我们的AMC12辅导课程配有独家自研教材,授课老师均为海内外名校毕业,具有丰富的竞赛教学经验,并根据不同基础学生开设了不同的班课,真正做到有的放矢,事半功倍!
导师阵容(部分)
G老师
美国内布拉斯加林肯大学硕士
AMC认证优秀教练员
曾在南美、欧洲多个国家及英国参与交流项目,熟悉不同的教育体系。并在数学教学领域拥有多年丰富的实践经验,在教学过程中,通过启发式教学帮助学生深入理解各个知识点,引导培养学生的创造性思维和基本逻辑能力。
Z老师
美国罗切斯特大学理论数学博士
复旦大学上海数学中心博士后研究员
官方认证AMC优秀教练
7年理论数学的研究和相关教学经验,曾系统教授过大学数学系本科至研究生大部分专业课程。读博期间曾参与了大量AMC与美国大学生数学竞赛(Putnam、Virginia Tech等)的讲座与培训工作。
L老师
本科毕业于南方科技大学数学系
新加坡国立大学量化金融硕士
AMC认证优秀教练员,多年海外学习、生活、工作经历,扎实的数学教育背景与理科知识基础,多次获得国家、校奖学金。丰富的一线数学教学经验,教学注重整理内在逻辑,举一反三。
AMC12数学竞赛基础辅导课程
课程须知
基础班(40小时):面向基本无比赛经验,无数学竞赛学习经验的学生。
AMC12前测成绩正确题目小于等于7题进入基础(预备班)学习。
课程目标是帮助学生初步建立系统化的(中学)数学竞赛知识体系,并对竞赛中典型化的解题技巧和分析思路有初步的了解。课程结束后,可以根据学生学习的实际情况,进一步选择AMC10/12的全程班或强化班学习
课程大纲
Number theory
(1)Divisor Problems of integers
Exponents, Prime factorization, Number of divisors, LCM and GCD
(2)Remainder/Divisibility Problems of integers
Modulus, Congruence, simple Modular algebra; Divisibility rules; Venn diagram, Union formula for two/three sets
(3)Digit Problems in different base representations
Base-10 representation, Base-2 representation, Different base conversion
Algebra
(1)Sequences
Arithmetic Sequences, Geometric sequences, Periodic Sequences and Simple Recursive Sequences
(2)Algebraic Manipulations and Polynomials
Expansion and Factorization Formulas; Binomial theorem, Pascal Triangle; Polynomials, Division Algorithm, Remainder Theorem, Vieta's Theorem for higher deg
(3)Inequalities and Extreme Value Problems
Polynomial inequalities; AM-GM inequality
(4)Trigonometry
Trigonometric Functions: Definition, graph and properties; Baisc Trigonometric identities
(5)Logarithm
Definition and Algebraic Properties of logarithm; Change Base formula
(6)Complex Number
Definition and basic algebraic rules of complex numbers; Coordinate and vector representation of complex numbers; Conjugates, Modulus; *The Polar Form
Geometry
(1)Basics in Geometry
Basic facts in geometry; Area problems and the Area method; Heron's Formula; The Law of Sine/Cosine
(2)Triangles
Similar and Congruent; Angle bisector and the Angle Bisector Theorem, Incenter, Median and the Centroid;
(3)Circles
Chords, Arcs, Angles and Areas; Inscribed Circles and Circumscribed Circles; Four Concyclic Points; The Power of a Point Theorem;
(4)Simple Solid Geometry
Prisms, and Pyramids; Sphere and Cones; Lines and Planes in Space; Three Perpendicular Theorem
Combinatorics
(1)Counting Problems
Sum rules and Product rules
(2)Permutation Problems and Combination Problems
Permutation Numbers and Combination Numbers; Balls into Boxes Problems
(3)Simple Probability Problems
The Concept of Probability and basic Properties; Simple Geometric Probability
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AMC12数学竞赛强化辅导课程
课程须知
面向有较多数学竞赛学习经验,且在部分比赛中已经获得过一定成绩,目标为AMC12 Distinction(TOP5%)及以上的优秀学员。AMC12前测成绩正确题目介于14题与17题之间(包含)进入强化学习。
课程目标是帮助学生快速巩固、梳理数学竞赛的核心知识框架,在知识点上做进一步的深化和拓展,增加难题(Q20+)解析的数量和强度,进一步增进学生对于竞赛解题技巧和思维方式的深刻理解和熟练掌握,并为晋级之后的AIME备考打下基础。
课程大纲
1. Number theory
(1)Prime Factorization: Number of divisors, Sum/Product of divsiors; Factorization Method for Solving LCM and GCD; Euclidean Algorithm and *Bezout's Theorem
(2)Congruence Theory and Divisibility: Modulus and Residue, Properties of Congruence, *Modular Inverse; Divisibility Rules; Principle of Inclusion and Exclusion; *Euler's Theorem/Fermat's little Theorem, *Chinese Remainder Theorem(CRT), *Wilson's Theorem
(3)Digit Representation and Base conversion, Short Division Algorithm; Infinite repeating decimal
2. Algebra
(1)Arithmetic sequences, Geometric sequences, Periodic sequences; Recursive sequences and *Characteristic Equation Method
(2)Algebraic Manipulation; Pascal Triangle and Binomial Theorem, Hockey-stick Theorem; Polynomials and Division Algorithm, Fundamental Theorem of Algebra, Generalized Remainder Theorem, Rational Root Theorem, Vieta's Theorem for higher degree polynomials
