Math 030 College Algebra Corequisite Course Syllabus Study Guide

Math 030 College Algebra Corequisite Course Syllabus Study Guide

Course Overview

The Math 030 course is a corequisite support class for students enrolled in Math 130 (College Algebra) who require additional preparation. The course is designed to build foundational algebra skills and strategies necessary for success in college-level algebra.

• Course Description: Focuses on algebraic expressions, linear equations, radicals, coordinate systems, factoring, square root property, inequalities, intercepts, polynomials, slope, quadratic equations, exponents, complex numbers, and introductory topics for college algebra readiness.

• Pre-requisite: None

• Co-requisite: Concurrent enrollment in Math 130

• Course Goal: To help students build essential mathematical skills and succeed in Math 130.

Course Objectives

Upon completion, students should be able to:

• Simplify and evaluate expressions

• Simplify radicals

• Solve linear and radical equations

• Plot coordinates on a graph

• Factor polynomials

• Use the square root property

• Solve for an indicated variable

• Solve linear inequalities and write solutions in interval notation

• Graph equations using intercepts and tables of ordered pairs

• Multiply polynomials

• Find the slope of a line

• Identify values that make a rational expression undefined

• Write polynomials in descending order and identify degree, leading coefficient, leading term, and constant term

• Solve quadratic equations by factoring and using the quadratic formula

• Apply exponent rules

• Perform operations on complex numbers

Course Content by Week

The course is structured to cover key algebra topics in a logical sequence. Below is a summary of weekly content:

Week	Content
1	Simplifying Expressions, Evaluating Expressions, Solving Equations
2	Simplifying Radicals, Coordinate System, Completing the Square, Factoring (Leading Coefficient 1), Systems and Circles (Supplementary)
3	Square Root Property, Interval Notation, Intercepts, Multiply Polynomials
4	Factoring (Leading Coefficient ≠ 1), Binomials, Functions (Supplementary)
5	Slope, Graphing Using Table of Ordered Pairs, Average Rate of Change, Transformations (Supplementary)
6	Solve Quadratic Equations by Factoring, Undefined Values, Inequalities
7	Complex Fractions, Solving for y, Solving Radical Equations, Combinations, Compositions, Inverse Functions (Supplementary)
8	Review of Systems, Circles, and Functions
9	Intercepts, Complex Numbers, Polynomial Functions, Factoring by Grouping, Quadratic Functions (Supplementary)
10	Quadratic Formula, Rational Exponents, Exponents, Polynomial Functions (Supplementary)
11	Rational Functions, Polynomial and Rational Inequalities (Supplementary), Review for Comprehensive Assessment
12	Review for Comprehensive Assessment
13	Comprehensive Course Assessment
14	Exponential and Logarithmic Functions (Supplementary)
15	Exponential and Logarithmic Equations (Supplementary), Review for Math 130 Exam
16	Review for Math 130 Exam

Key Algebra Topics Explained

Simplifying and Evaluating Expressions

Algebraic expressions are mathematical phrases that can contain numbers, variables, and operations. Simplifying involves reducing expressions to their simplest form, while evaluating means substituting values for variables and calculating the result.

• Example: Simplify $2x + 3x = 5x$; Evaluate $x^2 + 2x$ for $x = 3$ gives $9 + 6 = 15$.

Simplifying Radicals

Radicals involve roots, most commonly square roots. Simplifying radicals means expressing them in their simplest form.

• Example: $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$

Solving Linear and Radical Equations

Linear equations are equations of the first degree, while radical equations contain roots.

• Linear Equation Example: $2x + 5 = 11 \Rightarrow x = 3$

• Radical Equation Example: $\sqrt{x} = 4 \Rightarrow x = 16$

Coordinate System and Graphing

The coordinate system is used to plot points, lines, and curves. Graphing equations helps visualize solutions and relationships.

