Uploaded November 2023 | Updated September 2026, 1 week ago
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 don't forget to check out the AMC 12 Crash Course Video:
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.
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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 Vandermonde's identity
24:51 1.16 Pascal's 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 Germain's 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: 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
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 don't forget to check out the AMC 12 Crash Course Video:
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 Vandermonde's identity
24:51 1.16 Pascal's 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 Germain's 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: 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