(3)Polynomial Inequalities; Fundamental Inequality, Cauchy's inequality and Extreme Value Problems
(4) Trigonometric Functions and Trigonometric identities; *Product-Sum and Sum-Product Identities
(5)Logarithm and its Calculation
(6)Complex Numbers; Properties of Conjugates and Modulus; Vector representation of Complex Numbers; Polar Form; DeMoivre' Theorem, Roots of unity
3. Geometry
(1)Basics in Geometry; The Law of Sine and the Law of Cosine; Heron's fomula, Area and Area Method
(2)Triangles: Similar Triangles; Angle Bisector and the Angle Bisector Theorem, *Angle bisector length formula; Median and Centroid, Median length formula; Centers of Triangle; Menelaus and Ceva's Theorem, Stewart's Theorem
(3)Circles: Basic geometric properties of circles; Cyclic quadrilaterals; Power of a Point Theorem; *Ptolemy's theorem
(5)Solid Geometry: Box, Cube, Prism; Pyramids; Surface Area and Volume; *Frustums; Cylinder and Sphere; *Theorem of Three Perpendiculars, *Euler's Polyhedron Formula
4. Combinatorics
(1)Basic Counting Principles: Sum rules and Product rules; Geometric Counting Problems
(2)Permutations and Combinations; Circular Permutation; Grouping Theorem; Balls into Boxes; *Advanced Combinatorics Identities, *Recursive Method in Combinatorics
(3)Elementary probability and Simple Stats.
*(较全程班节奏更快,及更侧重难题练习和知识点的高阶引申)
AMC12数学竞赛考前辅导课程
课程须知
冲刺班一般在9月秋季开学之后,比赛两个半月之前开设。班级默认学员已经对于AMC或数学竞赛有过一定程度系统性的学习,在比较紧凑的课时内快速扼要地给学生梳理各个重要板块的核心知识点,并主要以典型真题讲解的方式来帮助学生在冲刺阶段高效率备考。
课程大纲
1. Number theory
(1)Prime Factorization: Number of divisors, Sum/Product of divsiors; Factorization Method for Solving LCM and GCD; Euclidean Algorithm and *Bezout's Theorem
(2)Congruence Theory and Divisibility: Modulus and Residue, Properties of Congruence, *Modular Inverse; Divisibility Rules; Principle of Inclusion and Exclusion; *Euler's Theorem/Fermat's little Theorem, *Chinese Remainder Theorem(CRT), *Wilson's Theorem
(3)Digit Representation and Base conversion, Short Division Algorithm; Infinite repeating decimal
2. Algebra
(1)Arithmetic sequences, Geometric sequences, Periodic sequences; Recursive sequences and *Characteristic Equation Method
(2)Algebraic Manipulation; Pascal Triangle and Binomial Theorem, Hockey-stick Theorem; Polynomials and Division Algorithm, Fundamental Theorem of Algebra, Generalized Remainder Theorem, Rational Root Theorem, Vieta's Theorem for higher degree polynomials
(3)Polynomial Inequalities; Fundamental Inequality, Cauchy's inequality and Extreme Value Problems
(4) Trigonometric Functions and Trigonometric identities; *Product-Sum and Sum-Product Identities
(5)Logarithm and its Calculation
(6)Complex Numbers; Properties of Conjugates and Modulus; Vector representation of Complex Numbers; Polar Form; DeMoivre' Theorem, Roots of unity
3. Geometry
(1)Basics in Geometry; The Law of Sine and the Law of Cosine; Heron's fomula, Area and Area Method
(2)Triangles: Similar Triangles; Angle Bisector and the Angle Bisector Theorem, *Angle bisector length formula; Median and Centroid, Median length formula; Centers of Triangle; Menelaus and Ceva's Theorem, Stewart's Theorem
(3)Circles: Basic geometric properties of circles; Cyclic quadrilaterals; Power of a Point Theorem; *Ptolemy's theorem
(5)Solid Geometry: Box, Cube, Prism; Pyramids; Surface Area and Volume; *Frustums; Cylinder and Sphere; *Theorem of Three Perpendiculars, *Euler's Polyhedron Formula
4. Combinatorics
(1)Basic Counting Principles: Sum rules and Product rules; Geometric Counting Problems
(2)Permutations and Combinations; Circular Permutation; Grouping Theorem; Balls into Boxes; *Advanced Combinatorics Identities, *Recursive Method in Combinatorics
(3)Elementary probability and Simple Stats.
