2023 AMC10数学竞赛基础班
该AMC10数学竞赛基础班旨在帮助学生备战AMC10数学竞赛，提高他们的数学思维和解题能力。该课程将涵盖AMC10数学竞赛中的常见题型和解题技巧，包括代数、几何、概率等方面，并为学生提供模拟测试和个性化反馈，以强化他们的技能和自信心。该课程将为参与者提供全面的指导和支持，帮助他们克服难关，顺利完成AMC10数学竞赛的考试。
- 课时： 60小时
Product Details
项目介绍
课程大纲
Number theory
TOPIC
Divisor Problems of integers
Remainder Problems of integers
Digit Problems in different base representations
Divisibility Problems
Details
Exponents, Prime factorization, Number of divisors, LCM and GCD
Modulus, Congruence and its properties, simple Modular algebra
Base-10 representation, Base-2 representation, Different base conversion
Divisibility rules; Venn diagram, Sets, *Union formula for two/three sets
Algebra
TOPIC
Sequences
Algebraic Operations and Polynomials
Functions and Graphs
Solving Equations
Inequalities and Extreme Value Problems
Details
Arithmetic Sequences, Geometric sequences, Simple Repeating Sequence
Expansion and Factorization Formulas; *Binomial theorem, Pascal Triangle; Polynomials, Division Algorithm, Remainder Theorem
Linear Functions, Quadratic Functions, *Rational Functions, Absolute Value Functions
Linear equations and quadratic equations, Vieta’s theorem for quadratic equations
Linear inequalities and System of linear inequalities; AM-GM inequality, Absolute value inequality
Geometry
TOPIC
Triangles
Polygons
Circles
Simple Solid Geometry
Details
Similar and Congruent; Angle bisector and the Angle Bisector Theorem, Median and the Centroid; Pythagorean Theorem, *Heron's formula
Trapezoid, Parallelogram, Rhombus, Rectangle, Square
Chords, Arcs, Angles and Areas; Inscribed Circles and Circumscribed Circles; *Four Concyclic Points
Rectangular Box, Prisms, and Pyramids; Sphere and Cones; Lines and Planes in Space
Geometry Total:
Combinatorics
TOPIC
Counting Problems
Permutation Problems and Combination Problems
Simple Probability Problems
Details
Sum rules and Product rules
Permutation Numbers and Combination Numbers; Balls into Boxes Problems
The Concept of Probability and basic Properties; Simple Geometric Probability
