Precalculus Mathematics
I. Course Description
This is a 4credit hour course. The prerequisite for this course is qualification
through
placement. The material for this course is precalculus: equations and
inequalities, functions and
their graphs, exponential and logarithm functions, polynomial and rational
functions,
trigonometric functions and analytic trigonometry. Students may not receive
credit for both Math
111 and Math 115 or both Math112 and Math 115.
Goals and Learning Outcomes
The overall goal of Math 115 is to make students understand mathematical
concepts using
real-world data and questions. The measurable learning outcomes
used to determine the
degree to which this goal is being met follow:
Students will solve linear and quadratic
equations.
Students will review the Cartesian plane: they will calculate the distance and
midpoint
between two points.
Students will plot graphs of equations.
Students will be able to determine if a relationship is a function, if
functions are one-to-
one, graph functions, and perform operations and
composition of functions.
Students will divide polynomials using both long and synthetic division.
Students will factor polynomials, determine zeros of polynomials and graph
polynomial
and rational functions.
Students will graph exponential functions and their inverses, logarithmic
functions.
Students will use their properties to solve exponential and logarithmic
equations
Students will define trigonometric functions three ways.
Students will graph trigonometric function and solve applications involving
trigonometric functions.
Students will verify trigonometric identities and solve trigonometric
equations.
III Overall Structure of the Course:
1.1
Linear Equations
1.2
Applications Linear Equations
1.3
Quadratic Equations
1.4
Radical Equations
1.5
Linear Inequalities
1.6
Polynomial and Rational Equations
1.7
Absolute Value Equations and Inequalities
2.1
Cartesian Plane, Distance and Midpoint
2.2
Graphing Equations
2.3
Straight Lines
2.4
Circles
3.1
Functions
3.2
Graphs of Functions
3.3
Transformations
3.4
Operations with Functions and Composition
3.5
One-to-one Functions and Inverse Functions
4.1
Quadratic Functions
4.2
Polynomial Functions of Higher Degree
4.3
Dividing Polynomials
4.4
Zeros of Polynomial Functions
4.5
Rational Functions
5.1
Exponential Functions
5.2
Exponential Functions with Base e
5.3
Logarithmic Function
5.4
Properties of Logarithms
5.5
Exponential and Logarithmic Functions
6.1
Angles, Degrees, and Triangles
6.2
Definition 1 of Trigonometric Functions: Right Triangle Ratios
6.3
Solving Right Triangles
6.4
Definition 2 of Trigonometric Functions: Cartesian Plane
6.5
Trigonometric Functions of Nonacute Angles
6.6
Radian Measure and Applications
6.7
Definition 3 of Trigonometric Functions: Unit Circle Approach
6.8
Graphs of Sine and Cosine Functions
6.9
Graphs of Other Trigonometric Functions
7.1
Basic Trigonometric Functions
7.2
Verifying Trigonometric Identities
7.3
Sum and Differences Identities
7.4
Double-Angle Identities
7.5
Half-Angle Identities
7.6
Product-to-Sum and Sum-to –Product Identities
7.7
Inverse trigonometric Functions
7.8
Trigonometric equations
8.1
Law of Sines
8.2
Law of Cosines
8.3
Area of a Triangle
VII Assessment and Grading
| Activity | Value |
| Daily Activities (homework, quizzes) | 30% |
| 3 Chapter Tests | 15% each (45% total) |
| Final Exam | 25% |
To get your final average in the class, do this:
.30(your daily activity points/total number of points) + .15(all your test
points) + .25(your final exam grade)
Grades
Grades
| If your final average is . . . | You will receive this grade in the course. . . |
| 90 through 100 | A |
| 85 through 89 | B+ |
| 80 through 84 | B |
| 75 through 79 | C+ |
| 70 through 74 | C |
| 65 through 69 | D+ |
| 60 through 64 | D |
| 0 through 59 | F |
VIII Course Schedule
We’ll do our best to stick to this schedule, but we may get ahead or behind,
depending on
how well the class understands the material. Homework is due by 11
pm on the Due Date. All
homework will be completed on WileyPLUS.
