College Algebra Course Syllabus and Weekly Topic Guide

Course Overview and Structure

This syllabus outlines the weekly topics, important dates, and assessment schedule for a College Algebra course. It provides a structured guide to the progression of mathematical concepts and skills throughout the semester.

Week-by-Week Topic Breakdown

Week	Dates	Math Topic
1	Aug 25 – Aug 31	Course Overview, Syllabus, Class Expectations, Introduction to Algebraic Notation, Properties of Real Numbers
2	Sept 1 – Sept 7	Fraction Notation, Real Numbers, Addition & Subtraction of Real Numbers
3	Sept 8 – Sept 14	Multiplication & Division of Real Numbers, Exponential Notation, Order of Operations, Evaluating Formulas, Solving for a Variable
4	Sept 15 – Sept 21	Test #1 (Sections 1.1-2.3)
5	Sept 22 – Sept 28	Equations – Applications with Percent, Solving Equations, Formulas, Graphs – Linear Equations
6	Sept 29 – Oct 5	Graphs – Linear Equations, Slope, Intercept Form
7	Oct 6 – Oct 12	Slope Intercept Form, Functions, Systems of Equations – Substitution & Elimination
8	Oct 13 – Oct 16	Test #2 (Sections 2.4-3.7, 7.1-7.2)
9	Oct 20 – Oct 26	Polynomials – Add & Subtract, Multiply, Special Cases
10	Oct 27 – Nov 2	Polynomials – Add & Subtract, Multiply, Special Cases
11	Nov 3 – Nov 9	Factoring – GCF & Factoring by Grouping, Trinomials
12	Nov 10 – Nov 16	Factoring – Trinomials, Test #3 (Sections 4.1-5.2)
13	Nov 17 – Nov 23	Factoring – Difference of Squares, Quadratic Equations by Factoring
14	Nov 24 – Nov 30	Square Roots
15	Dec 1 – Dec 7	Review for Final
16	Dec 8 – Dec 13	Comprehensive Final Exam

Key College Algebra Topics

Introduction to Algebraic Notation

Algebraic notation is the language of mathematics used to represent numbers, variables, and operations. Understanding this notation is essential for solving equations and expressing mathematical relationships.

• Variables: Symbols (often letters) that represent unknown values.

• Constants: Fixed values in an expression or equation.

• Operations: Addition (+), subtraction (−), multiplication (×), division (÷).

• Example: In the equation $x + 5 = 12$, x is the variable.

Properties of Real Numbers

Real numbers follow several important properties that are foundational to algebraic manipulation.

• Commutative Property: $a + b = b + a$ and $ab = ba$

• Associative Property: $(a + b) + c = a + (b + c)$ and $(ab)c = a(bc)$

• Distributive Property: $a(b + c) = ab + ac$

• Example: $2(3 + 4) = 2 imes 3 + 2 imes 4 = 6 + 8 = 14$

Fraction Notation and Operations

Fractions represent parts of a whole and are used extensively in algebraic expressions and equations.

• Fraction Notation: $rac{a}{b}$, where a is the numerator and b is the denominator.

• Operations: Addition, subtraction, multiplication, and division of fractions.

• Example: $rac{2}{3} + rac{1}{6} = rac{4}{6} + rac{1}{6} = rac{5}{6}$

Order of Operations

The order of operations ensures that mathematical expressions are evaluated consistently.

• PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

• Example: $2 + 3 imes (4^2 - 1) = 2 + 3 imes (16 - 1) = 2 + 3 imes 15 = 2 + 45 = 47$

Solving Equations and Formulas

Solving equations involves finding the value of the variable that makes the equation true.

• Linear Equations: Equations of the form $ax + b = c$

• Example: $2x + 3 = 7$; subtract 3: $2x = 4$; divide by 2: $x = 2$

Graphing Linear Equations

Linear equations can be represented graphically as straight lines on the coordinate plane.

• Slope-Intercept Form: $y = mx + b$, where m is the slope and b is the y-intercept.

• Example: $y = 2x + 1$ has a slope of 2 and a y-intercept of 1.

Functions

A function is a relation that assigns exactly one output for each input.

• Function Notation: $f(x)$

• Example: If $f(x) = x^2$, then $f(3) = 9$

Systems of Equations

Systems of equations involve finding values that satisfy multiple equations simultaneously.

• Substitution Method: Solve one equation for a variable and substitute into the other.

• Elimination Method: Add or subtract equations to eliminate a variable.

• Example: Solve $x + y = 5$ and $x - y = 1$

Polynomials and Factoring

Polynomials are algebraic expressions with multiple terms. Factoring is the process of expressing a polynomial as a product of its factors.

• Polynomial Example: $x^2 + 5x + 6$

• Factoring Example: $x^2 + 5x + 6 = (x + 2)(x + 3)$

Quadratic Equations

Quadratic equations are equations of the form $ax^2 + bx + c = 0$.

• Factoring Method: Express as a product of binomials and solve for roots.

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

• Example: Solve $x^2 + 5x + 6 = 0$ by factoring.

Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number.

• Notation: $\sqrt{x}$

• Example: $\sqrt{9} = 3$

Assessment and Important Dates

• Tests: Three major tests covering specified sections.

• Final Exam: Comprehensive, scheduled for the week of December 8–December 12.

• Breaks: College closed for Labor Day, Thanksgiving, and other specified dates.

Additional info: This syllabus provides a general outline and may be adjusted based on class progress. Students are advised to review the relevant sections before each test and utilize recommended mid-chapter reviews for practice.