Precalculus—Final Exam Review
Chapter 1
1) Find the domain of the function
.
2) What transformation must be applied to the graph of
? Sketch the graphs of
and
to obtain the graph of
.
Chapter 2
3) Find the solution(s) of the equation
.
4) Find the solution(s) of the equation
5) Find the solution set of the compound inequality
interval notation and plot the solution set on a number line.
. Give your answer in
6) Find the solution set of the inequality
7) Simplify the following complex number to the form
, where
and are real numbers:
Chapter 3
8) Consider the function
a. What is the leading coefficient?
b. What is the degree?
c. As the graph goes to the right, does it go up or down?
d. As the graph goes to the left, does it go up or down?
e. What does the Intermediate Value Theorem tell us about whether
zeros between 0 and 2? between 0 and 4?
f. Find the intercepts of the graph of
.
g. Sketch the graph of
, labeling as appropriate.
9) Find the intercepts and asymptotes of the rational function
and then sketch its graph.
has any
10) Find the solution set of the inequality
write it in interval notation, and plot it on a number line.
Chapter 4
11) Find the inverse of the function
.
12) Plot the graph of the function
just by looking at the graph of .
13) Plot the graph of
, and then plot the graph of its inverse function
.
14) Plot the graph of
.
15) Compute:
a.
b.
c.
16) Solve:
a.
b.
17) Expand:
18) Simplify:
Chapter 5
19) If
and is in the third quadrant, find the values of the other five trigonometric
functions for the angle .
20) Compute
21) Plot the graphs of
22) Plot the function
,
,
.
and
on the same axes.
Chapters 6, 7
Study Test 4 and Quiz 5
Chapter 10
23) Find an explicit formula for the th term
24) Evaluate the sum:
of the sequence
.
25) Find an explicit formula for the th term
12th term 40.
of the arithmetic sequence with 1st term 7 and
26) Find the sum of the first 10 terms of the sequence in problem 6.
27) Consider the geometric sequence
. Find the sum of the first 6 terms and
the sum of all of the terms.
28) Find fraction notation for
.
29) How many 4-letter words can be made out of the letters abcdefg with no repetition of
letters? with repetition allowed? using exactly the letters aabbbc?
30) How many ways can 2 soccer teams be chosen for a match out of 10 total teams?
31) What is
32) What is the probability of getting either 3 or 4 heads when flipping a coin 5 times?