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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.
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Prerequisite: MTH203: Geometry and MTH303: Algebra II (or equivalents)
Unit 1: Introduction to Trigonometry: Linear Relationships
Unit 2: Trigonometric Ratios
Students begin a three unit exploration into trigonometry. In this unit, students review their understanding of the three basic trigonometric functions learned in geometry; sine, cosine and tangent; and extend this to include their reciprocal functions. Students learn radian measure and are introduced to the unit circle, the foundation of all of trigonometry.
Unit 3: Graph Trigonometric Functions
Students learn the graphs of the parent functions of the six trigonometric functions, as an extension of the unit circle, and explore transformations of these graphs. Students learn about inverse trigonometric functions and restrictions placed on them. Through applications of real-world problems involving trigonometric functions, students form connections between the algebra, the graph, and the description of scenarios that can be modeled with trigonometric functions.
Unit 4: Trigonometric Laws and Identities
The study of trigonometry provides an opportunity to investigate the algebra of trigonometry. This extends to the verification of trigonometric identities, applications of sum, difference, double, and half angle formulas, derivations and applications of the laws of sine and cosine, alternate methods of determining the area of a triangle, and an exploration into angular and linear velocities and how they are related to one another.
Many K12 courses utilize physical materials in addition to the online content. These materials may include the following.
K12 Standard Kits
STANDARD kits contain K12 course materials that are required for completion of the course. These kits include K12 authored materials and/or difficult to procure materials that a student needs to complete a course. Printed reference guides are not included in Standard kits.
CONSUMABLE kits contain only those materials from the standard kit that are intended for one time use. Families who purchase a Standard kit for Child A could later purchase a Consumable kit for Child B to complete the same course.
Offered for added convenience, ADDITIONAL kits contain easily obtained materials needed for the course which a family may already have in their home.
Learning Coach and/or Student Reference Guides are available for purchase with some courses. Electronic versions of these reference guides are also available within digital courses.
Courses with a teacher have designated start dates throughout Fall, Spring, and Summer. Full-year courses last 10 months and semester courses last 4 months. Courses are taught by teachers in K12 International Academy. For details on start dates, click here.
To use this course, you'll need a computer with an Internet connection. Some courses require additional free software programs, which you can download from the Internet.
CPU: 1.8 GHz or faster processor (or equivalent)
RAM: 1GB of RAM
Browser: Microsoft Internet Explorer 9.0 or higher, Mozilla Firefox 10.0 versions or higher, Chrome 17.0 or higher
CPU: PowerPC G4 1 GHz or faster processor; Intel Core Duo 1.83 GHz or faster processor
Browser: Firefox 10.0 versions or higher, Chrome 17.0 or higher (Safari is not supported!)
It is highly recommended that a broadband connection be used instead of dial up.
(excludes shipping, other exclusions apply)