AGES 14  - 18

Pre-Calculus

A comprehensive textbook covering precalculus topics. Specific topics covered include trigonometry, complex numbers, vectors, and matrices. Includes many problems from the AIME and USAMO competitions.

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Who is this course for
This course is for students who have completed our beginner level math courses.
This course typically takes 3-6 months to complete. This depends on the student's experience and how fast they can master the concepts and the knowledge. Our instructors move at the pace of the student, it may take extra time for some students to reinforce what they have learned.
Curriculum
Chapter 1: Functions Review
Definition of functions, graph of functions, composition, and inverse functions
Chapter 2: Introduction to trigonometric functions
Unit Circle, Radians, graphs, transformations of trig functions, and inverse trig
Chapter 3: Trigonometric Identities
Sum and differences, double and half, sum-to-product identities
Chapter 4: Applications to Geometry
Law of cosines, law of sines
Chapter 5: Parameterization and trigonometry coordinate system
Parameterization, polar coordinates
Chapter 6: Basics of Complex Numbers
Arithmetics of complex numbers, complex plane
Chapter 7: Trigonometry and Complex numbers
Trig ratios in exponential form, roots of unity
Chapter 8: Vectors in two dimensions
Definition, dot product, lines and linear dependence
Chapter 9: Vectors and Matrices in Three dimensions
Lines and Planes in three dimensions
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