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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

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.