Math 120 College Algebra: 16-Week Course Structure and Key Topics

Course Overview

This study guide summarizes the main topics and structure of a typical College Algebra course (Math 120), organized by weekly units and sections. The course covers foundational algebraic concepts, equations, functions, and applications essential for further study in mathematics and related fields.

Unit 1: Foundations of Algebra

Week 1: Introduction to Algebraic Concepts

• Key Topics: Basic algebraic operations, properties of real numbers, and introductory problem-solving.

• Sections: 1.3 & 1.4

• Definition: Algebra is the branch of mathematics dealing with symbols and the rules for manipulating those symbols.

• Example: Simplifying expressions such as $2(x + 3) - 4x$.

Week 2: Linear Equations and Inequalities

• Key Topics: Solving linear equations, inequalities, and applications.

• Sections: 1.6, 1.9 & 2.1

• Formula: The general form of a linear equation is $ax + b = c$.

• Example: Solve $3x - 7 = 2$.

Week 3: Systems of Linear Equations

• Key Topics: Methods for solving systems (substitution, elimination), applications.

• Sections: 2.2, 2.3 & 2.4

• Definition: A system of equations is a set of two or more equations with the same variables.

• Example: Solve the system: $x + y = 5$, $2x - y = 3$.

Week 4: Quadratic Equations and Functions

• Key Topics: Quadratic equations, factoring, completing the square, quadratic formula.

• Sections: 3.1, 3.2 & 3.3

• Formula: The quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Example: Solve $x^2 - 5x + 6 = 0$.

Week 5: Polynomial Functions

• Key Topics: Properties of polynomials, graphing, zeros of polynomials.

• Sections: 3.4, 3.5 & 3.6

• Definition: A polynomial function is a function of the form $f(x) = a_nx^n + ... + a_1x + a_0$.

• Example: Graph $f(x) = x^3 - 2x^2 + x - 5$.

Unit 2: Advanced Functions and Applications

Week 7: Rational Expressions and Functions

• Key Topics: Simplifying rational expressions, operations, solving rational equations.

• Sections: 4.1 & 4.2

• Definition: A rational expression is a fraction in which the numerator and/or denominator are polynomials.

• Example: Simplify $\frac{x^2 - 4}{x - 2}$.

Week 8: Radical Expressions and Equations

• Key Topics: Properties of radicals, solving radical equations.

• Sections: 4.3 & 4.4

• Formula: $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$

• Example: Solve $\sqrt{x + 3} = 5$.

Week 10: Exponential and Logarithmic Functions

• Key Topics: Exponential growth and decay, properties of logarithms, solving exponential and logarithmic equations.

• Sections: 5.1 & 5.2

• Definition: An exponential function is of the form $f(x) = a \cdot b^x$.

• Formula: $\log_b(a) = c \iff b^c = a$

• Example: Solve $2^x = 16$.

Week 11: Further Applications of Exponential and Logarithmic Functions

• Key Topics: Compound interest, continuous growth, applications in science and finance.

• Sections: 5.3 & 5.4

• Formula: Compound interest: $A = P(1 + \frac{r}{n})^{nt}$

• Example: Calculate the future value of $1000$ at $5\%$ annual interest compounded monthly for $3$ years.

Unit 3: Advanced Topics and Review

Week 13: Sequences and Series

• Key Topics: Arithmetic and geometric sequences, series, summation notation.

• Sections: 7.1 & 7.2

• Definition: An arithmetic sequence has a constant difference between terms; a geometric sequence has a constant ratio.

• Formula: $a_n = a_1 + (n-1)d$ (arithmetic), $a_n = a_1 r^{n-1}$ (geometric)

• Example: Find the 5th term of the sequence $2, 5, 8, ...$

Week 14: Series and Summation

• Key Topics: Summing series, sigma notation, applications.

• Sections: 7.5 & 7.6

• Formula: $S_n = \frac{n}{2}(a_1 + a_n)$ (sum of arithmetic series)

• Example: Find the sum of the first 10 terms of $3, 6, 9, ...$

Week 15-16: Review and Final Exam

• Key Topics: Comprehensive review of all topics, practice problems, and final exam preparation.

• Application: Use practice quizzes and proctored exams to assess understanding and readiness.

Course Schedule Table

The following table summarizes the weekly topics and main sections covered:

Week	Main Topic	Sections
1	Algebraic Foundations	1.3, 1.4
2	Linear Equations	1.6, 1.9, 2.1
3	Systems of Equations	2.2, 2.3, 2.4
4	Quadratic Equations	3.1, 3.2, 3.3
5	Polynomials	3.4, 3.5, 3.6
7	Rational Expressions	4.1, 4.2
8	Radicals	4.3, 4.4
10	Exponential & Logarithmic Functions	5.1, 5.2
11	Applications of Exponentials & Logs	5.3, 5.4
13	Sequences & Series	7.1, 7.2
14	Series & Summation	7.5, 7.6

Additional info: The schedule includes regular quizzes, proctored tests, and comprehensive exams to reinforce learning and assess mastery of College Algebra concepts.