Introduction to AMC8

Combinatorics

Chapter1 Counting

1.1 Counting Basics
1.2 Venn Diagrams
1.3 Three-set Venn Diagrams
1.4 Gauss formula
1.5 Regrouping the numbers in a sum and product
1.6 Practice problems


Chapter2 Permutations

2.1 Permutation Definition
2.2 Factorials
2.3 Permutations Fundamentals
2.4 Digit Permutations
2.5 Circular Arrangements
2.6 Practice problems


Chapter3 Combinations

3.1 Combination Definition
3.2 Binomial Identity
3.3 Tricky Question


Chapter4 Probability

4.1 Probability Definition
4.2 Probability of Independent events and Dependent Events
4.3 Complementary Counting and Probability
4.4 Practice problems


Chapter5 Casework Problems

5.1 Practice problems
5.2 Harder Question


Chapter6 Principles of inclusion and exclusion(PIE)

6.1 PIE Strategy
6.2 PIE for 2 Events
6.3 PIE for 3 Events
6.4 PIE for number of events
6.5 Practice Question


Chapter7 Stars and Bars

7.1 Stars and Bars Fundamentals
7.2 Stars and Bars with constraints
7.3 Practice Question


Chapter8 Geometric Counting

8.1 Geometric Counting Fundamentals
8.2 Number of Squares in Grid
8.3 Number of Rectangles in Grid
8.4 Path counting
8.5 Practice Counting


Chapter9 Recursion

9.1 Recursion Fundamentals
9.2 Recursion with Constraints
9.3 Probability Recursion
9.4 Practice Problems



Algebra

Chapter10 Ratio and Percentage

10.1 Ratio Fundamentals
10.2 Rate and work
10.3 Practice Problems


Chapter11 Linear Function and Quadratic Function

11.1 Linear Function and Quadratic Function
11.2 Word Problem
11.3 Practice Problem


Chapter12 Speed Distance and Time

12.1 Speed, Distance and Time
12.2 Harmonic Mean
12.3 Practice Problems


Chapter13 sequence and Series

13.1 Arithmetic Sequence
13.2 Geometric Sequence
13.3 Practice Problems


Chapter14 Mean, Median and Mode
14.1 Mean, Median, Mode
14.2 Mean, Median Mode conditions Example
14.3 Practice Problems


Chapter15 Telescoping
15.1 Telescoping
15.2 Telescoping Sum and Product
15.3 Practice Problems



Number Theory

Chapter16 Primes and Divisibility

16.1 Primes
16.2 Divisibility Rules
16.3 Primes Factorization
16.4 Practice Problems


Chapter17 Factors

17.1 Number of Factors
17.2 Sum of Factors
17.3 Product of Factors
17.4 Practice Problems


Chapter18 GCF and LCM

18.1 GCF and LCM Fundamentals
18.2 GCF and LCM Product
18.3 GCF and LCM Properties
18.4 Euclidean Algorithm
18.5 Practice Problems


Chapter19 Modular Arithmetic

19.1 Modular Definition
19.2 Product Rule
19.3 Exponent Rule
19.4 Multiple Modular Congruence
19.5 Digit Cycle



Geometry

Chapter20 Angle Chasing

20.1 Angle Chasing Tricks
20.2 Inscribed Angle
20.3 Polygons
20.4 Advanced Circle Angle Chasing Theorems
20.5 Practice Problems


Chapter21 Triangle
21.1 Area of Triangle
21.2 Special Triangle
21.3 Pythagorean Theorem
21.4 Triangle Properties
21.5 Angle Bisector Theorem
21.6 Practice Problems


Chapter22 Quadrilateral

22.1 Square
22.2 Rectangle
22.3 Rhombus
22.4 Parallelogram
22.5 Trapezoid
22.6 Practice Problems


Chapter23 Circles

23.1 Circle Theorem
23.2 Circular Area
23.3 Length Inside Circles
23.4 Practice Problems


Chapter24 Similarity and Congruence

24.1 Congruent Triangle
24.2 Similar Triangle
24.3 Practice Problems


Chapter25 Area of Polygon

25.1 Area of Polygon
25.2 Practice Problems


Chapter26 3D Geometry

26.1 Cube
26.2 Prism
26.3 Pyramid
26.4 Cylinder
26.5 Cone
26.6 Sphere
26.7 Practice Problems