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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  
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.