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 
  • Quadratic functions 
  • Vieta’s formula 
  • Fundamental theorem of algebra 
  • Probability and count: two commonly-used approaches 
  • Multiplication and addition principles 
  • 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 
  • Quadrilaterals, Rhombus, Rectangles, Squares 
  • 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

For more information about SpringLight Education Math courses, click HERE.

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.