Math 140 – Precalculus Final
Exam Review
I. Expressions:
Simplify
each expression. Answers should be
COMPLETELY simplified.
(Remove
parentheses, lowest terms, positive exponents, simplest radical form,
rationalize denominators, etc.)
1. Simplify:
a. 
b. 
c. 
2. Simplify:
a. 
b. 
c. 
3. Factor
Completely:
a. 
b. 
c. 
d. 
4. Simplify:
a. 
b. 
c. 
d. 
5. Write
as a single trigonometric function:
a. 
b. 
II. Equations and
Inequalities:
Solve
the following equations, inequalities and systems of equations. Write the solutions to the inequalities using
interval notation and graph the solution set on a number line.
6. a. 
b. 
c. 
d. 
7. a. 
b. 
8. a. 
b. 
c. 
d. 
9. a. Solve on 
: 
b. Solve on : 
c. Solve on : 
10. Solve
the system:
a. 
b. 
c. 
III. Functions:
11. Given
the function 
.
a. Find
the domain of the function in interval notation.
b. Find the zero(s) of the function, if any
exist.
c. Find the y-intercept(s) of the function
if any exist.
d. Find the vertical asymptote(s), if any
exist.
e. Find the horizontal (or slant)
asymptote(s), if any exist.
12. Graph the exponential function
, then use transformations of this graph to graph 
. Please include a
written explanation as part of your work, using phrases like “shifted ___ units
to the ____”.
13. Given
the functions :
and 
a. Evaluate 
b. Find
c. Find
14. Given
the function: 
(a) Find the domain and range of the function.
(b) Determine if the function is 1-1.
(c) If the function is 1-1, find the inverse
of the function.
15. If 
and 
, find:
a. 
b. 
16. For the function 
find:
a. amplitude
b. period
c. find the phase shift of 
d. sketch a graph of one period of
17. For the function 
find:
a. amplitude
b. period
c. find the phase shift of
d. sketch a graph of one period of
IV. Applications:
18. The annual yield per walnut tree is fairly
constant at 50 pounds per tree when the number of trees per acre is 30 or
fewer. For each additional tree over 30,
the annual yield per tree for all trees on the acre decreases by 1.5 pounds due
to overcrowding.
a. Express the yield per tree, Y, in pounds,
as a function of the number of walnut trees per acre, x.
b. Express the total yield for an acre, T,
in pounds, as a function of the number of walnut trees per acre, x.
19. A closed rectangular box with a square base
has a volume of 8000 cubic centimeters.
Express the surface area of the box, A, as a function of the length of a
side of its square base, x.
20. You have 600 yards of fencing to enclose a
rectangular field, and the separate the field into two pens by running fence
parallel to one of the sides. Express
the area of the enclosed field, A, as a function of one of its dimensions, x.
21. A power company would like to run a
high-voltage power line across a canyon.
It must extend from point A on the south side of the canyon to point C
on the north side. A surveyor has marked
point B on the south side of the canyon 100 feet from point A and has
determined that 
and 
. What is the minimum
length of power line that will be needed?
22. Two ships leave port at the same time. One travels in the direction N 35° E at a rate of 25 miles per
hour. The other travels in the direction S 70°
E at a rate of 30 miles per hour. How
far apart are the ships after 90 minutes?
23. The scatter plot below shows corporate
profits, in billions of dollars, from 1990 through 2000. Also shown is the line that passes through or
near the points.
a. Use the two points whose coordinates are
shown to find the point-slope equation of the line that models corporate
profits, y, in billions of dollars, x years after 1990.
b. Explain what the slope of the line you
found in part (a) represents in terms of the context of the situation.
24. Suppose that $1000 is deposited into an
account paying 8.25% interest compounded quarterly. How long will it take to reach a balance of
$10,000?
Math 140 – Precalculus Final
Exam Review Answer Key
|
1. a. b.
c. |
8. a. b. c. d. |
|
2. a.
b.
c. |
9. a. b. c. |
|
3. a. b. c.
d. |
10. a. b. c. |
|
4. a. b. c.
d. |
11. a. so: b. c. d. e. |
|
5. a.
b. |
12.
See graphs on last page. |
|
6. a.
b.
c.
d. |
13.
a.
b. c. |
