描述
课程须知
1.一对一定制辅导:个性定制,专属辅导,弹性时间,高效高质
2. 3-8人小班辅导:小组教学,针对辅导,及时反馈,性价比高
3.线上辅导班:克服地域,网络授课,节约时间,课程回放
课程大纲
Fundamentals(新秀组) | Advanced Complementaries(专业组) | |
Number Theory | Prime factorization; Number of divisors, Sum of divisors,
Product of divisors; LCM and GCD |
Prime factorization; Number of divisors, Sum of divisors, Product of divisors;
LCM and GCD |
Euclidean Algorithm and Bezout's Theorem | Euclidean Algorithm and Bezout's Theorem | |
Congruence and Divisibility | Congruence and Divisibility | |
Chinese remainder theorem(CRT), Fermat’s little theorem
Euler’s function and theorem, Wilson's Theorem |
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Diophantine Equations | ||
Algebra | Algebraic identities and Algebraic manipulations | Algebraic identities and Algebraic manipulations |
Function Composition and Functional Equations
(Induction and iteration Method) |
Function Composition and Functional Equations (Induction and iteration Method) | |
Polynomials and Vieta's Theorem | Polynomials and Vieta's Theorem; Newton's Sum; | |
Fundamental inequalities, Cauchy inequality | Fundamental inequalities, Cauchy inequality, other advanced inequalities | |
Rescursive Sequence | Rescursive Sequence; Characteristic Equation | |
Geometry | Basics in Geometry( Polygon; Area Method;
The law of Cosine and the law of Sine) |
Basics in Geometry( Polygon; Area Method; The law of Cosine and the law of Sine) |
Triangles, Centers of triangle | Triangles, Centers of triangle; Menelaus's theorem, Ceva's theorem, Stewart Theorem | |
Circles; Cyclic Quadrilateral;Power of Point Theorem | Circles; Cyclic Quadrilateral;Power of Point Theorem: Ptolemy's theorem; Radical Axis; | |
Probability and Statistic | Counting Principles (Sum Rules, Product Rules,
Permutation and Combinations) |
Counting Principles (Sum Rules, Product Rules, Permutation and Combinations) |
Classical probability theory | Geometric probability; Conditional Probability; Bayes Theorem | |
Logic reasoning (Pigeon Hole's Principle;
Winning Strategy; Prove by contradiction; Principles of Inclusion and Exclusion) |
Logic reasoning (Pigeon Hole's Principle; Winning Strategy; Prove by contradiction;
Principles of Inclusion and Exclusion) |
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Elementary Graph Theory; Coloring Problem and Labelling Method | ||
College Topics | Limit, Differentiation, and simple Integration, | |
Simple Series and convergency test | ||
Simple Group Theory |
参赛须知
【个人能力挑战 Individual Contest】
10道简答问题被分为5组,每15分钟发下一组2道题,选手要在短暂的时间内迅速解答给出最简答案(挑战难度:3星,时长1小时40分钟)。
【团队能力挑战 Team Contest】
✔团队力量 Power Round
以团队为单位,解答一道多步证明题,并且要求答案和数学证明或解答过程都清晰明了(挑战难度:5星,时长60分钟)。
✔团队协作 Team Round
以团队为单位,解答10道简答题,给出最简洁的数字答案(挑战难度:4星,时长30分钟)。
✔分组接力 Relay Round
(1)每个团队被分为3组,编号为A、B、C;
(2)每组分到不同的题目,C组题目的一个关键条件是B组解出的答案,B组题目的一个关键条件是A组解出的答案。因此,后一组成员需要获得前一组成员的答案后才能解题;C组提交最终答案给监考人员
(3)每轮限时10分钟,5分钟内提交正确答案,得10分;10分钟提交正确答案,得5分。错误答案不给分。团队最高得分20分(挑战难度系数:2星,接力共两轮,总时长25分钟)。