Course Description:
This Precalculus video course puts together the many concepts taught in Algebra 1, Geometry, and Algebra 2 in order to prepare students for Calculus and other subsequent math courses. In general, this course covers unit circle trigonometry, analytical trigonometry, right triangle trigonometry, the polar coordinate system, vectors, complex numbers, proofs by mathematical induction, the fundamental theorem of algebra, and an introduction to linear algebra. In each of the lessons, students are exposed to the basics skills of the concepts and challenged to use and improve their critical thinking skills.
The course includes:
12+ hours of video
5 units
34 instructional videos
34 blank pdf notes for students to use and fill in while watching the instructional videos
34 practice worksheets for students to practice and master the concepts being taught
34 answers key and videos (I explain step by step how to arrive at the correct answer)
350+ practice problems and step by step resolutions
5 tests (1 at the end of each unit)
5 test answer keys (one for each unit test)
Course Goals: Upon completion of this course, students will be well prepared for Calculus and have an introduction to a Linear Algebra course. Students will have a solid foundation on trigonometry, vectors, and matrices. Students will not only be able to use these skills to solve problems, but they will also be able to apply them to different situations.
Target Audience: This course is for students who have mastered the concepts taught in a traditional Algebra 2 course and are planning to take Calculus, or for those currently enrolled in a Precalculus class but need additional practice with the concepts being taught.
Technology: Although the course is taught such that a calculator is not necessary, a student may be more comfortable using one. If a student chooses to use a calculator make sure it has trigonometric functionality (a basic scientific calculator would not suffice).
Course Concepts:
Unit 1 – Unit Circle Trigonometry
The Unit Circle
Angle Measures in both radians and degrees
Sine and Cosine Ratios
Inverse Sine and Cosine
Graphing Sine and Cosine
Modeling real world situations with trigonometric functions
Tangent and Cotangent Ratios
Secant and Cosecant Ratios
Tangent and Slope
Unit 2 – Analytical Trigonometry
Pythagorean Identities
Addition and Subtraction Formulas
Half and Double Angle Formulas
Solving trig equations
Unit 3 – Triangular Trigonometry
Right Triangular Trig
Law of Sines
Law of Cosines
Area of a Triangle
Applying trig to real world situations
Unit 4 – Polar Coordinates, Vectors, and Complex Numbers
Polar Coordinates
Converting between polar and cartesian coordinates
Basics of vectors in cartesian coordiantes
Operations with vectors in cartesian coordiantes
Vectors in polar coordinates
Basics of Complex Numbers
More on Complex Numbers
De'Moivre's Theorem
Unit 5 – Proofs by Mathematical Induction, The Fundamental Theorem of Algebra, and Intro to Linear Algebra
Proofs by Mathematical Induction
Fundamental Theorem of Algebra
Intro to Linear Algebra and Matrices
Row Operations with Matrices
Row Echelon and Reduced Row Echelon Form
Coefficient Matrices
Guassian and Guass-Jordan Elimination
Basic Operations on Matrices
