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Scholars Math 10: 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.
Required Text:
Precalculus

22 weeks

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

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

Schedule

Wednesday
May 13 - Oct 7
7:30 - 9:00
PM ET
May 13 - Oct 7
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
$715 (~$33/lesson)
$777 w/books
$715 (~$33/lesson)
With Books $777
CLOSED
Sunday
May 31 - Nov 8
7:30 - 9:00
PM ET
May 31 - Nov 8
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
$715 (~$33/lesson)
$777 w/books
$715 (~$33/lesson)
With Books $777
ENROLL
Few Spots Left!
Thursday
Jun 25 - Nov 19
7:30 - 9:00
PM ET
Jun 25 - Nov 19
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
$715 (~$33/lesson)
$777 w/books
$715 (~$33/lesson)
With Books $777
ENROLL
Wednesday
Aug 12 - Jan 27
7:30 - 9:00
PM ET
Aug 12 - Jan 27
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
$715 (~$33/lesson)
$777 w/books
$715 (~$33/lesson)
With Books $777
ENROLL
Monday
Sep 14 - Mar 8
7:30 - 9:00
PM ET
Sep 14 - Mar 8
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
$715 (~$33/lesson)
$777 w/books
$715 (~$33/lesson)
With Books $777
ENROLL
Sunday
Oct 4 - Mar 28
7:30 - 9:00
PM ET
Oct 4 - Mar 28
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
$715 (~$33/lesson)
$777 w/books
$715 (~$33/lesson)
With Books $777
ENROLL
Thursday
Oct 15 - Apr 1
7:30 - 9:00
PM ET
Oct 15 - Apr 1
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
$715 (~$33/lesson)
$777 w/books
$715 (~$33/lesson)
With Books $777
ENROLL
Sunday
Dec 13 - Jun 6
7:30 - 9:00
PM ET
Dec 13 - Jun 6
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
$715 (~$33/lesson)
$777 w/books
$715 (~$33/lesson)
With Books $777
ENROLL
Spring 2027This course will be offered in Spring 2027. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes July 3 ‐ 5, September 5 ‐ 7, November 23 ‐ 29, December 21 ‐ January 3, February 13 - 15, and May 29 ‐ May 31 2027.

Who Should Take?

This class typically follows our Scholars Math 9: 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 Scholars Math 9: Intermediate Algebra class prior to taking our Precalculus class. Our Scholars Math 9: 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

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

Required Text

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.
Related course: Scholars Math 10: Precalculus

Overall a fantastic course! The instructors were very responsive and personable. Absolutely fantastic.