Uploaded November 2023 | Updated September 2026, 1 week ago
To get a copy of the AMC 12 Crash Course document shown in the video, please submit this feedback form. https://forms.gle/E5mtnG3aWWgCPYDKA
For those who have watched the AMC 10 Crash Course, the AMC 12 specific topics start at 3:12:19.
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
---
3:12:18 5.5 Logarithm
3:12:43 5.6 Logarithm Formulas
---
3:20:08 5.7-8 Trigonometric Identities
3:20:26 5.10 Unit circle identities
3:21:14 5.11 Pythagorean identities
3:21:27 5.12 Double Angle Identities
3:21:43 5.13 Addition and Subtraction Identities
3:22:55 5.14 Half angle identities
3:23:28 5.15-16 Sum to product/product to sum identities
3:24:08 summing up trigonometry and algebra
3:27:45 5.17 Graphing to solve trigonometry problems
3:28:33 5.18 Periods and graphs of trigonometric functions
3:29:03 5.19 Area of a triangle using geometry
3:29:14 5.20 Law of Sines
3:29:41 5.21 Law of cosines
3:29:48 summary of when to use which identities
---
3:31:19 5.22 Complex numbers
3:43:57 5.23 Complex numbers in Polynomials
3:43:57 5.24 Complex numbers in Trigonometry
===
3:51:09 Ending/conclusions
-------------------------------------------------------------------------------------------------------------------------------------
If you are taking the AMC 10, then you can just check out Ultimate AMC 10 Crash Course Video:
youtu.be/vImrH84wwKc
-------------------------------------------------------------------------------------------------------------------------------------
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 12 Crash Course document shown in the video, please submit this feedback form. https://forms.gle/E5mtnG3aWWgCPYDKA
For those who have watched the AMC 10 Crash Course, the AMC 12 specific topics start at 3:12:19.
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
---
3:12:18 5.5 Logarithm
3:12:43 5.6 Logarithm Formulas
---
3:20:08 5.7-8 Trigonometric Identities
3:20:26 5.10 Unit circle identities
3:21:14 5.11 Pythagorean identities
3:21:27 5.12 Double Angle Identities
3:21:43 5.13 Addition and Subtraction Identities
3:22:55 5.14 Half angle identities
3:23:28 5.15-16 Sum to product/product to sum identities
3:24:08 summing up trigonometry and algebra
3:27:45 5.17 Graphing to solve trigonometry problems
3:28:33 5.18 Periods and graphs of trigonometric functions
3:29:03 5.19 Area of a triangle using geometry
3:29:14 5.20 Law of Sines
3:29:41 5.21 Law of cosines
3:29:48 summary of when to use which identities
---
3:31:19 5.22 Complex numbers
3:43:57 5.23 Complex numbers in Polynomials
3:43:57 5.24 Complex numbers in Trigonometry
===
3:51:09 Ending/conclusions
-------------------------------------------------------------------------------------------------------------------------------------
If you are taking the AMC 10, then you can just check out Ultimate AMC 10 Crash Course Video:
youtu.be/vImrH84wwKc
-------------------------------------------------------------------------------------------------------------------------------------
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
