Precalculus
(Math 105/106)

Instructor: Prof. Jeffrey Schierenbeck

Textbook: Precalculus Mathematics, Sobel & Lerner, 5th edition.

Calculator: Each student must have a graphing calculator available to use in and outside of class. If a calculator is not available, a TI-83 may be rented from the ILC Bookstore. If you are considering the purchase of a calculator, you are encouraged to talk with the instructor first.

Duration/Credits: High School--Two semesters/1.0 credits per semester
                              College:  Math 105--4 credits; Math 106--4 credits

Prerequisites: Successful completion of algebra II and geometry.

Course Objectives: To establish a deeper understanding of concepts of algebra and trigonometry. In particular, to equip the student with a mathematical background sufficient to prepare him or her to take a college-level calculus course.

Topics Covered:

   First Semester (Math 105):

• Fundamentals of algebra
  • A review of basic algebra notation and operations such as inequalities, absolute value, exponents and radicals, polynomial operations, factoring polynomials, complex numbers.
• Linear and Quadratic Functions
  • Concept of a function; linear equations and graphs, piecewise linear functions, systems of linear equations; graphing quadratic functions, quadratic formula; applications.
• Polynomial and Rational Functions
  • Graphing techniques; polynomial and rational functions; equations and inequalities with fractions; variation; synthetic division and factor theorems; solving polynomial equations; partial fractions.
• Circles, Additional Curves, and the Algebra of Functions
  • Circles; radical functions, equations, and graphs; combining and decomposing functions; inverse functions.
• Exponential and Logarithmic Functions
  • Exponential functions and equations; logarithmic functions; laws of logarithms; e; applications.
• Linear Systems and Matrices
  • Solving linear systems using matrices; matrix algebra; solving linear systems using matrix inverses.

   Second semester (Math 106)

• The Trigonometric Functions
  • Angle measure; trigonometric functions and the unit circle; graphs of trigonometric functions; inverse trigonometric functions.
• Right Triangle Trigonometry, Identities, and Equations
  • Acute angle trigonometry; right triangle trigonometry; identities, addition and subtraction formulas, double and half-angle formulas; solving trigonometric equations.
• Additional Applications of Trigonometry
  • Law of Sines and Law of Cosines; trigonometric form of complex numbers; De Moivre's Theorem; polar coordinates, graphing polar equations; parametric equations.
• The Conic Sections
  • Equations and graphs of ellipse, hyperbola, and parabola; solving nonlinear systems.
• Sequences and Series:
  • Sequences; sums of finite sequences; arithmetic and geometric sequences; infinite geometric series; mathematical induction.
• Permutations, Combinations, Probability
  • Permutations; combinations; introduction to probability.

Homework: Daily homework will be assigned to be completed before the next class period. The homework will be collected and reviewed periodically, with selected problems being corrected and graded. Also, class periods will sometimes begin with a quiz which consists of a few problems selected from the assignment that is due at that time. It is vital that all of the homework is done every day. Opportunities will be given at the beginning of class to ask questions about specific homework problems. However, if you have more than minor difficulties with the assignment, you should meet with me during office hours for assistance. In mathematics, to understand one day's material you normally must have a solid grasp of the material presented the previous day.

Exams: There will ordinarily be an exam upon completion of a chapter. Occasionally two chapters might be covered before an exam is given. This amounts to 5-6 exams each semester. Each semester, the lowest exam score for each student is not averaged into the course grade.

Projects: A few additional projects may be assigned. The specifics regarding the completion and grading of these projects will be discussed when they are assigned.

Final Exam: A cumulative final exam will be given at the end of each semester

Extra Credit: On most homework assignments, additional problems will be assigned as optional work. These problems will be due before the exam for that chapter is taken. Extra credit points will be given for completion (or partial completion) of these problems. These points will be added to your exam total.

Grading:

Tests 60% (lowest dropped each sem.)
Final Exam 20%
Homework/Projects 20%
Letter Grade Conversions

Office Hours: It is not expected that you should be able to succeed in this course without ever having any contact with the instructor outside of class time. You can anticipate that you will have questions throughout the year. You must make it a point to get those questions answered to your satisfaction. This can hopefully be achieved through your own thinking and reading, consultation with classmates or others, and through communication with the instructor in and outside of class time. I will generally be available in my Northwest Hall office during the office hours posted on my office door. You are welcome to come by any time I am available in my office. If you would like to arrange a specific time at which to meet, that could certainly be arranged. You may always contact me by telephone at either my office or at home. My office number is 836-6630 and my home number is 839-8938. There is an answering machine at both locations, so you can leave me a message if I am not there. Do not feel timid about calling me at home on evenings or weekends; it's not a problem at all. But, if calling my home, please call before 10:00 pm. You may also contact me via Email at jeff.schierenbeck@ilc.edu.

Late Assignments: Unless otherwise specifically stated, all work assigned to be turned in on a particular date is due at the beginning of the class period on that day. NO CREDIT WILL BE RECEIVED FOR HOMEWORK THAT IS HANDED IN LATE! If, because of an excused absence, you are unable to be in class on the day that work is due, you will be expected to turn in that assignment at the beginning of the next class period which you are able to attend.

If circumstances arise which would not allow you to get your assignment in on time, then let me know as early as you can. It may be possible for you to receive an extension. However, if you inform me of your situation just before class on the day that the work is due, do not expect me to be too gracious! Start on the assignment early so that you can get questions answered that arise.

Information Missed Due To Absence: Whether present or absent (excused or unexcused), you are responsible for any information given out during the class periods. This includes lecture material, activities, homework assignments, quizzes, announcements of test/quiz dates, or any other matter that is discussed. Therefore, if you are absent for a class period, be sure to contact a responsible classmate, or me, to be filled in on any important information that you may have missed. Of course, if you need help catching up on any material that you missed, I will be happy to assist you.

If you miss a period in which a test or quiz is given, you will be responsible for contacting me as soon as possible to arrange a time to make up the test. If I don't hear from you, be prepared to take the test during the next class period which you are able to attend.