# AMC 10/12

### How the class is planned

The class will cover topics of algebra, geometry, counting & probility and number theory.

Counting & probility is either missed in high school math or is taught in a shallow way, like a dragonfly touching the water surface. We teach probability and count in more profound way for AMC + AIME problems.

We plan to do significant work on geometry since students’ ability to solve medium to difficult geometry problems plays a crucial factor for them to be able to pass AMC or AMC + AIME or not.

Every week students get two problem sets as homework: one full set of AMC (25 multiple-choice) and another problem set of current or recent topics. By this way, for each topic, students will see this type of problems in 3-4 weeks and accumulate their knowledge, problem solving skills, and proficiency level on the topic.

On the way, we help students to develop trial, fearless spirit: try whatever they can think about to tackle a given problem. Roughly for students who do all assignments, fully understand our class materials and be able to use them to solve AMC and AIME problems, they significantly raise their chance to pass AMC, even to pass AIME.

Pre-requisites: Algebra I and Geometry

Total number of classes: 12

Class Outline

This class covers essential topics in AMC 10, 12, and AIME in more profound way. Most examples and problems in weekly assignments will be real AMC and AIME problems in the past: roughly 80% AMC and 20% AIME. Every week students get two problem sets as homework: one full set of AMC (25 multiple-choice questions) and another problem set about current or recent topics. At the beginning of class 2 – 12, we will fully discuss these problems in weekly assignment, and then continue to review new topics.

Three books listed in the curriculum provide additional materials for students to study, and they are optional. Students are expected to do weekly assignments.

We encourage group discussion in class.

Class 1

• Integer equations
• Vieta’s formula
• Fundamental theorem of algebra
• Probability and count: two commonly-used approaches
• Permutation and combination

Class 2

• To fully discuss AMC and AIME problems in homework 1
• Probability and count (continued)
• Binomial theorem
• Pigeon-hole principle
• Venn Diagram
• Exponents and Log
• Function and inverse function

Class 3

• To fully discuss AMC and AIME problems in homework 2
• Sequence and series
• Arithmetic and geometric sequences
• Recursive sequences
• Complex numbers, Complex plane, DeMorvre theorem

Class 4

• To fully discuss AMC and AIME problems in homework 3
• Triangles
• Similar and congruent triangles, Triangle inequalities
• Ratio of areas of triangles
• Medians and centroid
• Angle bisectors and incenter
• Perpendicular bisectors and circumcenter
• Triangle areas (7 approaches)
• Laws of sine and cosine
• Stewart theorem

Class 5

• To fully discuss AMC and AIME problems in homework 4
• Circles
• Tangent lines
• Inscribed angles
• Power theorem
• External secant theorem
• Circular sectors
• Parallel lines
• Tangent circles

Class 6

• To fully discuss AMC and AIME problems in homework 5
• Polygon and angles
• Circles and polygon
• Ptolemy’s theorem
• Pick’s theorem
• 3D geometry
• Euler’s formula

Class 7

• To fully discuss AMC and AIME problems in homework 6
• Trigonometry
• Polar coordinates
• Inverse trig functions
• Trig identities
• Laws of sine and cosine

Class 8

• To fully discuss AMC and AIME problems in homework 7
• Analytic geometry
• 2D, 3D distance
• Point-line distance, point-plane distance
• Vectors, Inner product, Angle theorem
• Lines and vectors
• Vectors and matrices
• Rotation

Class 9

• To fully discuss AMC and AIME problems in homework 8
• Number theory
• Even and odd numbers
• Integer remainder
• Prime factorization
• Number of divisors
• GCD and LCM
• Diophantine equation

Class 10

• To fully discuss AMC and AIME problems in homework 9
• Absolute value
• Statistics, mean, median, modes
• Arithmetic and geometric means
• Basic algebra formulas
• Floor function
• Proportion and application problems
• Direct and inverse relations

Class 11

• To fully discuss AMC and AIME problems in homework 10
• Function domain and range
• Inverse function
• Polynomial remainder
• Descarte’s rule
• Graphs of functions
• Composition of functions

Class 12

• To fully discuss AMC and AIME problems in homework 11
• Graph theory
• Euler path, Euler cycle
• Inequalities
• Comprehensive review

Three books: 1. First Steps for Math Olympians by J. Douglas Faires 2. the Art of Problem Solving Volume 1: the BASICS by Sandor Lehoczky, Richard Rusczyk 3. the Art of Problem Solving Volume 2: and Beyond by Richard Rusczyk, Sandor Lehoczky