Course Description

Pre-calculus weaves together concepts of algebra and geometry into a preparatory course for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. Topics include quadratic, exponential, logarithmic, radical, polynomial, and rational functions; matrices; and conic sections in the first semester. The second semester covers an introduction to infinite series, trigonometric ratios, functions, and equations; inverse trigonometric functions; applications of trigonometry, including vectors; polar equations and polar form of complex numbers; arithmetic of complex numbers; and parametric equations.

Connections are made throughout the course to calculus and a variety of other fields related to mathematics. Purposeful concentration is placed on how the concepts covered relate to each other. Demonstrating the connection between the algebra and the geometry of concepts highlights the interwoven nature of the study of mathematics.

Prerequisite: MTH203: Geometry and MTH303: Algebra II (or equivalents)

Course Outline

SEMESTER 1

Unit 1: Introduction to Precalculus and Polynomial Functions

Students extend their understanding of quadratic, radical and rational equations to encompass inequalities of the same. Concepts and theorems of polynomial and rational equations and functions are reviewed and extended to include holes, slant asymptotes and limit notation to end behavior.

• Introduction to Precalculus
• Polynomial Functions: Introduction
• Polynomial Functions
• Quadratic Functions
• Roots of Polynomial Equations
• Rational Equations and Radical Equations
• Polynomial Functions Unit Review

Unit 2: Polar Form of Complex Numbers

• Polar Form of Complex Numbers: Introduction
• The Polar Coordinate System
• Polar and Rectangular Form
• Operations with Complex Numbers
• Polar Form of Complex Numbers
• Polar Form of Complex Numbers Unit Review

Unit 3: Conic Sections

Conic sections are real-life phenomena that are found in architecture, space, nature, and more. Students explore how and where they occur as they progress through this unit, learning about four conic sections—circles, ellipses, hyperbolas, and parabolas. Derivations of the standard form of these conic sections are included to help foster student appreciation for the relationship that exists between algebra and geometry.

• Conic Sections: Introduction
• Conic Sections
• Circles
• Ellipses
• Hyperbolas
• Parabolas
• Conic Sections Unit Review

Unit 4: Exponential and Logarithms

A thorough understanding of logarithmic expressions and functions is necessary for success in higher mathematics. Students deepen their understanding of the relationship between exponential and logarithmic functions as they explore how the properties of logarithms allow for equivalent forms of logarithmic expressions, and for a variety of logarithmic and exponential equation to be solved. Concentration is on real-world application of exponential equations.

• Exponents and Logarithms: Introduction
• Exponential Functions
• Logarithmic Functions
• Exponents and Logarithms Unit Review

Unit 5: Discrete Mathematics

Students build on their understanding of finite arithmetic and geometric sequences and series to explore infinite sequences and series. Students learn sigma notation, and properties of limits, as well as the ratio test as a method of determining if an infinite series converges or diverges. Students explore two different (but closely related) methods of expanding binomials.

• Discrete Mathematics: Introduction
• Discrete Mathematics
• Sequences and Series: Terms, Sums, and Limits
• Sequences and Series: Convergence, Divergence, and Applications
• Discrete Mathematics Unit Review