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Precalculus I
Welcome to Precalculus
The focus of this two quarter sequence is the study of the elementary functions
and their
graphs, and to provide a good foundation for the study of calculus. The course
is the
first half of a pre-calculus sequence which continues with Precalculus II (Math
142). After
a general introduction to functions, we’ll look at polynomial functions and the
theory of
equations, rational functions, an introduction to exponential & logarithmic
functions, and
right-triangle trigonometry. The course will probably make more sense if you can
read or
at least browse through the relevant sections of the book before each class.
Generally we’ll
cover a section of the book in one to two days.
Keeping up with the new concepts through homework exercises is essential to
success in the
course. I will not collect homework exercises from the book, but we will spend
class time
discussing the exercises. I may collect some additional homework exercises.
There will be
short quizzes about once a week.
I’m planning to give two tests and a final exam. The final exam will contain a
section on
right-triangle trigonometry and a part covering test one and test two material.
Some of the
tests may have a take-home part. There will be an opportunity to make-up one
test by the
way I score the final exam. I look at each section of the comprehensive final (a
test one part
, a test two part , etc. ) and look to see on which section you have improved
the most. If
you have, for example, improved the most on the test two part of the final exam,
then the
score on the test two portion of the final replaces your original test two
score. Of course, if
the final exam scores are all lower, your original test scores are left
unchanged.
what you’ll need
book: “Precalculus, Concepts Through Functions, A Right Angle Approach To
Trigonometry”,.
by Michael Sullivan & Michael Sullivan III, Pearson/Prentice Hall, 2007
prerequisite: completion of Intermediate Algebra (Mathematics 098) or
placement.
calculator: You will need a scientific calculator. Graphing calculators
are not required.
please turn off the sound on all cellphones, pagers, etc. during class
grades
Each of the two tests will be worth 100 points. The final exam will count as 150
points (
one hundred points for the test one and test two material, and fifty points for
the rightangle
trigonometry material). The weekly quiz will be scored at 15 points. I will drop
the
lowest quiz score. Collected homework assignments will be scored between 5 and
30 points
depending on length. The course grade is based on a percentage which may be
calculated
at any time. Add together all your points. Then divide by the sum of the
possible points.
Multiply by 100 for the course percentage. Course grades are then determined by
the
following scale:
| 93% and up |
3.9 or 4.0* |
| 90% |
3.8 |
| 80% |
3.0 |
| 70% |
2.0 |
| 60% |
1.0 |
| 50% |
0.7 |
| under 50% |
0.0 or NC |
* A course percentage of at least 93%,
and a score of at least 90% on each test
earns a 4.0.
Other grades are linearly interpolated. For example, a score of 85% corresponds
to a grade
of 3.4.
test dates
| test 1 |
Tuesday, February 3 |
| test 2 |
Tuesday, March 3 |
| final exam |
Tuesday, March 24
8–10 a.m. |
course outline
naturally the schedule is approximate
Distance Formula, Graphs, and Circles
| Mon Jan 5 |
distance formula
midpoint formula |
F1 |
19, 23, 27, 31, 39, 43, 45, 55 |
| Tue Jan 6 |
graphs of equations |
F2 |
15, 19, 23, 29, 31, 39, 41, 45, 51, 53,
57, 59, 65, 69 |
| Wed Jan 7 |
circles |
F3 |
7, 9, 11, 15, 19, 21, 23, 27, 33, 37, 39, 49 |
Functions and Graphs
Thu Jan 8
Fri Jan 9 |
functions |
1.1 |
5, 7, 11, 15, 17, 19, 25, 27, 31, 32, 39,
45, 47, 51, 55, 63, 68, 73, 75, 85, 91, 99 |
Mon Jan 12
Tue Jan 13 |
graphs of functions |
1.2 |
3, 4, 6, 9,11, 13, 16, 19, 23, 25, 37 |
Tue Jan 13
Wed Jan 14 |
properties of
functions |
1.3 |
1–5, 8, 10, 11–20, 21, 25, 27, 31, 35, 37,
