Course Overview

Introduction to Intermediate Algebra with Support

This course is designed to bridge the gap between beginning algebra and precalculus, providing students with foundational skills necessary for success in higher-level mathematics. The syllabus outlines key algebraic concepts, operations, and problem-solving strategies that are essential for college algebra and related courses.

• Course Title: Intermediate Algebra with Support (MTH 140S)

• Credit Hours: 5

• Schedule: MWF 9am-10:40am

• Instructor: Richard Pescarino

• Required Materials: MyLab Math with Pearson eText (Elayn Martin-Gay)

Course Learning Outcomes

Key Algebraic Skills and Concepts

Upon completion of the course, students will be able to demonstrate proficiency in the following areas, which align closely with College Algebra topics:

• Variables and Algebraic Expressions: Use variables to represent unknowns and simplify expressions using algebraic rules.

• Linear Equations and Inequalities: Solve linear equations and inequalities in one variable, and graph solutions on a number line.

• Applications of Linear Equations: Apply linear equations to solve real-world problems.

• Functions: Identify functions, use function notation, and determine domain and range.

• Graphing Functions: Graph basic functions by plotting points and using intercepts.

• Slope and Equations of Lines: Find the slope of a line using the formula , graph lines using slope and a point, and determine equations of lines from various descriptions.

• Exponent Laws: Simplify expressions using integer and rational exponents.

• Polynomials: Perform addition, subtraction, multiplication, and division of polynomials; factor polynomials using various techniques.

• Rational Expressions and Functions: Simplify, add, subtract, multiply, and divide rational expressions; determine domains and solve rational equations.

• Radicals and Radical Functions: Simplify radicals, graph radical functions, and solve radical equations.

• Complex Numbers: Perform operations with complex numbers.

• Quadratic Equations: Solve quadratic equations by factoring, square root method, completing the square, and quadratic formula .

• Graphing Quadratic Functions: Use transformations and intercepts to graph quadratic functions.

• Inverse Functions: Find and graph the inverse of a function.

• Exponential and Logarithmic Functions: Plot points to graph these functions, convert between exponential and logarithmic forms.

• Scientific Notation: Translate numbers between standard and scientific notation.

Expanded Topic Explanations

Equations & Inequalities

Solving equations and inequalities is fundamental in algebra. Linear equations involve expressions of the form , while inequalities use symbols such as , , , and .

• Solving Linear Equations: Isolate the variable using inverse operations.

• Solving Linear Inequalities: Similar to equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number.

• Graphing Solutions: Represent solutions on a number line.

• Example: Solve ; ; .

Functions

A function is a relation in which each input (domain) corresponds to exactly one output (range). Function notation is .

• Identifying Functions: Use the vertical line test on graphs.

• Domain and Range: The domain is the set of possible input values; the range is the set of possible output values.

• Example: has domain and range .

Polynomial Functions

Polynomials are expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication.

• Operations: Add, subtract, multiply, and divide polynomials.

• Factoring: Use techniques such as greatest common factor, grouping, and special patterns.

• Example: Factor .

Rational Functions

Rational functions are ratios of polynomials. Their domains exclude values that make the denominator zero.

• Simplifying Rational Expressions: Factor numerator and denominator, then reduce.

• Solving Rational Equations: Find common denominators and solve for the variable.

• Example: ; ; ; .

Exponential & Logarithmic Functions

Exponential functions have the form , and logarithmic functions are their inverses.

• Converting Forms: is equivalent to .

• Graphing: Plot points for and .

• Example: ; .

Quadratic Equations

Quadratic equations are of the form . They can be solved by several methods.

• Factoring: Find two numbers that multiply to and add to .

• Quadratic Formula: .

• Completing the Square: Rearrange and add terms to form a perfect square trinomial.

• Example: Solve ; ; .

Radicals and Complex Numbers

Radical expressions involve roots, such as square roots. Complex numbers include a real and an imaginary part.

• Simplifying Radicals: for .

• Operations with Complex Numbers: .

• Example: ; .

Scientific Notation

Scientific notation expresses numbers as a product of a coefficient and a power of ten.

• Standard to Scientific: .

• Scientific to Standard: .

Grading Policy

Assessment Structure

Student performance is evaluated through tests, homework, and a final exam.

• Tests: 4 tests, 60% of grade

• Homework: 20% of grade

• Final Exam: 20% of grade

Technology and Support

Calculator Recommendations

A scientific calculator is recommended for this course. Examples include TI-36X Pro, TI-30XS MULTIVIEW, and TI-30XIIS.

Math Tutoring

Free tutoring is available both in-person and online. Students are encouraged to utilize these resources for additional support.

Course Outline Table

Summary of Major Topics

Additional Info

• All topics listed in the syllabus are foundational for College Algebra and Precalculus.

• Students are encouraged to master each skill independently for exam success.

• Support services, academic integrity, and college policies are integral to the course environment.