# Pre-Calculus Algebra

7. Content and Method

 Topic Lectures Chapter 1: Fundamentals 3 1.1 Sets of Real Numbers 1.2 Absolute Value 1.3 Solving Equations (Review and Preview) 1.4 Rectangular Coordinates. Visualizing Data 1.5 Graphs and Graphing Utilities 1.6 Equations of Lines 1.7 Symmetry and Graphs. Circles Chapter 2: Equations and Inequalities 3 2.1 Quadratic Equations: Theory and Examples 2.2 Other Types of Equations 2.3 Inequalities 2.4 More on Inequalities Chapter 3: Functions 5 3.1 The Definition of a Function 3.2 The Graph of a Function 3.3 Shapes of Graphs. Average Rate of Change 3.4 Techniques in Graphing 3.5 Methods of Combining Functions (Skip iteration) 3.6 Inverse Functions Chapter 4: Polynomial and Rational Functions : Applications to Optimization 4 4.1 Linear Functions 4.2 Quadratic Functions 4.4 Setting Up Equations That Define Functions 4.5 Maximum and Minimum Problems Chapter 12: Roots of Polynomial Equations 4 12.1 The Complex Number System 12.2 Division of Polynomials 12.3 The Remainder Theorem and the Factor Theorem 12.4 The Fundamental Theorem of Algebra 12.5 Rational and Irrational Roots (optional) 12.6 Conjugate Roots and Descartes's Rule of Signs (Descartes's Rule optional) 12.7 Introduction to Partial Fractions (optional) 12.8 More About Partial Fractions (optional) Chapter 4: Polynomial and Rational Functions: Applications to Optimization 3 4.6 Polynomial Functions 4.7 Rational Functions Chapter 5: Exponential and Logarithmic Functions 7 5.1 Exponential Functions 5.2 The Exponential Function y = ex 5.3 Logarithmic Functions 5.4 Properties of Logarithms 5.5 Equations and Inequalities with Logs and Exponents 5.6 Compound Interest 5.7 Exponential Growth and Decay Chapter 10: Systems of Equations 5 10.1 Systems of Two Linear Equations in Two Unknowns 10.2 Gaussian Elimination 10.3 Matrices 10.4 The Inverse of a Square Matrix (optional) 10.5 Determinants and Cramer’s Rule 10.6 Nonlinear Systems of Equations (optional) 10.7 Systems of Inequalities (optional) Total 34

8. Methods of Assessment

The primary methods of assessment are, in decreasing order of importance : essay
examinations, quizzes and homework. Typically, there will be two or three hour-long
examinations during the quarter, and a comprehensive final examination. Students are required
to show their work, and are graded not only on the correctness of their answers, but also on
their understanding of the concepts and techniques. Quizzes are usually given once or twice a
week to provide a spot check of student learning. Homework is required daily. Since this class
satisfies a General Education requirement, at least 10% of the grade must be based on writing
using correct mathematical notation.

a. The syllabus is tightly packed, and the course moves at a rapid pace; students should be
forewarned of this at the first class meeting. Students finding difficulty with the pace should
instead take Math 116 followed by Math 117.

b. The text has many interesting applications. Also note the review sections at the end of
each chapter.

c. The text is readable; students should be advised to read each section before coming to class.

d. The text is bundled with an interactive Video Skill-Builder CD-ROM.

e. Additional supplements (test banks, Instructor’s Resource CD, etc.) are available from the
course supervisor.

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