### Math Seminar

### Sample AMC 10 Class

This class is designed for students who are interested to tackle contest programs on AMC10/12 levels. The classes will be on Zoom, live. A successful student attending this class will already have background on the introductory AMC8 level. Specifically, students have already been exposed to the following typical topics:

- (Algebra) Quadratic equation, statistics, arithmetic and geometric sequences/series, exponents and radicals, Vieta formula, Binomial expansion.
- (Combinatorics) Venn diagrams, factorials, permutations, combinations, sticks and stones, Pascal triangle, complementary counting, expectation value.
- (Geometry) Geometry basics, 3D geometry, similar figures, power of a point, centroid, incenter, orthocenter, circumcenter, special triangles, sine and cosine laws, Heron.
- (Number Theory) Sum/product of factors, divisibility rules, bases, modular arithmetic.

Some typical topics discussed will be:

- (Algebra) Simon’s factorization, Sophie Germain, Gauss functions, complex numbers, logarithm, Diophantine equations, AM-GM, Cauchy inequality.
- (Combinatorics) Partitions, conditional probability.
- (Geometry) Menelaus, Ceva, Stewart, Ptolemy, rotation/transformation/mass point techniques, vectors.
- (Number Theory) Fermat’s little theory, Euler’s phi function, modular equations, system of modular equations, Chinese remainder theorem.

Class dates and times:

15 lectures 6:00-9:00pm 7/12-7/30

Watch Dr. Liu's Math Contest Talk https://youtu.be/67mpZIC2g68

Check SpringLight's math classes at http://springlighteducation.com/courses/math/.