MATH 101
FINAL EXAM REVIEW
College Algebra
The Final Exam is cumulative. The Final Exam is worth 125 points. Many of the problems will be similar to those
you have seen on previous quizzes and the midterm exam. You should review material from these items as well as
homework problems and this review.
Part I. Multiple Choice. The exam will have 10 multiple choice questions.
Part II. There will be 16 short answer questions. Analytical (algebraic) solutions are expected for partial credit.
Graphs should be clearly labeled.
The following questions represent important concepts covered in Math 101.
1.
Find and simplify the following:
(a)
(b)
(c)
2. Describe each transformation. Use the graph of
(a)
(b)
(c)
3. Graph the piecewise function:
(d)
(e)
given to sketch each transformation.
4. Use the graph to solve for
5. Graph the function
[Label the scale clearly.]
(a) What is the vertex?
(b) Over what interval(s) is
increasing?
(c) Over what interval(s) is
decreasing?
(d) Find the real zero(s) for
.
6. The profit that a vendor makes per day selling pretzels is given by the function
. Find the number of pretzels that must be sold to maximize the profit.
7. The height of a model rocket launched from a 112 foot cliff is given by
, where
is the time, in seconds, from when the rocket is launched. Find the maximum height the rocket attains
above the cliff.
8. Decide whether
is a factor of
9. Predict the end behavior of
10. For the polynomial function
Determine whether the graph of
11. Factor
.
.
, list the zeros and their multiplicities.
touches or crosses at each zero.
into linear factors given that 2 is a zero of
.
12. Use the Rational Zeros Theorem to list the possible rational zeros for
.
13. Give the equations for any vertical, horizontal, or oblique asymptotes of
(a)
(b)
(c)
14. Sketch a graph of
15. Solve each inequality analytically (sign test). Verify graphically.
(a)
(b)
16. Find the equation for the inverse of
(a) What is the domain for
(b) What is the domain for
.
?
?
17. (a) Write in logarithmic form:
(b) Evaluate:
(c) Evaluate:
18. Solve for :
19. Solve for :
20. Solve for :
21. Solve for :
22. Solve for :
23. Solve for :
24. Use properties of logarithms to express the following as a sum, difference, or product of simpler
logarithms:
.
25. Suppose $15,000 is invested at 3.25%. Find the total amount present at the end of 5 years if interest is
compounded (a) quarterly; (b) continuously.
26. If Tim has $1000 to invest at 7% compounded continuously, how long will it be before he has $1500? How
long before his investment is doubled?
27. If Seattle had a population of 2.3 million in 1990 and 1.75 million in 1950, use the continuous growth
model
to find the rate of growth and predict the population for 2015.
28. A sheet of heavy-duty cardboard measuring 40 inches by 30 inches is to be made into an open box by
cutting out equal-sized squares of side length
from each corner and folding up the sides.
(a) What are the restrictions on the values for ?
(b) Write a function , which will give the volume of the open box.
(c) Find the volume is a square that is 4.5 inches on a side is cut out.
(d) For what values of
will the volume be a maximum? What is the maximum volume?
Answers:
1. (a) 8
(b)
(c)
(d)
2. (a) The new graph is shifted 1 unit right and 2 units up. Key points:
(b) The new graph is a vertical shrink by a factor of . Key points:
(c) The new graph is reflected over the -axis. Key points:
3. Open circle on
and
4.
5.
(a)
(b)
(c)
(d)
(e) 1
6. 700 pretzels
7. Maximum height above the cliff: 144 feet
8. Yes;
9. Falls on the left (as
10. Crosses at
; falls on the right (as
(each multiplicity 1) and touches at
11.
(multiplicity 2)
or
12.
13. (a)
VA:
(b) VA:
(c) VA:
HA: none
HA:
OA:
OA: none
14.
VA:
HA:
15.
(a)
(b)
Shows Test
Shows Test
Critical Values:
Test Intervals:
Work:
Answer:
16.
17. (a)
(a)
(b)
;
(c)
(b)
18.
19.
20.
21.
22.
23.
24.
25. (a) $17, 635.14
(b) $17, 646.72
26. 5.79 years; 9.9 years
27.
28. (a)
(c)
(b)
cubic inches
(d)
inches,
cubic inches