Course Overview

Introduction

This course, Math 244 – Precalculus, is a comprehensive college-level precalculus class covering a wide range of foundational mathematical topics. The course is designed to prepare students for calculus and other advanced mathematics courses by emphasizing functions, graphing, equations, inequalities, matrices, sequences, series, and trigonometry. The course also includes applications and the use of graphing calculators.

Major Topics and Subtopics

1. Functions and Their Graphs

• Definition: A function is a relation that assigns exactly one output value for each input value.

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

• Graphing: Visual representation of functions on the coordinate plane.

• Piecewise Functions: Functions defined by different expressions for different intervals of the domain.

• Transformations: Includes shifts, reflections, stretches, and compressions of function graphs.

• Modeling: Using functions to represent real-world situations.

• Example: is a piecewise function.

2. Linear and Quadratic Functions

• Linear Functions: Functions of the form .

• Quadratic Functions: Functions of the form .

• Quadratic Models: Using quadratic functions to model data.

• Inequalities: Solving linear and quadratic inequalities.

• Example: The graph of is a parabola.

3. Polynomial and Rational Functions

• Polynomial Functions: Functions of the form .

• Rational Functions: Functions expressed as the ratio of two polynomials.

• Graphing: Includes identifying zeros, asymptotes, and end behavior.

• Real & Complex Zeros: Solutions to may be real or complex.

• Example: is a rational function.

4. Exponential and Logarithmic Functions

• Exponential Functions: Functions of the form .

• Logarithmic Functions: Functions of the form .

• Properties of Logarithms: Includes product, quotient, and power rules.

• Solving Equations: Techniques for solving exponential and logarithmic equations.

• Example: because .

5. Trigonometric Functions and Applications

• Angles and Radian Measure: Measuring angles in degrees and radians.

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

• Unit Circle: Defines trigonometric functions for all real numbers.

• Graphing Trigonometric Functions: Includes periodicity, amplitude, phase shift, and translation.

• Inverse Trigonometric Functions: Functions that reverse the effect of trigonometric functions.

• Identities and Formulas: Fundamental identities such as .

• Applications: Solving problems involving arc length, area of a sector, linear and angular velocity.

• Example: in a right triangle.

6. Polar Coordinates, Complex Numbers, and Vectors

• Polar Coordinates: Representing points using radius and angle.

• Complex Numbers: Numbers of the form ; can be represented in algebraic and trigonometric form.

• Vectors: Quantities with both magnitude and direction.

• Example: can be written in trigonometric form as where .

7. Analytic Geometry (Conic Sections)

• Conic Sections: Includes circles, ellipses, parabolas, and hyperbolas.

• Graphing: Identifying and graphing conic sections based on their equations.

• Example: The equation represents a circle.

8. Systems of Equations and Inequalities

• Solving Systems: Methods include substitution, elimination, and matrix (augmented matrix) methods.

• Example: Solving yields .

9. Sequences, Series, and Binomial Theorem

• Sequences: Ordered lists of numbers defined by a rule.

• Series: The sum of terms in a sequence.

• Infinite Geometric Series: converges if .

• Binomial Theorem: Provides a formula for expanding .

• Example: .

Course Structure and Assessment

Grading Breakdown

Letter Grade Scale: A = 90–100%, B = 80–89%, C = 70–79%, D = 60–69%, F < 60%

Calculator Policy

• TI-83/84 recommended; TI-85/86 allowed.

• TI-89 and TI-92 NOT allowed on exams.

Important Dates

• Last Day to Add: 6/21/2026

• Last Day to Drop without a Grade: 6/21/2026

• Last Day to Drop with a Grade: 7/23/2026

• Final Exam: August 6, Thursday, 8:30-10:30 am

Tentative Weekly Schedule

Student Learning Outcomes

• Analyze properties and behavior of functions and implement appropriate techniques to solve applications.

• Use a variety of methods to solve systems of equations and implement those methods to solve application problems.

• Recognize and graph conic sections.

• Analyze the behavior of sequences and series.

• Apply the binomial expansion theorem.

• Analyze properties and behavior of trigonometric functions and implement appropriate techniques to solve applications.

• Use polar coordinates; represent complex numbers in rectangular and trigonometric forms; perform operations with complex numbers.

Additional Info

• Students are expected to attend all class meetings and participate actively.

• Homework is assigned via MyLabMath (Pearson) and must be completed before due dates.

• Free tutoring is available at the Academic Success Center.

• Disability Support Services are available for students needing accommodations.