| Monday | Tuesday | Wednesday | Thursday |
| 8/20 Classes Begin Introduction (syllabus,WileyPLUS) Section 1.1 |
|||
| 8/24 Section 1.2
|
8/25 Section 1.3
|
8/26 Section 1.4 Last day to register, change a schedule or drop a course without a grade of "W" |
8/27 Section 1.5 Due: Assignment Zero and sections 1.1, 1.2, 1.3 |
| 8/31 Section 1.6
|
9/1 Section 1.7 Due: Sections1.4, 1.5, 1.6 |
9/2 Section 2.1 Quiz 1 (1.1, 1.2, 1.3) |
9/3 Section 2.2 Due: Sections 1.7, 2.1 |
| 9/7 Labor Day—No Class |
9/8 Section 2.3 Due: Section 2.2 |
9/9 Section 2.4 |
9/10 Section 3.1 Due: Sections 2.3, 2.4 |
| 9/14 Section 3.2 Quiz 2 (2.1, 2.2, 2.3) |
9/15 Section 3.3 Due: Sections 3.1, 3.2 |
9/16 Section 3.4 |
9/17 Section 3.5 Due: Sections 3.3, 3.4 |
| 9/21 Review Exam 1 |
9/22 Exam1:Chapters1,2&3 Due: Section 3.5 |
9/23 Section 4.1 |
9/24 Section 4.2 Due: Section 4.1 |
| 9/28 Section 4.3
|
9/29 Section 4.4 Due: Sections 4.2, 4.3
|
9/30 Section 4.5 Quiz 3 (4.1, 4.2, 4.3)
|
10/1 Section 5.1 Last day to drop a course or withdraw without a grade of "WF" (Oct 2) Due: Sections 4.4, 4.5 |
| 10/5 Section 5.2 |
10/6 Section 5.3 Due: Sections 5.1, 5.2 |
10/7 Section 5.4 Quiz 4 (5.1, 5.2, 5.3) |
10/8 Fall Break |
| 10/12 Section 5.5
|
10/13 Review Exam 2 Due: Sections 5.3, 5.4 5.5 |
10/14 Exam 2: Chapters4&5
|
10/15 Section 6.1
|
| 10/19 Section 6.2 |
10/20 Section 6.3 Due: Section 6.1, 6.2 |
10/21 Section 6.4 Quiz 5 (6.1, 6.2, 6.3) |
10/22 Section 6.5 Due: Sections 6.3, 6.4 |
| 10/26 Section 6.6 |
10/27 Section 6.7 Due: Sections 6.5, 6.6 |
10/28 Exercises 6.8 |
10/29 Section 6.9 Due: Sections 6.7,6.8 |
| 11/2 Section 7.1 |
11/3 Section 7.2 Due: Sections 6.9, 7.1 |
11/4 Section 7.3 |
11/5 Section 7.4 Due: Sections 7.2, 7.3 |
| 11/9 Section 7.5 |
11/10 Section 7.6 Due: Sections 7.4, 7.5 |
11/11 Section 7.7 Quiz 6 (7.1, 7.2, 7.3) |
11/12 Section 7.8 Due: Sections 7.6, 7.7 |
| 11/16 Review Exam 3 |
11/17 Review Exam 3 Due: Sections 7.8 |
11/18 Exam 3:Chapters 6 $7 |
11/19 Section 8.1 |
| 11/23 Section 8.2 |
11/24 Section 8.3 Due: Sections 8.1, 8.2 |
11/25 Thanksgiving |
11/26 Thanksgiving |
| 11/30 Advanced Topics |
12/1 Advanced Topics Due: Section 8.3 |
12/2 Review for Final Exam |
12/3 Review for Final Exam |
Final Exam: Wednesday December 9, 2009 9:00 a.m. -11:30
a.m.
IX Where to get help
Academic Success Center
The Academic Success Center is a free tutoring lab, located on the second floor
of Medford
Library. I will give you a handout with more information as soon as
it’s available (probably
next week).
WileyPLUS Technical Support
WileyPLUS Two-Minute Tutorials
Student Solutions Manual/Additional Homework
If you feel like you need more practice, you may do homework from the textbook.
WileyPLUS
provides a student solution manual that contains solutions to Algebra
Aerobics and to the odd
numbered exercises. To access it, log in to WileyPLUS.
Go to Read, Study and Practice. Choose
the appropriate chapter. Scroll down to
Student Hints and Solution Manuals.
Additional WileyPLUS Homework
I provided some additional problems on WileyPLUS. You will not receive any
credit for
competing these. However, some of you will find that you need the
extra practice in order to
better prepare for the tests.
Office Hours
You are always welcome to come to my office hours. You can also make an
appointment to
meet at some other mutually-convenient time.