Final Exam Study Guide
November 27
Final Exam time and location:
Wednesday, 12/18/2013 at 3:30PM - 5:30PM in JTB 140
Notice this location is not in the same classroom in which we have lecture.
The study guide is divided into three parts. The first presents study tips.
The second lists sections. Review this list and prioritize the sections for
you to study. The last part is extra problems. They are collected from the
text across sections and gathered in one place.
It is likely there will be questions on the Final Exam that are not exactly
from Part Three. I am confident the skills used in various sections will aid
you in answering them. As additional practice, review your quizzes and
exams.
Part One - General Study Tips
When to study: In short, begin studying well in advance for the final.
You want to allow yourself time to answer questions prior to the exam
and avoid procrastination. Remember that this class is 100% solving exercises. That in mind, it would be helpful to reserve time from each day
to regularly solve problems from the book. As a rule of thumb, the University recommends 2 - 3 hours of study per week for each credit hour.
This is a 4 credit hour class, totalling 8 - 12 hours per week. I recommend
at least 30 minutes each day during the week of December 2, at least 60
minutes each day during the week of December 9th, and gradually increase
time up to the exam date. Reserve these minutes for the Final Exam alone.
For the rest of the time each day, you ought to focus on the current lessons.
How to study: These brief tips may enhance your current study habits.
This section is not meant for replacing skills you already have, but because
the final exam is the last part of the class, you may have to use something
new.
The textbook has very good study tips at the beginning of every chapter.
Chapter 10 (which is not on our curriculum) has helpful tips at this time.
(page 654) This is titled, ”Avoid Test-Taking Errors.” Here are three useful
tips, (1) read test instructions carefully, (2) check for careless errors like
carrying a (plus or minus) sign, directions of > or < signs, etc, (3) check
for concept errors. Using previous quizzes and exams are useful for this
last step, and try to get someone else - a tutor, me, or another student to watch your problem solving process.
Each of the chapters have very good study summaries. Take some time
to read them, and try out ideas that you like. Above all, however, keep
using study skills that you have been using, and you know work well for you.
What to study: Apart from the given problems below, treat the book’s midchapter and chapter exams, our past quizzes, and past exams as a source
for additional content. It is helpful to also build a checklist of topics and
prioritize what to study. The textbook offers sections called, ”What Did
You Learn?” if you want help getting started.
Part Two - List of Topics
Use the list below to priortize what parts to study. I recommend reading
through, ”What You Should Learn” at the very beginning for each section.
These points are numbered, so write down each number and a symbol to
indicate how much you need to review it.
§1.1 - 1.5; §2.1, 2.2, 2.4, 2.5; §3.1 - 3.4, 3.6, 3.7; §4.1, 4.2; §5.1 - 5.6; §6.1
-6.3, 6.6; §7.1 - 7.4, 7.6; §8.1 - 8.3, 8.5; §9.1 - 9.6
Example: (p 107) §2.5 What You Should Learn
1. Solve absolute value equations.
2. Solve inequalities involving absoute values.
Your study notes: §2.5
1. B - study an example or two
2. A - this showed up often on tests and quizzes, study many examples
Part Three - Practice Problems
Very Important: These problems will not be the only types on the final exam, and you must study outside this list in order to do a complete
review. Remember this is a guide; the above tips will help round out the
rest of the review.
1. Find two possible values for a: |a − 3| = 7.
2. Evaluate the expression for the specified values:
(i) −(x − 2)2 + 8 for x = 0, 1, 2, 3, 4.
x
(ii) x−y
for (a) x = 0, y = 10, (b) x = 2, y = 2.
3. Simplify:
(i) 43 (2x − 6) − 5x + 6
(ii) x2(x − 5) − 4(4 − x)
4. There are 255 members of a club. In a recent election, p% of the members voted. Write an expression for the total number of members that
did not vote.
5. Solve for the variable, if there is exactly one solution. If not, describe
the solution.
x
(i) 18
+ 3x
4 = 2
(ii) −5(t − 10) = 6(t − 10)
(iii) 4(2y − 3) = 8y − 12
6. Determine which values are solutions to the inequality:
5x − 18 > 0
(i) x = 83
(ii) x = 5
(iii) x = 3
(iv) x = 18
5
7. Solve the inequalities:
(i) 12 − 5x ≤ 5
(ii) |x − 2| > 27
8. Solve the equations, if solutions exists:
(i) |4 − x| = −2
(ii) 5x − 3 = −3(4 − x)
9. Find the distance between the points (0, 43 ) and (5, − 32 )
10. Sketch a graph of the equation y = |x + 2|. Label at least 5 points.
11. Write the equation of the line through (10, 21 ) and ( 23 , 47 ).
12. Sketch a graph of the function and give the domain.
g(x) =
√
x+2−1
13. Solve the systems of equations. Note if the systems are consistent or
inconsistent.
(
12x − 5y − 2 = 0
(i)
10y − 6
= 25x
(
4x + 3y = 6
(ii)
x − 6y = −5
14. Simplify the rational expression. Write the domain.
x2 − 36
(i)
6−x
x3 − 4x
(ii) 2
x − 5x + 6
15. Solve the rational equations.
1
8
7
−
=
x 3x 3
3x
4
+
=3
(ii)
x−2 x+1
3x
12
(iii)
= 2
+2
x+1 x −1
(i)
16. Simplify the radical expressions.
p
(i) 3√48x4y 3
3
128x2
(ii) √
4 3 2x
8
(iii) √
18
3
(iv) √
12b3
√
√
17. Subtract: √200y − 3 8y
√
Subtract: 25x + 50 − x + 2 √
√
√
Multiply and simplify: (3 x + 4)( 7 − x)√
x−5
Rationalize the denominator and simplify: √
2 x−1
18. Solve the quadratic equations.
(i) 10x − 8 = 3x2 − 9x + 12
(ii) (y − 12)2 + 4 = 0
(iii) x4 − 10x2 + 9 = 0
(iv) u2 − 5u + 2 = 0
19. Plot the functions.
(i) g(x) = 3x − 1
(ii) h(x) = 5 − 2 log x
20. Solve the equations, if possible. Otherwise state why there may be not
solution.
(i) log5 x + 3 − log5 x = 1
(ii) 6x = 216
(iii) 50 − 5ex+2 = 35