# AMC 10/12 12 lessons

### About AMC

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 12 lessons

Class Outline

This class covers essential topics in AMC 10 12 in 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 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
• Quadratic functions
• Vieta’s formula
• Fundamental theorem of algebra
• Geometry: Similar triangles
• Inscribed angle
• Inequality and equation
• Similar shapes
• Probability and count: two commonly-used approaches

Class 2

• Multiplication and addition principles
• Permutation and combination
• Star and Bars
• Binomial theorem
• Pigeon-hole principle
• Dichotomy problems in probability and count
• Venn Diagram

Class 3

• Probability and count: Recursion
• Exponents and Log
• Function and inverse function
• Finding roots of polynomials
• Polynomial remainder
• Sequence and series
• Arithmetic and geometric sequences
• Recursive sequences

Class 4

• Inequality
• Linear functions
• Parabolas
• Ellipses
• Hyperbolas
• Absolute value
• Algebraic identities and equivalent transformations
• Complex numbers
• Complex plane
• DeMorvre theorem

Class 5

• Triangles
• Ratio of areas of triangles
• Similar and congruent triangles
• Triangle inequalities
• Similar shapes
• Medians and centroid
• Angle bisectors and in-center
• Triangle areas (7 approaches)
• Perpendicular bisectors and circum-center
• Shoelace theorem
• Pick’s theorem

Class 6

• Circles
• Tangent lines
• Inscribed angles
• Power theorem
• External secant theorem
• Circular sectors
• Parallel lines
• Tangent circles
• Polygon and angles
• Circles and polygon
• Quadrilaterals, Rhombus, Rectangles, Squares
• Cyclic quadrilaterals
• Ptolemy’s theorem

Class 7

• 3D geometry
• Euler’s formula
• Trigonometry
• Trig identity
• New period and starting point
• Trig equation
• Polar coordinates
• Inverse trig functions
• Cos law, sin law
• Stewart theorem

Class 8

• Analytic geometry
• 2D, 3D distance
• Lines and vectors
• Vectors, Inner product, Angle theorem
• Point-line distance, point-plane distance
• Vectors and matrices
• Rotation

Class 9

• Number theory
• Even and odd numbers
• Integer remainder
• Mod equations
• Prime factorization
• Number of divisors
• GCD and LCM

Class 10

• Diophantine equation
• Fermat theorem
• Absolute value
• Arithmetic and geometric means
• Statistics, mean, median, modes
• Floor function
• Direct and inverse relations
• Proportion and application problems
• Inverse function

Class 11, 12

• Comprehensive review
• Problem solving skills

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. 3. the Art of Problem Solving Volume 2: and Beyond by Richard Rusczyk, Sandor Lehoczky

### Instructors

Mr. Felix Huang has taught math, computer science, and physics to high school students 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 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.

### AMC 10/12 Course for 12 lessons

Class Outline

This class covers essential topics in AMC 10 12 in 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 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
• Quadratic functions
• Vieta’s formula
• Fundamental theorem of algebra
• Geometry: Similar triangles
• Inscribed angle
• Inequality and equation
• Similar shapes
• Probability and count: two commonly-used approaches

Class 2

• Multiplication and addition principles
• Permutation and combination
• Star and Bars
• Binomial theorem
• Pigeon-hole principle
• Dichotomy problems in probability and count
• Venn Diagram

Class 3

• Probability and count: Recursion
• Exponents and Log
• Function and inverse function
• Finding roots of polynomials
• Polynomial remainder
• Sequence and series
• Arithmetic and geometric sequences
• Recursive sequences

Class 4

• Inequality
• Linear functions
• Parabolas
• Ellipses
• Hyperbolas
• Absolute value
• Algebraic identities and equivalent transformations
• Complex numbers
• Complex plane
• DeMorvre theorem

Class 5

• Triangles
• Ratio of areas of triangles
• Similar and congruent triangles
• Triangle inequalities
• Similar shapes
• Medians and centroid
• Angle bisectors and in-center
• Triangle areas (7 approaches)
• Perpendicular bisectors and circum-center
• Shoelace theorem
• Pick’s theorem

Class 6

• Circles
• Tangent lines
• Inscribed angles
• Power theorem
• External secant theorem
• Circular sectors
• Parallel lines
• Tangent circles
• Polygon and angles
• Circles and polygon
• Quadrilaterals, Rhombus, Rectangles, Squares
• Cyclic quadrilaterals
• Ptolemy’s theorem

Class 7

• 3D geometry
• Euler’s formula
• Trigonometry
• Trig identity
• New period and starting point
• Trig equation
• Polar coordinates
• Inverse trig functions
• Cos law, sin law
• Stewart theorem

Class 8

• Analytic geometry
• 2D, 3D distance
• Lines and vectors
• Vectors, Inner product, Angle theorem
• Point-line distance, point-plane distance
• Vectors and matrices
• Rotation

Class 9

• Number theory
• Even and odd numbers
• Integer remainder
• Mod equations
• Prime factorization
• Number of divisors
• GCD and LCM

Class 10

• Diophantine equation
• Fermat theorem
• Absolute value
• Arithmetic and geometric means
• Statistics, mean, median, modes
• Floor function
• Direct and inverse relations
• Proportion and application problems
• Inverse function

Class 11, 12

• Comprehensive review
• Problem solving skills

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. 3. the Art of Problem Solving Volume 2: and Beyond by Richard Rusczyk, Sandor Lehoczky

### Instructors

Mr. Felix Huang has taught math, computer science, and physics to high school students 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 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.

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