Uploaded December 2022 | Updated September 2026, 1 week ago
Mastering AMC 8 book: omegalearn.org/mastering-amc8
The book covers the most important concepts on the AMC 8 contest, and includes video lectures for every chapter, formulas for every topic, and hundreds of examples and practice problems with detailed video solutions.
Mastering AMC 10/12 book: omegalearn.org/mastering-amc1012.
The book includes video lectures for every topic on the AMC 10/12 contests, along with many useful formulas and hundreds of examples and practice problems with detailed video solutions.
Join our Discord server to discuss problems from our books or any help with math competitions in general: bit.ly/OmegaLearnDiscord
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In this video, we will cover Diophantine Equations on the AMC 8.
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To get notifications for new videos, click here to subscribe:
bit.ly/2JjEDqr
For more practice, watch the following Video Series:
1. AMC 8 Fundamentals:
youtube.com/playlist?list=PLT9bNzqjDoMmMNsMAJ3g7C4ptRnPMMrpT
2. AMC 8 Advanced:
youtube.com/playlist?list=PLT9bNzqjDoMmjM-PFJktrlab4-bkWwFMP
3. AMC 10/12 Fundamentals:
youtube.com/playlist?list=PLT9bNzqjDoMkoIg9K_bs4EjdpHYlS0L51
4. Mastering AMC 10/12
youtube.com/playlist?list=PLT9bNzqjDoMlmyxKw2bp5nHsEu-Zn9dac:
More resources available at: omegalearn.org
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Tags:
AMC 8, AMC 8 Preparation, AMC 8 Crash Course, AMC 8 Concepts, AMC 8 Review, AMC 10, AMC 12, MATHCOUNTS, MathLeague, Number Theory, Primes, Factors, Competition math, Number of Factors, Sum of Factors, Product of Factors, Permutations, Combinations, Combinatorics, Modular Arithmetic, Recursion, Probability, Divisibility, Competition Math, Area of a Triangle, Similar Triangles, Cyclic Quadrilateral, Power of a Point, 3D Geo, Polygons, Coordinate Geometry
Mastering AMC 8 book: omegalearn.org/mastering-amc8
The book covers the most important concepts on the AMC 8 contest, and includes video lectures for every chapter, formulas for every topic, and hundreds of examples and practice problems with detailed video solutions.
Mastering AMC 10/12 book: omegalearn.org/mastering-amc1012.
The book includes video lectures for every topic on the AMC 10/12 contests, along with many useful formulas and hundreds of examples and practice problems with detailed video solutions.
Join our Discord server to discuss problems from our books or any help with math competitions in general: bit.ly/OmegaLearnDiscord
-------------------------------------------------------------------------------------------------------------------------------------------------
In this video, we will cover Diophantine Equations on the AMC 8.
-------------------------------------------------------------------------------------------------------------------------------------------------
To get notifications for new videos, click here to subscribe:
bit.ly/2JjEDqr
For more practice, watch the following Video Series:
1. AMC 8 Fundamentals:
youtube.com/playlist?list=PLT9bNzqjDoMmMNsMAJ3g7C4ptRnPMMrpT
2. AMC 8 Advanced:
youtube.com/playlist?list=PLT9bNzqjDoMmjM-PFJktrlab4-bkWwFMP
3. AMC 10/12 Fundamentals:
youtube.com/playlist?list=PLT9bNzqjDoMkoIg9K_bs4EjdpHYlS0L51
4. Mastering AMC 10/12
youtube.com/playlist?list=PLT9bNzqjDoMlmyxKw2bp5nHsEu-Zn9dac:
More resources available at: omegalearn.org
-------------------------------------------------------------------------------------------------------------------------------------------------
Tags:
AMC 8, AMC 8 Preparation, AMC 8 Crash Course, AMC 8 Concepts, AMC 8 Review, AMC 10, AMC 12, MATHCOUNTS, MathLeague, Number Theory, Primes, Factors, Competition math, Number of Factors, Sum of Factors, Product of Factors, Permutations, Combinations, Combinatorics, Modular Arithmetic, Recursion, Probability, Divisibility, Competition Math, Area of a Triangle, Similar Triangles, Cyclic Quadrilateral, Power of a Point, 3D Geo, Polygons, Coordinate Geometry








![Ultimate AMC 10 Crash Course - Combinatorics, Algebra, Number Theory, Geometry
To get a copy of the AMC 10 Crash Course document shown in the video, please submit this feedback form.
https://forms.gle/E5mtnG3aWWgCPYDKA
If you are taking the AMC 12, then dont forget to check out the AMC 12 Crash Course Video:
https://youtu.be/jcZip-YtSn4
The AMC 12 Crash Course video includes all the AMC 10 concepts along with AMC 12 specific topics like Logarithms, Trigonometry and Complex Numbers which are essential for anyone taking the AMC 12.