• Key Terms: x-axis, y-axis, origin, ordered pairs $(x, y)$

• Example: Plot $(2, 3)$ on the coordinate plane.

Factoring Polynomials

Factoring is the process of expressing a polynomial as a product of its factors.

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

Square Root Property

The square root property states that if $x^2 = a$, then $x = \pm \sqrt{a}$.

• Example: $x^2 = 9 \Rightarrow x = \pm 3$

Solving Linear Inequalities and Interval Notation

Linear inequalities are solved similarly to equations, but solutions are often written in interval notation.

• Example: $2x - 3 < 7 \Rightarrow x < 5$; Interval notation: $(-\infty, 5)$

Graphing Using Intercepts and Tables

Intercepts are points where a graph crosses the axes. Tables of ordered pairs help plot equations.

• Example: For $y = 2x + 1$, x-intercept: $x = -0.5$, y-intercept: $y = 1$

Multiplying Polynomials

Multiplying polynomials involves distributing each term in one polynomial to each term in another.

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

Finding the Slope of a Line

The slope measures the steepness of a line, calculated as the ratio of the change in y to the change in x.

• Formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

• Example: Points $(1, 2)$ and $(3, 6)$: $m = \frac{6 - 2}{3 - 1} = 2$

Identifying Undefined Values in Rational Expressions

Rational expressions are undefined when the denominator equals zero.

• Example: $\frac{1}{x - 2}$ is undefined for $x = 2$

Polynomial Structure

Polynomials can be written in descending order. Key terms include degree, leading coefficient, leading term, and constant term.

• Example: $3x^4 + 2x^3 - x + 5$; Degree: 4, Leading coefficient: 3, Leading term: $3x^4$, Constant term: 5

Solving Quadratic Equations

Quadratic equations can be solved by factoring or using the quadratic formula.

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

• Example: $x^2 + 5x + 6 = 0 \Rightarrow x = -2, -3$

Exponent Rules

Exponent rules govern operations involving powers.

• Product Rule: $a^m \cdot a^n = a^{m+n}$

• Quotient Rule: $\frac{a^m}{a^n} = a^{m-n}$

• Power Rule: $(a^m)^n = a^{mn}$

Complex Numbers

Complex numbers have the form $a + bi$, where $i = \sqrt{-1}$.

• Example: $(2 + 3i) + (1 - 4i) = 3 - i$

Assessment and Grading

• Assignments via publisher software: 10%

• Skills assessments (quizzes/tests): 15%

• In/out of class assignments: 40%

• Comprehensive course assessment: 35%

Grading follows a standard 10-point scale:

Letter Grade	Percentage
A	90% - 100%
B	80% to below 90%
C	70% to below 80%
D	60% to below 70%
F	Below 60%
FN	Failure due to insufficient participation

Textbook and Resources

• Textbook: Beginning and Intermediate Algebra, 7th Edition, Lial, Hornsby, and Mcginnis

• Calculator: TI-30IIb or TI-30xIIs (required)

• Publisher Software: Pearson or similar

• Math Labs: Available on City Park and West Bank campuses; virtual tutoring available

Policies and Academic Integrity

• Attendance and participation are required; non-attendance may result in being dropped from the course.

• Academic honesty is expected; plagiarism and cheating are strictly prohibited.

• Accommodations are available for students with disabilities through the Office of Student Accessibility.

• Title IX compliance ensures a safe and non-discriminatory educational environment.

Additional Information

• Midterm and comprehensive assessments are departmental and cannot be exempted.

• Grades are posted on Canvas; keep all graded materials for reference.

• Contact your instructor or department chair for classroom concerns.

Additional info: This syllabus covers all major topics listed in the beginning-intermediate algebra curriculum, including prealgebra review, real number system, linear equations, polynomials, factoring, rational expressions, inequalities, functions, roots, quadratic equations, exponentials, and logarithms. The structure and objectives align with the chapter titles provided for college algebra readiness.