# AMC 10/12

The AMC—organized by the Mathematical Association of America—is a prestigious nationwide mathematics competition in the United States. Started in the 1950s, the AMC has been the exclusive pathway for a student to advance to the USA Mathematical Olympiad. The AMC is an opportunity for students to excel in an academic sphere, and gives students a chance to stimulate their mathematical curiosity and skills. Many well-known colleges and universities have access to AMC contest scores and use them for recruiting and admissions.

This mathematics course will prepare students for the AMC 10/12, the first exam in the series of exams used to challenge students on the path toward choosing the team that represents the United States at the International Mathematics Olympiad. The AMC 10 and 12 are 25-question, 75-minute, multiple choice examinations. The AMC 10 is for 10th grade students and below, and covers high school curriculum up to the 10th grade. The AMC 12 is for 12th grade students and below, and covers the entire high school curriculum. This course will teach students to apply classroom learned skills to unique problem-solving challenges in a low-stress and friendly environment. Students who perform well at the AMC 10/12 are invited to take the AIME.

### Course Description

This class covers essential topics including algebra, geometry, counting & probability and number theory in AMC 10, 12, and AIME in a more profound way. Most  examples and problems in weekly assignments will be actual AMC and AIME problems in the past. Every week students get homework and in the next class, we will fully discuss these problems  in weekly assignments, and then continue to review new topics.

Counting & probability 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.

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.

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.

### AMC 10/12 Course for 20 lessons

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 actual AMC and AIME problems in the  past: roughly 85% AMC and 15% AIME. Every week students get homework and in next class,  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

 Geometry: Similar triangles

 Similar shapes

 Probability and count: two commonly-used approaches

Class 2

 Permutation and combination

 Binomial theorem

 Pigeon-hole principle

 Venn Diagram

Class 3

 Probability and count: Recursion

 Exponents and Log

 Function and inverse function

 Polynomial remainder

 Sequence and series

 Arithmetic and geometric sequences

Class 4

 Recursive sequences

 Sequence and inequality

 Linear functions

 Algebraic identities and equivalent transformations   Absolute value

Class 5

 Complex numbers

 Complex plane, DeMorvre theorem

 Triangles

 Similar and congruent triangles, Triangle inequalities   Ratio of areas of triangles

 Similar shapes

Class 6

 Medians and centroid

 Angle bisectors and in-center

 Perpendicular bisectors and circum-center   Triangle areas (7 approaches)

 Circles

 Tangent lines

Class 7

 Inscribed angles

 Power theorem

 External secant theorem

 Circular sectors

 Parallel lines

 Tangent circles

Class 8

 Polygon and angles

 Quadrilaterals, Rhombus, Rectangles, Squares   Circles and polygon

 Ptolemy’s theorem

 Shoelace theorem

 Pick’s theorem

Class 9

 3D geometry

 Euler’s formula

 Trigonometry

 Trig identity

 New period and starting point

 Trig equation

Class 10

 Polar coordinates

 Inverse trig functions

 Cos law, sin law

 Stewart theorem

 Analytic geometry

Class 11

 2D, 3D distance

 Point-line distance, point-plane distance   Vectors, Inner product, Angle theorem   Lines and vectors

 Vectors and matrices

 Rotation

Class 12

 Number theory

 Even and odd numbers

 Integer remainder

 Prime factorization

 Number of divisors

 GCD and LCM

Class 13

 Diophantine equation

 Absolute value

 Statistics, mean, median, modes   Arithmetic and geometric means   Basic algebra formulas

Class 14

 Floor function

 Proportion and application problems   Direct and inverse relations

 Function domain and range

 Inverse function

Class 15

 Polynomial remainder

 Descarte’s rule

 Graphs of functions

 Composition of functions

 Graph theory

Class 16

 Euler path, Euler cycle

 Inequalities

 Comprehensive review

Class 17

 Application problems

 Comprehensive review

Class 18

 AMC 10 12 problems

 Comprehensive review

Class 19

 AMC 10 12 problems

 Comprehensive review

Class 20

 AMC 10 12 problems

 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

### AMC 10/12 Course Plan for 8 Lessons

Class Outline

This class covers essential topics in AMC 10, 12, and AIME in a more profound way. Most  examples and problems in weekly assignments will be actual AMC and AIME problems in the  past. Every week students get homework and in the next class, we will fully discuss these problems  in weekly assignments, 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

 Vieta’s formula

 Fundamental theorem of algebra

 Probability and count: two commonly-used approaches

 Permutation and combination

 Binomial theorem

 Star and bars (flag and banners)

 Pigeon-hole principle

 Venn Diagram

 Probability and count: Recursion

Class 2

 Integer equations

 Geometry: Similar triangles

 Similar shapes

 Exponents and Log

 Function and inverse function

 Integer equations

 Polynomial remainder

 Sequence and series

 Arithmetic and geometric sequences

Class 3

 Recursive sequences

 Sequence and inequality

 Linear functions

 Algebraic identities and equivalent transformations   Absolute value

 Complex numbers

 Complex plane, DeMorvre theorem

 Triangles

 Similar and congruent triangles, Triangle inequalities   Ratio of areas of triangles

 Similar shapes

Class 4

 Medians and centroid

 Angle bisectors and in-center

 Perpendicular bisectors and circum-center   Triangle areas (7 approaches)

 Circles

 Tangent lines

 Inscribed angles

 Power theorem

 External secant theorem

 Circular sectors

 Parallel lines

 Tangent circles

Class 5

 Polygon and angles

 Quadrilaterals, Rhombus, Rectangles, Squares   Circles and polygon

 Ptolemy’s theorem

 Shoelace theorem

 Pick’s theorem

 3D geometry

 Euler’s formula

 Trigonometry

 Trig identity

 New period and starting point

 Trig equation

Class 6

 Polar coordinates

 Inverse trig functions

 Cos law, sin law

 Stewart theorem

 2D, 3D distance

 Point-line distance, point-plane distance   Vectors, Inner product, Angle theorem   Lines and vectors

 Vectors and matrices

 Rotation

 Analytic geometry

Class 7

 Number theory

 Even and odd numbers

 Integer remainder

 Prime factorization

 Number of divisors

 GCD and LCM

 Diophantine equation

 Absolute value

 Statistics, mean, median, modes   Arithmetic and geometric means

Class 8

 Basic algebra formulas

 Floor function

 Proportion and application problems   Direct and inverse relations

 Function domain and range

 Inverse function

 Polynomial remainder

 Descarte’s rule

 Graphs of functions

 Composition of functions

### AMC 10/12 Class Plan for 12 Lessons

Pre-requisites: Algebra I and Geometry

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

### Teacher Introduction

Mr. Felix Huang has taught math, computer science, and physics to high school students in learning centers in the Bay Area for over 10 years. He has helped many students pass the AMC 10, 12, and AIME. He also helped several students to advance on USACO Bronze, Silver, Gold to Platinum. He is passionate about helping students overcome their barriers and reach challenging goals. He helped students gain profound understanding on these subjects. He works as software engineer in multiple areas including Java, C++, Python programming, backend data, and optimization problems. As background, he received a M.S. in Math from U of Washington, M.S. in Computer Science from U of Arizona, and a B.S. in Math from National Taiwan University.