39, 44, 53, 61, 63a–c |
Thu Jan 15
Fri Jan 16 |
library of functions
piece-wise defined
functions |
1.4 |
4, 6, 9–23, 25, 27, 29, 35, 41, 43, 45, 65 |
Fri Jan 16
Tue Jan 20 |
graphing using
shifts, stretches, &
reflections |
1.5 |
1, 7–31 odd, 35, 37, 39, 42, 45, 53, 56,
63, 65, 77, 83 |
| Wed Jan 21 |
constructing
functions–math
models |
1.6 |
1, 3a,b, 7a,b, 9a,b,c, 13, 15a,b, 17a,b,
19a,b, 23, 27a, 29, 31 |
Linear, Quadratic, Polynomial & Rational Functions
| Thu Jan 22 |
linear functions |
2.1 |
2, 6, 7, 9–12, 13, 15, 17, 27, 29, 33, 37,
41, 47, 51, 53, 59 |
absolute value
function |
2.8 |
7, 8, 12, 13, 19, 35, 47, 49, 55, 59, 63,
65 |
Fri Jan 23
Mon Jan 26 |
quadratic functions |
2.3 |
7–9, 11, 17, 21, 27, 31, 33, 37, 41, 53,
59, 65, 69, 75, 85, 89, 93 |
Mon Jan 26
Tue Jan 27 |
quadratic function
graphs |
2.4 |
5, 6, 9, 11–17 odd, 21, 27, 31, 33, 37,
41, 47, 53, 55, 61, 65, 67, 71 |
Wed Jan 28
Thu Jan 29 |
quadratic function
models |
2.6 |
3, 5, 7a,b,c, 15, 19, 21, 23, 27, 35 |
| Fri Jan 30 |
complex zeroes of a
quadratic function |
2.7 |
3, 4, 6, 7, 9, 13, 21, 23, 25, 27, 29, 31 |
| Mon Feb 2 |
review |
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| Tue Feb 3 |
test one |
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Wed Feb 4
Thu Feb 5 |
graphs of
polynomials |
3.1 |
2, 8, 9, 11–19 odd, 25, 27, 33, 35, 39,
43, 45, 49, 55, 57–60, 62, 63, 67, 69,
73, 79, 85, 87, 108 |
Fri Feb 6
Mon Feb 9
Tue Feb 10 |
graphs of rational
functions |
3.2 |
5, 6, 13, 15, 21, 23–29 odd, 31, 35, 38,
41, 43, 47, 51, 54 |
| Wed Feb 11 |
polynomial &
rational inequalities |
3.3 |
3–6, 7, 9, 15, 19, 29, 35, 41, 47, 49a,b,
53a |
Thu Feb 12
Fri Feb 13
Tue Feb 17 |
real & complex
zeroes of
polynomials |
3.4 |
3, 5, 9, 13,17, 21, 29, 33, 35, 45, 49, 51 |
| 3.5 |
5–8, 11, 13, 21, 25, 29, 33, 39, 45, 47,
49, 55, 57, 59, 65, 69, 73, 83, 85, 89, 95 |
| 3.6 |
2–7, 9, 13, 21, 23, 27, 31, 35, 37 |
Exponential and Logarithmic Functions
Wed Feb 18
Thu Feb 19 |
composition of
functions |
4.1 |
4, 5, 7, 9, 11, 17, 21, 27, 29, 31, 35, 39,
43, 44, 45, 47, 49, 53, 55, 63, 73 |
Thu Feb 19
Fri Feb 20 |
inverse functions |
4.2 |
1, 4, 6, 7, 9, 11, 19, 21, 25, 27, 31, 33,
37, 41, 45, 49, 51, 55, 57, 65, 71, 75,
99, 100 |
Mon Feb 23
Tue Feb 24 |
exponential
functions |
4.3 |
1, 3, 6, 8, 11, 19, 21, 23, 25, 31, 35, 37,
41, 43, 47, 49, 55, 57, 59, 63, 69, 71,
75, 79, 83, 89, 91, 101, 111 |
Tue Feb 24
Wed Feb 25 |
logarithmic
functions |
4.4 |
4, 5–19 odd, 23, 25–31 odd, 35, 37, 41,
45, 47, 49, 51, 55, 57, 59, 63, 69, 71,
74, 85, 87, 89, 91, 93, 99, 103, 109,
113, 115, 121b,c,d,e, 125 |
Thu Feb 26
Fri Feb 27 |
logarithm properties |
4.5 |
1, 4, 6, 7, 9, 11, 12, 15, 19, 23–37 odd,
41, 47, 51, 53, 59, 63, 65, 71, 79, 81,
87, 95, 98, 101 |
| Mon Mar 2 |
review |
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| Tue Mar 3 |
test two |
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Trigonometry
| Wed Mar 4 |
geometry review |
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Mon Mar 5
Tue Mar 6 |
radian measure of
angles |
5.1 |
1–3, 11, 13, 14, 15, 23, 31, 35, 39, 43,
47, 49, 51, 61, 67, 71, 75, 77, 79, 89,
91, 99, 101, 114, 115 |
Mon Mar 9
Tue Mar 10 |
right-triangle
trigonometry |
5.2 |
3, 5, 6, 9, 11, 13, 19, 21, 27, 29, 35, 37,
39, 43, 47, 51, 55, 57, 63, 73 |
| Wed Mar 11 |
trigonometric exact
values |
5.3 |
1, 5, 6, 7–13 odd, 17, 21, 23, 25, 27, 29,
33, 38, 41, 43, 51, 55, 59, 61, 67, 71 |
| Thu Mar 12 |
right triangle
applications |
7.1 |
5, 8, 9, 19, 23, 25, 27a, 29, 31, 34 |
Fri Mar 13
Mon Mar 16 |
trigonometric
identities |
6.3 |
1, 4, 9–19 odd, 23, 25, 29, 35, 41, 45,
51, 61, 71, 75, 85, 95 |
| Tue Mar 17 |
law of sines |
7.2 |
3, 8, 9–23 odd, 25, 29, 35, 37, 39, 41, |
| Wed Mar 18 |
law of cosines |
7.3 |
3–9, 11, 13, 17, 23, 33, 47 |
Thu Mar 12
Fri Mar 13 |
review |
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| Tue Mar 24 |
final exam
8-10 a.m. |
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