Precalculus Online Math Course

Precalculus

Introduction and evaluation of trigonometric functions, trigonometric identities, geometry with trigonometry, parametric equations, special coordinate systems, complex numbers, exponential form of complex numbers, De Moivre's Theorem, roots of unity, geometry with complex numbers, two-dimensional and three-dimensional vectors and matrices, determinants, dot and cross product, applications of vectors and matrices to geometry.

22 weeks

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

SYLLABUS
22 weeks ARE YOU READY? DO YOU NEED THIS? SYLLABUS  

Schedule

Thursday
Sep 17 - Mar 4
7:30 - 9:00
PM ET
Sep 17 - Mar 4
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$570
$627 w/books
$570
With Books $627
CLOSED
Tuesday
Nov 3 - Apr 20
7:30 - 9:00
PM ET
Nov 3 - Apr 20
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$570
$627 w/books
$570
With Books $627
CLOSED
Monday
Dec 7 - May 17
7:30 - 9:00
PM ET
Dec 7 - May 17
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$570
$627 w/books
$570
With Books $627
ENROLL
Thursday
Jan 21 - Jun 17
7:30 - 9:00
PM ET
Jan 21 - Jun 17
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$595
$652 w/books
$595
With Books $652
ENROLL
Tuesday
Feb 23 - Jul 20
7:30 - 9:00
PM ET
Feb 23 - Jul 20
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$595
$652 w/books
$595
With Books $652
ENROLL
Sunday
Mar 7 - Aug 15
7:30 - 9:00
PM ET
Mar 7 - Aug 15
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$595
$652 w/books
$595
With Books $652
ENROLL
Friday
Mar 19 - Aug 13
7:30 - 9:00
PM ET
Mar 19 - Aug 13
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$595
$652 w/books
$595
With Books $652
ENROLL
Wednesday
Apr 28 - Sep 22
7:30 - 9:00
PM ET
Apr 28 - Sep 22
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$595
$652 w/books
$595
With Books $652
ENROLL

AoPS Holidays

There are no classes December 21–January 3, May 29–31, July 3–5, and September 4–6.

Who Should Take?

This class typically follows our Intermediate Algebra course. Students should have completed an honors Algebra 2 or an equivalent course before considering this class. Students who have already taken a standard trigonometry or precalculus class should not simply assume this class is too easy for them. Instead, they should take the diagnostic test above to determine if this class is appropriate for them. Similarly, a student who has completed an honors Algebra 2 course should consider taking our Intermediate Algebra class prior to taking our Precalculus class. Our Intermediate Algebra class includes the non-trigonometric topics of a typical precalculus class, plus a great many interesting topics left out of most standard curricula.

Lessons

Lesson 1 Basic Trigonometry
Lesson 2 Graphing Trig and Inverse Trig Functions
Lesson 3 Trigonometric Identities I
Lesson 4 Trigonometric Identities II
Lesson 5 Law of Cosines and Law of Sines
Lesson 6 More Geometry with Trigonometry
Lesson 7 Parametric Equations
Lesson 8 Polar, Cylindrical, and Spherical Coordinates
Lesson 9 Introduction to Complex Numbers and the Complex Plane
Lesson 10 Trigonometry and Complex Numbers
Lesson 11 Exponential Form
Lesson 12 Roots of Unity
Lesson 13 Geometry Using Complex Numbers
Lesson 14 Vectors in Two Dimensions
Lesson 15 Vectors and Matrices in Two Dimensions
Lesson 16 Matrices in Two Dimensions
Lesson 17 Matrices in Two Dimensions II
Lesson 18 Determinants of 2x2 Matrices and Introduction to 3D Vectors
Lesson 19 Matrices in Three Dimensions
Lesson 20 Lines and Planes in Three Dimensions
Lesson 21 Cross Product and Determinant
Lesson 22 Applications of Vectors to Euclidean Geometry

Required Textbook

Precalculus
By Richard Rusczyk

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.

I have loved all the Art of Problem Solving courses that I've taken in the past, and this one was no exception. The instructor was very knowledgeable and fun to work with, and I learned many new concepts every week. It is a great privilege to take these classes; Art of Problem Solving has truly changed my life.

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