0:00 Introduction
[Chapter 1: Combinatorics 0:29 ]
0:33 1.1 Factorials
0:38 1.2 Permutations
1:48 1.3 Word rearrangements
3:34 1.4 Combinations
4:57 1.5 Subsets
5:33 1.6 Probability
5:40 1.7 Distinguishability
8:06 1.8-9 Probability of independent/dependent events
9:25 1.10 Casework
12:17 1.11 Complementary counting
13:39 1.12 Principle of Inclusion and Exclusion
15:20 1.13 Stars and bars
20:33 1.14 Combinatorial identities
21:49 1.15 Vandermondes identity
24:51 1.16 Pascals and hockey stick identity
27:03 1.17 Rectangle counting
29:18 1.18 Square counting
31:17 1.19 Path counting
32:24 1.20 Geometric probability
34:43 1.21 Expected value
39:20 1.22 Recursion
40:48 1.23 Probability States
[Chapter 2: Algebraic Manipulations 47:31 ]
47:34 2.1 Algebraic manipulations (Exponent rules)
47:38 2.2 Binomial expansions
51:04 2.3 Quadratic factorisations
51:08 2.4 Cubic factorisations
51:33 2.5 Higher power factorisations
54:23 2.6 Algebraic equations
59:08 2.7 Polynomials
1:03:42 2.8 Polynomial Root representation
1:06:35 2.9 Symmetric polynomials
1:09:29 2.10 Polynomial Manipulations
1:20:50 2.11 Arithmetic Sequences
1:21:33 2.12 Geometric sequences
1:22:39 2.13 Special sequences
1:23:15 2.14 Telescoping
1:25:28 2.15 Mean Median Mode
1:26:14 2.16 Work and rate
1:26:39 2.17 Speed distance time
[Chapter 3: Number theory 1:27:08 ]
1:27:11 3.1 Primes
1:27:38 3.2 Sum of Factors
1:28:16 3.3 Product of Factors
1:28:45 3.4 Divisibility
1:29:10 3.5 GCF and LCM
1:31:43 3.6 Modular Arithmetic
1:49:55 3.7 Algebraic Number Theory
1:49:56 3.8-11 skipped (overlapped with algebra)
1:50:17 3.12 Sophie Germains Identity
1:51:19 3.13 Diophantine Equations
1:57:28 3.14 Bases
1:58:27 3.15 Palindromes
1:58:27 3.16 Miscellaneous (Chicken McNugget, Legendre)
[Chapter 4: Geometry 2:00:32 ]
2:00:40 4.1 Angle Chasing (empty subchapter)
2:00:40 4.2 Basics of Angle Chasing
2:14:51 4.3 Area of a triangle
2:20:15 4.4 Triangle properties
2:22:30 4.5 Equilateral triangles
2:22:43 4.6 Right triangles
2:24:06 4.7 Similar Triangles (MOST IMPORTANT!)
2:30:02 4.8 Angle Bisector Theorem
2:32:18 4.9-13 Square, Rectangle, Rhombus, Parallelogram, Trapezoid
2:33:19 4.14-15 circle, circle length
2:34:27 4.16 Power of a point
2:37:37 4.17 Cyclic Quadrilaterals
2:40:18 4.18 Polygons
2:40:23 4.19 Hexagons
2:40:39 4.20 Octagons
2:41:09 4.22-23 Cube, Rectangular prism (4.21 Pentagons blank)
2:41:31 4.24 Cylinder
2:41:47 4.25 Cone
2:43:52 4.26 Sphere
2:43:58 4.27 Tetrahedron
2:44:19 4.28 Pyramid (+demo 4.29 vol. complex polyhedrons)
2:45:07 4.30 Cross sections
2:50:09 4.31 Area of complex shapes
2:50:54 4.32 Length of complex shapes
2:51:54 4.33 Line in coordinate plane
2:53:44 4.34 Circle in coordinate plane
2:53:51 Why use coordinates in geometry?
2:55:44 4.35 Shoelace Theorem to find Area
2:59:40 4.26 Picks Theorem (optional)
[Chapter 5: Advanced Topics 3:00:27 ]
3:00:27 5.1 Floor and Ceiling Functions
3:03:16 5.2 Trivial Inequality
3:04:23 5.3 AM-GM
3:07:55 5.4 Cauchy Schwarz
3:10:41 small revision - techniques for optimisation problem
Mastering AMC 10/12 book: https://www.omegalearn.org/mastering-amc1012.
The book includes video lectures for every topic on the AMC 10/12 contests, along with many useful formulas and hundreds of examples and practice problems with detailed video solutions.
Join our Discord server to discuss problems from our books or any help with math competitions in general: https://bit.ly/OmegaLearnDiscord Ultimate AMC 10 Crash Course - Combinatorics, Algebra, Number Theory, Geometry](https://i.ytimg.com/vi/vImrH84wwKc/mqdefault.jpg)

