Fundamentals of Algebra and Trigonometry I Enhanced (MATH 101E) – Syllabus and Study Guide

Course Overview

This syllabus outlines the structure, objectives, and policies for Fundamentals of Algebra and Trigonometry I Enhanced (MATH 101E), a foundational course designed to accelerate students into college-level mathematics. The course integrates Pre-College Algebra and introductory Algebra & Trigonometry, providing essential skills for further study in mathematics and related fields.

Course Topics and Relevance to Precalculus

• Elementary properties of real numbers

• Basic algebraic operations

• Solving quadratic equations using multiple methods

• Number properties

• Polynomials and rational expressions

• Rational exponents and radicals

• Equations and inequalities in one variable

• Relations and functions

Note: These topics directly align with the standard precalculus curriculum, including functions, equations, inequalities, polynomials, and introductory trigonometry.

Learning Objectives

Algebraic Reasoning and Computation

• Exponents: Apply rules of exponents for multiplication, division, and powers.

• Radicals: Evaluate and simplify radical expressions.

• Polynomials: Add, subtract, multiply, and divide polynomials; factor polynomials.

• Equations: Solve linear, quadratic, and polynomial equations; solve rational equations by factoring.

• Functions: Evaluate and simplify function values; simplify the difference quotient of functions.

• Arithmetic Operations: Perform basic arithmetic operations and apply them to real-world contexts.

• Applications: Solve application problems using algebraic rules and formulas.

Graphing and Function Analysis

• Graph basic functions and their transformations.

• Perform basic operations on functions (addition, subtraction, multiplication, division).

• Solve equations and inequalities involving absolute value.

• Add, subtract, multiply, and divide complex numbers.

Mathematical Communication and Modeling

• Read and interpret mathematical documents.

• Articulate mathematical information clearly in written and online formats.

• Construct and interpret mathematical models using numerical, graphical, symbolic, and verbal representations.

• Recognize the limits of mathematical and algebraic methods.

Key Concepts and Examples

Exponents and Radicals

Definition: Exponents represent repeated multiplication of a base. Radicals are the inverse operation of exponents.

• Exponent Rules:

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

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

  • Power Rule: $(a^m)^n = a^{mn}$

• Radical Simplification: $\sqrt[n]{a^m} = a^{m/n}$

• Example: Simplify $\sqrt{16x^4} = 4x^2$

Polynomials and Factoring

Definition: A polynomial is an expression consisting of variables and coefficients, involving only non-negative integer exponents.

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

• Factoring: Express a polynomial as a product of its factors.

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

Solving Equations and Inequalities

• Linear Equations: $ax + b = 0 \implies x = -\frac{b}{a}$

• Quadratic Equations: $ax^2 + bx + c = 0$

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

• Absolute Value Equations: $|x| = a \implies x = a$ or $x = -a$

• Example: Solve $2x^2 - 8 = 0 \implies x^2 = 4 \implies x = \pm2$

Functions and Their Properties

Definition: A function is a relation that assigns exactly one output to each input.

• Notation: $f(x)$ denotes the value of the function at $x$.

• Difference Quotient: $\frac{f(x+h) - f(x)}{h}$

• Example: For $f(x) = x^2$, the difference quotient is $\frac{(x+h)^2 - x^2}{h} = 2x + h$

Graphing and Transformations

• Graph basic functions such as linear, quadratic, and absolute value functions.

• Apply transformations: shifts, reflections, stretches, and compressions.

• Example: The graph of $f(x) = (x-2)^2 + 3$ is a parabola shifted right by 2 units and up by 3 units.

Complex Numbers

Definition: A complex number is of the form $a + bi$, where $i = \sqrt{-1}$.

• Operations: Add, subtract, multiply, and divide complex numbers.

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

Assessment and Grading

Component	Weight
Labs	10%
Module Tests (lowest dropped)	40%
Quizzes	15%
Homework	15%
Attendance & Participation	10%
Comprehensive Final Exam	10%

Course Policies and Success Strategies

• Attendance is required and contributes to your grade.

• Assignments must be submitted on time; late work is only accepted with official documentation.

• Academic integrity is strictly enforced; cheating or plagiarism results in disciplinary action.

• Use of calculators is permitted, but cell phones are not allowed during assessments.

• Active participation, including engagement with online resources and in-class activities, is essential for success.

Recommended Study Practices

• Review PowerPoint slides and attempt homework before class meetings.

• Utilize MyLabMath for personalized practice and self-assessment.

• Attend all class sessions and structured academic support meetings.

• Organize notes in a dedicated binder and use recommended materials (calculator, pens, highlighters).

• Seek help from tutoring services and office hours as needed.

Support and Resources

• MyLabMath with Pearson eText (access provided with course fees)

• Pre-College Algebra Math In Focus (available at bookstore and Blackboard)

• Fundamentals of Algebra & Trigonometry Workbook

• University tutoring and academic support services

• Technical support for Blackboard and MyLabMath

Additional Information

• Students with disabilities should contact the Office of Accessibility Resources for accommodations.

• All university and college policies regarding academic integrity, grade appeals, and student conduct apply.

• For more information on the Quality Enhancement Plan (QEP: TEAM), visit the university website.