Math 245 Tentative Schedule: College Algebra Chapter Overview

Math 245 Tentative Schedule: College Algebra Chapter Overview

Course Structure and Chapter Topics

This schedule outlines the sequence of topics for a college algebra course, covering foundational concepts and progressing through advanced algebraic topics. Each chapter corresponds to a major area of study in college algebra, as follows:

• Ch. R - Review: Fundamental concepts and prerequisite skills for algebra.

• Ch. 1 - Equations and Inequalities: Solving and analyzing equations and inequalities.

• Ch. 2 - Graphs: Understanding and interpreting various types of graphs.

• Ch. 3 - Functions and Their Graphs: Introduction to functions, their properties, and graphical representations.

• Ch. 4 - Linear and Quadratic Functions: Study of linear and quadratic equations, graphs, and applications.

• Ch. 5 - Polynomial and Rational Functions: Exploration of higher-degree polynomials and rational expressions.

• Ch. 6 - Exponential and Logarithmic Functions: Analysis of exponential growth, decay, and logarithmic relationships.

• Ch. 8 - Systems of Equations and Inequalities: Methods for solving systems algebraically and graphically.

• Ch. 9 - Sequences; Induction; the Binomial Theorem: Introduction to sequences, mathematical induction, and binomial expansion.

Additional info: Chapters 7 and 10 are not listed in the schedule, but the included chapters align closely with standard college algebra curricula.

Sample Weekly Progression

The course is organized by weeks, with each week focusing on specific sections within a chapter. Tests and reviews are scheduled at the end of each chapter to reinforce learning and assess understanding.

• Weeks 1-2: Review of prerequisite material (R.1-R.8).

• Weeks 3-4: Introduction and mastery of equations and inequalities (1.1-1.7).

• Weeks 5-6: Graphs and their properties (2.1-2.5, 3.1-3.5).

• Weeks 7-8: Functions and their graphs, linear and quadratic functions (3.6, 4.1-4.5).

• Weeks 9-10: Polynomial and rational functions (5.1-5.6).

• Weeks 11-12: Exponential and logarithmic functions (6.1-6.7).

• Weeks 13-14: Systems of equations and inequalities (8.1-8.6), sequences and binomial theorem (9.1-9.5).

• Weeks 15-17: Final review and exam.

Chapter Test and Review Schedule

Each chapter concludes with a test and review session, providing students with opportunities to consolidate their understanding and prepare for assessments.

Summary Table: Chapter Sequence and Topics

Chapter	Main Topic	Key Concepts
R	Review	Arithmetic, algebraic manipulation, basic properties
1	Equations and Inequalities	Solving linear, quadratic, and other equations; inequalities
2	Graphs	Coordinate plane, graphing equations, intercepts
3	Functions and Their Graphs	Definition of function, domain/range, transformations
4	Linear and Quadratic Functions	Forms of linear/quadratic equations, graphing, applications
5	Polynomial and Rational Functions	Factoring, roots, asymptotes, graphing rational functions
6	Exponential and Logarithmic Functions	Exponential growth/decay, logarithms, properties
8	Systems of Equations and Inequalities	Solving systems by substitution, elimination, graphing
9	Sequences; Induction; Binomial Theorem	Arithmetic/geometric sequences, induction, binomial expansion

Key Concepts and Examples

• Solving Equations: Techniques for solving linear and quadratic equations, such as factoring and the quadratic formula. Example: Solve $ax^2 + bx + c = 0$ using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Graphing Functions: Plotting functions on the coordinate plane, identifying intercepts and transformations. Example: The graph of $y = mx + b$ is a straight line with slope $m$ and y-intercept $b$.

• Exponential and Logarithmic Functions: Understanding growth and decay, and properties of logarithms. Example: $y = a e^{kt}$ models exponential growth or decay. Logarithm property: $\log_b(xy) = \log_b x + \log_b y$

• Systems of Equations: Solving multiple equations simultaneously. Example: Solve the system: $\begin{cases} x + y = 5 \\ 2x - y = 1 \end{cases}$

• Sequences and Binomial Theorem: Working with arithmetic and geometric sequences, and expanding binomials. Example: The $n$th term of an arithmetic sequence: $a_n = a_1 + (n-1)d$ Binomial Theorem: $(x + y)^n = \sum_{k=0}^n \binom{n}{k} x^{n-k} y^k$

Additional info: This schedule provides a comprehensive overview of the topics covered in a standard college algebra course, serving as a guide for exam preparation and review.