College Algebra and Trigonometry (MA120) – Syllabus and Study Guide

Course Overview

Introduction

This course, College Algebra and Trigonometry (MA120), provides a comprehensive review of algebraic and trigonometric concepts essential for precalculus. It is designed for students preparing for further studies in mathematics, physics, and related fields.

• Location: Dearborn STEM Academy (Room 232)

• Schedule: Mondays & Wednesdays 8-9:30 am (Mandatory); Friday Support Sessions 8:30-9:30 am (Required if grade is below C+)

• Instructor: Cindy Nguyen (she/her)

• Contact: [e-mail]

Course Structure and Requirements

Credits and Prerequisites

• Credits: 3 (Lecture)

• Pre-requisites: MA 095, MA 105 (grade of C- or higher), MA 115 or Placement

• Credit Hour Definition: 3-credit course requires approximately 3 hours/week in lectures and 6 hours/week of homework.

Required Materials

• Textbook: Algebra and Trigonometry by Robert Blitzer, 7th ed. ISBN 978-0135922179

• Calculator: Scientific or graphing calculator (non-internet connected)

• Notebook: Standard spiral notebook for assignments

• Online Resources: Canvas LMS, Pearson MyLab (for homework)

Course Description

Scope and Goals

The course covers units of measurement, algebraic expressions, equations (polynomial, rational, radical, absolute value), functions and their graphs, and trigonometric operations. Emphasis is placed on problem-solving, critical reasoning, and communication of mathematical concepts.

• Review of units of measurement and the metric system

• Algebraic operations and equations

• Functions and their graphs

• Trigonometric functions and applications

• Application problems and word problems

Learning Outcomes

Upon Completion, Students Will Be Able To:

• Use mathematical reasoning to solve problems using symbolic, graphical, numerical, and written representations

• Demonstrate proficiency in algebraic concepts

• Apply mathematics and physics concepts to solve application problems

• Communicate quantitative information effectively

• Show proficiency in technical skills and concepts required for further study

• Access and utilize resources for continued learning in mathematics and physics

Course Outline

Main Topics and Subtopics

• Chapter 1: Algebraic Expressions and Equations

  • P.1 Mathematical Reasoning

  • P.2 Exponents

  • P.3 Radicals and Rational Exponents

  • P.4 Polynomials

  • P.5 Factoring Polynomials

  • P.6 Rational Expressions

• Chapter 2: Equations

  • 1.2 Linear and Rational Equations

  • 1.5 Quadratic Equations

  • 1.6 Other Types of Equations (Radical, Absolute Value, etc.)

  • 8.1 Systems of Linear Equations

• Chapter 3: Functions and Graphs

  • 2.1 Basics of Functions and their Graphs

  • 2.2 More Functions and their Graphs

  • 2.5 Transformations of Functions

  • 2.6 Combinations of Functions, Composite Functions

  • 2.7 Inverse Functions

• Chapter 5: Trigonometry

  • 5.1 Angles and Radian Measures

  • 5.2 Right Triangle Trigonometry

  • 5.3 Trigonometric Functions of Any Angle

  • 5.4 Trigonometric Functions of Real Numbers

Assignments and Grading

Assignment Types

• Homework: Due at 8:30 am each class day (except Day 1). Late work accepted for half credit.

• Quizzes: Weekly, usually Wednesdays. Lowest score dropped if Friday support session attended.

• Tests: Three major tests (end of Chapter P, Chapter 1, Chapter 2). No quizzes the week of a test.

• Final Exam: Covers Chapter 5 (Trigonometry) and selected earlier chapters.

Grading Criteria

• Homework assignments

• Quiz scores

• Test scores

• Final exam

• Participation and attendance

Key Mathematical Concepts

Algebraic Expressions and Equations

Algebraic expressions involve variables, constants, and operations. Equations set two expressions equal and are solved for unknowns.

• Polynomial: An expression of the form $a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$

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

• Factoring: Expressing a polynomial as a product of its factors

• Rational Expression: A ratio of two polynomials, $\frac{P(x)}{Q(x)}$

Functions and Their Graphs

A function is a relation that assigns each input exactly one output. Functions can be represented algebraically, graphically, or numerically.

• Function Notation: $f(x)$

• Domain and Range: The set of possible inputs (domain) and outputs (range)

• Transformation: Shifting, stretching, or reflecting the graph of a function

• Inverse Function: $f^{-1}(x)$, reverses the effect of $f(x)$

Trigonometric Functions

Trigonometry studies the relationships between angles and sides of triangles, and the properties of periodic functions.

• Angle Measures: Degrees and radians ($\pi$ radians = 180 degrees)

• Right Triangle Trigonometry: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

• Trigonometric Functions: Sine, cosine, tangent, and their reciprocals

• Unit Circle: A circle of radius 1 centered at the origin, used to define trigonometric functions for all real numbers

Support Services and Policies

Student Support

• Accessibility accommodations (IEP/504)

• IT support and library services

• Wellness and career services

• Academic integrity and professionalism

Attendance and Participation

• Regular attendance and active participation are required

• Engagement in coursework and class discussions is expected

Sample Course Schedule Table

Week	Topics	Assessment
1	P.1 Mathematical Reasoning, P.2 Exponents	Quiz P.1, P.2
2	P.3 Radicals and Rational Exponents, P.4 Polynomials	Quiz P.3, P.4
3	P.5 Factoring Polynomials, P.6 Rational Expressions	Quiz P.5, P.6
4	Test 1 Review	Test 1 (Chapter P)
5	1.2 Linear and Rational Equations, 1.5 Quadratic Equations	No Quiz/Test
6	1.6 Other Types of Equations, 8.1 Systems of Linear Equations	Quiz 1.2, 1.5, 1.6, 8.1
7	Test 2 Review	Test 2 (Equations & Systems)
8	2.1 Basics of Functions and their Graphs, 2.2 More Functions	Quiz 2.1, 2.2
9	2.5 Transformations of Functions	Quiz 2.5
10	2.6 Combinations of Functions, Composite Functions, 2.7 Inverse Functions	Quiz 2.6, 2.7
11	Test 3 Review	Test 3 (Functions & Graphs)
12	5.1 Angles and Radian Measures, 5.2 Right Triangle Trigonometry	No Quiz/Test
13	5.3 Trigonometric Functions of Any Angle, 5.4 Trigonometric Functions of Real Numbers	No Quiz/Test

Additional Info

• Students are expected to use a scientific calculator and access online homework via Pearson MyLab.

• Canvas LMS is used for course materials, assignments, and communication.

• Support services are available for accessibility, wellness, and academic success.