This section does not have problems, paper assignments, or material in the text.
It will probably
take less than 20 minutes overall. Think of it like a TV show where you don’t
have to
remember anything specifically, but are just trying to understand and ap preciate
the plot . The
plot is based on some amazing aspects of exponents . You could skip it if you
really want to, but
I hope that some of you will listen to it and tell me what you think.
Overview, Chapter 6, Lessons 6.1 and 6.2:
1. Notice that this material is not in the textbook. The “textbook material”
for this section is on the web.
2. Because this material is covered so close to the end of the course, sometimes
students do
not study it enough to be able to do these problems correctly on the final exam.
Take the
paper homework on this section very seriously. If you need additional practice
problems,
ask your instructor.
6.1. In this material, focus more on multiplication and powers of powers .
Division and powers
of zero will be covered in more detail in the next course. I strongly urge you
to do several
problems where you write out all the factors so that you can see why the rules
about adding and
subtracting exponents work. See p. 255 for examples like this.
6.2 In this material, focus on addition, subtraction, and multiplication. The
material on
division will be covered in more detail in the next course.
Because there is more material in these lessons than you are expected to use on
the remaining
tests in this course, it is important that you use the paper assignments to help
guide you about
which particular types of problems you must learn. The portion of the Test 4
Review over this
material is more extensive than usual in order to give you an opportunity for
additional practice.
Now back to the textbook. The remaining two chapters are important for your
general
mathematical knowledge and skill for dealing with math in practical problems,
but not as crucial
for your success in algebra courses . Our text has more types of problems in most
of these
lessons than you are required to learn. Use the paper assignments as a guide to
the types of
problems you must learn to do.
Chapter F5.
1. You may use a basic calculator on Test 4 and the Final Exam.
2. This chapter has many facts and words with special meanings. Print the study
sheet for
this chapter, which is available from the supplements page. As you go through
the
chapter, when you have questions about what you should memorize, refer to that
study
sheet.
3. Here is the one chapter in the course where it is possible and an
excellent idea to
work on more than one lesson at once. Lesson F5.3 and later ones DO NOT
depend
on Lesson F5.2. So if you get stuck on Lesson F5.2, send in a question and go on
to
Lesson F5.3. Students who are working most efficiently in this course will
probably
work on Lesson F5.2 while they are doing about three or four more lessons.
4. You won’t be tested over all the parts of Lesson F5.3.
Read the notes here carefully.
Section 1:
1. Although there are many words and concepts in this section, the only one that
students
usually have to work at remembering is the difference between complementary and
supplementary angles.
Section 2:
1. It is most important not to get “stuck” on this lesson. Some of the
problems use the
formulas in a rather straightforward fashion. Other problems require two
different
insights – maybe two different formulas or maybe seeing one side as a part of
two
different figures. Those latter problems are harder for most students. Go
through one or
two of the harder ones. If you’re having trouble with them, write down a
question and
send it in and then skip the rest of the two-insight problems at first.
Just do the one-formula
problems in the rest of the software lesson. Then do the paper homework for the
more straightforward problems.
2. In this section, you will use formulas quite a lot. First, look at the study
sheet to
de termine which of them you must memorize. As you go through the section, write
those
on your study sheet. Try to think of a way to remember them that makes sense to
you.
3. When you are using a formula to do a computation, be sure to write the
formula, with the
variables. Then under it, substitute the numbers for the variables. Only after
that should
you do the calculation and write your answer.
4. Often you will obtain answers that have long decimals and look as if they
should be
rounded. Keep at least two or three decimal places in your final answer.
Sometimes formulas with the quantity “pi” in them will lead to “back of the book
answers” with “pi” and other times they will be given as decimals. Both can be
correct.
For example 4*pi = 12.56. Sometimes the problem will specify that you must give
the
answer as a decimal number. Other times it will not specify how the answer
should be
given and then either is fine.
5. Be sure to include the units (dollars, millimeters, square feet , etc.) in
your answers. If the
answer in the back of the book has units, yours should also.
6. Back to the two-insight problems. (Example: a problem asking for the
area of the
shaded region, where part of the figure is shaded and part isn’t.) If you have
sent in a
question, then I will be working with you individually about how much of this
you should
master before going on. While the two-insight problems are a part of this
course, they are
only a minor part. And, without help, it is easy for students to get stuck for a
week or so
on this material. There isn’t time for that. I will help you do as much of this
as is
practical for you to do and still stay caught up in the course.
7. In the homework, problem 133 has an error. The length labeled 7 in should be
6.24 in.
In the answer, the perimeter is correct as given, but the revised area is
rectangle plus two
semi circles plus two triangles: 4*6.24 + 2*[(1/2)* pi*(2*2)] + 2*[(1/2)*6.24*3]
= 56.24.
Section 3:
1. This lesson in the software includes MUCH more material than you will be
expected to
do in this course. Use the homework problems as a guideline to what you must
master. If
you are struggling with the software, then stop using it and try to do the
homework by
just reading the suggested examples and fol lowing them . Don’t try to do more
types of
problems here or you are likely to get stuck and frustrated. In particular,
don’t try to do
problems in subsections in which no homework was assigned and don’t use the
practice
test.
2. Lesson F5.3 DOES NOT depend on the material from F5.2. So you can go
on to it
even if you are still waiting for answers to some questions in F5.2.
Equations:
No new material on equations and word problems was assigned since Test 3.
However, since all
tests in this class are cumulative, material on equations will be included on
Test 4 and the Final
Exam.
Review Eq. 6 and Eq. 7, in particular.