AMC12数学竞赛全程辅导课程
课程须知
面向有少量数学竞赛参赛和学习经验,校内数学基础较好,但尚未系统梳理过竞赛知识体系,各板块知识点遗漏欠缺较多的学生。AMC12前测成绩正确题目介于8题至13题(包含)进入全程班学习。
课程目标是帮助学生建立完整而系统的中学数学竞赛知识体系,并通过各知识板块的专项训练逐渐熟悉相关竞赛题目的解题技巧和思维方法。课程结束后,可进一步根据实际学习情况参加考前冲刺刷题训练和一对一强化巩固答疑。
课程大纲
1. Number theory
(1)Prime Factorization: Number of divisors, Sum/Product of divsiors; Factorization Method for Solving LCM and GCD; Euclidean Algorithm and *Bezout's Theorem
(2)Congruence Theory and Divisibility: Modulus and Residue, Properties of Congruence, *Modular Inverse; Divisibility Rules; Principle of Inclusion and Exclusion; *Euler's Theorem/Fermat's little Theorem, *Chinese Remainder Theorem(CRT), *Wilson's Theorem
(3)Digit Representation and Base conversion, Short Division Algorithm; Infinite repeating decimal
2. Algebra
(1)Arithmetic sequences, Geometric sequences, Periodic sequences; Recursive sequences and *Characteristic Equation Method
(2)Algebraic Manipulation; Pascal Triangle and Binomial Theorem, Hockey-stick Theorem; Polynomials and Division Algorithm, Fundamental Theorem of Algebra, Generalized Remainder Theorem, Rational Root Theorem, Vieta's Theorem for higher degree polynomials
(3)Polynomial Inequalities; Fundamental Inequality, Cauchy's inequality and Extreme Value Problems
(4) Trigonometric Functions and Trigonometric identities; *Product-Sum and Sum-Product Identities
(5)Logarithm and its Calculation
(6)Complex Numbers; Properties of Conjugates and Modulus; Vector representation of Complex Numbers; Polar Form; DeMoivre' Theorem, Roots of unity
3. Geometry
(1)Basics in Geometry; The Law of Sine and the Law of Cosine; Heron's fomula, Area and Area Method
(2)Triangles: Similar Triangles; Angle Bisector and the Angle Bisector Theorem, *Angle bisector length formula; Median and Centroid, Median length formula; Centers of Triangle; Menelaus and Ceva's Theorem, Stewart's Theorem
(3)Circles: Basic geometric properties of circles; Cyclic quadrilaterals; Power of a Point Theorem; *Ptolemy's theorem
(5)Solid Geometry: Box, Cube, Prism; Pyramids; Surface Area and Volume; *Frustums; Cylinder and Sphere; *Theorem of Three Perpendiculars, *Euler's Polyhedron Formula
4. Combinatorics
(1)Basic Counting Principles: Sum rules and Product rules; Geometric Counting Problems
(2)Permutations and Combinations; Circular Permutation; Grouping Theorem; Balls into Boxes; *Advanced Combinatorics Identities, *Recursive Method in Combinatorics
(3)Elementary probability and Simple Stats.