Pre-Calculus [Competency Based] (2nd semester)

Course Description\nPre-Calculus helps students gain the knowledge they need for success in calculus and other high-level math courses. Students focus on a variety of functions, including their solutions, characteristics, and graphs. They explore the inverse relationship between exponential and logarithmic functions. Students learn how to use advanced methods to solve systems of equations. Next, students work with trigonometric functions as they graph, find values with the unit circle, verify identities, and solve trigonometric equations. Students then work with series and sequences and relate certain types of functions to arithmetic and geometric sequences. Students end the course by learning about vectors, conic sections, and polar coordinates. By the end of this course, students gain knowledge and appreciation for higher-level math concepts and their applications.\n\nCourse Breakdown\n\n Unit circle\n Trigonometric ratios\n Graphs of trigonometric functions\n Applications of trigonometric functions\n Trigonometric identities and laws Sequences and series\n Counting principles\n Probability\n Vectors\n Ellipses and parabolas\n\nCourse Goals\n Apply radian and degree measures of angles and the unit circle to analyze trigonometric functions.\n Choose trigonometric functions to model periodic behavior, and describe the properties of their graphs.\n Apply the properties of trigonometric ratios and special right triangles to solve problems.\n Verify basic trigonometric identities and simplify expressions using these and other trigonometric identities.\n Evaluate and solve trigonometric equations. Construct and evaluate arithmetic and geometric sequences.\n Calculate partial and infinite sums of mathematical sequences.\n Apply methods of probability calculation to real-world examples.\n Analyze and compute basic calculations involving vectors.\n Construct and analyze equations for conic sections, as well as interpret their graphs.