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 | ||
| Tue Feb 3 | test one | ||
| 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 | ||
| Tue Mar 3 | test two |
Trigonometry
| Wed Mar 4 | geometry review | ||
| 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 | ||
| Tue Mar 24 | final exam 8-10 a.m. |