
5.) 𝑚∠2 = ?
6.) 𝑚∠3 = ?
7.) 𝑚∠4 = ?
8.) What is the volume of a basketball with radius 6 inches? Round answer to the nearest tenth.
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Use the following triangle to answer questions 9-13.
α
8
θ
9.) cos 𝜃 = ?
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10.) sin 𝛼 = ?
11.) tan 𝜃 = ?
12.) 𝜃 = ?
13.) 𝛼 = ?
14.) A kite’s string is 74 feet long when it makes a 72° angle of elevation with the ground. How high is the
kite?
15.) A pelican is flying over the ocean at a height of 50 feet. It spots a fish swimming on the surface of the
water with an angle of depression of 15°. What is the actual flying distance that the pelican will have to
fly to get the fish?
16.) At Baskin Robbins, you have the choice of ordering your ice cream in a cone or a dish, you can pick any
one of their 31 ice cream flavors, and you can choose any one of their 10 toppings. How many different
one-topping ice cream orders can be placed?
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17.) You are going to arrange your ten favorite books on a shelf. How many different orders can you make, if
you are ranking them from favorite to least favorite?
18.) How many different ways can you arrange the letters in the word TENNESSEE?
19.) Student Council has 50 members. How many different ways are there for them to elect a president, vicepresident, secretary, and treasurer?
20.) There are seven people on a board of directors. How many different ways can a three-person committee
be formed?
21.) Two dice are rolled and their values are added together. What is the probability of rolling a 9?
22.) If one card is randomly selected from a standard 52-card deck, what is the probability of picking a black 7?
23.) A committee consists of seven men and eight women. Four people are selected to attend a conference.
What is the probability that three men and one woman are picked to attend the conference?
24.) If one card is randomly selected from a 52-card deck, what is the probability of not selecting a face card?
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25.) A cooler contains 10 pepsis, 6 mountain dews, 9 sprites, and 13 waters. If one drink is selected at random,
what is the probability that you select a pepsi or a water?
26.) In a group of 100 students, 63 students take a math class, 52 students take a science class, and 35 students
take both a math and a science class. If one student is selected at random, what is the probability of
selecting a student that takes math or science?
27.) If a fair coin is flipped 10 times, what is the probability of getting tails all 10 times?
28.) A cooler contains 10 pepsis, 6 mountain dews, 9 sprites, and 13 waters. If three drinks are randomly
selected one at a time, what is the probability of selecting two sprites and a pepsi?
29.) A letter is randomly selected from the English alphabet. What is the probability of selecting a vowel,
given that the outcome is after the letter l and is before the letter x?
30.) You are dealt one card from a standard 52-card deck. What is the probability that you are dealt a heart,
given that you are dealt a red card?
31.) In the equation y 
12
, if x becomes one –fourth of its original value, what happens to y?
x
32.) What is the equation of the line that passes through the points (6, –3) and (4, –12)?
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33.) A tiger population obeys the logistic model of growth shown below, where P is the population of the black
bears at time t. P 
15,200
.
20  24e  4t
What is the eventual size of the population?
34.) Solve the quadratic equation ( x  4) 2  25.
35.) Find the solution of the system of equations x  2 y  4 and 2 x  3 y  1.
36.) Name an integer example of an acute angle.
37.) Using the Triangle Inequality Theorem, can a figure with sides 7 in., 6 in., and 4 in. form a triangle?
38.) What is the equation of the line that passes through the point (6, 15) and is perpendicular to the line
y = 3x + 8?
39.) List the angles from greatest to least using the figure to the right.
40.) A circle has an area of 52 square centimeters. Find its radius.
For questions 41-43, determine the total cost, including tax and discount (if applicable) of the given item
if it was bought in Pennsylvania.
41.) $29,500 car at 2% off
42.) $800 dress at 4.5% off
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43.) $300 iPod at 10% off
44.) You deposit $12,500 in a simple interest savings account that has a rate of 2.75%. How much interest will
you make after 12 years?
45.) If you currently have $2,500 to invest and your future value needs to be $4,800 in a year, what simple
interest rate do you need to get in order to make this happen?
46.) How much should you put in an investment paying a simple interest rate of 3.1% so the future value in
eight months is $10,000?
47.) A total of $11,800 is invested at 9%. Find the balance after 15 years if it is compounded monthly.
48.) A total of $3,250 is invested at 2%. Find the balance after 5 years if it is compounded continuously.
49.) How much time is necessary for $8,765 to double if invested at 8.5% compounded quarterly?
50.) How much time is necessary for $1,110 to triple if invested at 6% compounded continuously?
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