# 翰林学院Alevel Further Math进阶数学辅导

### 翰林学院 Further Math进阶数学辅导大纲

 Topic Subtopics Hours* Homework Roots of quations Coefficients of Equations Algebraic Combinations Substitution Recurrence Relations Rational functions Partial Fractions Vertical Asymptote Horizontal Asymptote Oblique Asymptotes Sign Tables Curve Sketching Polar coordinates Definitions Converting between Cartesian and Polar Sketching Polar Curves Extremes – Maxima, Minima & Tangents Calculus in Polar Curves Mathematical induction Proof by Induction Standard Results of Sums General Summation Rules Method of Differences Convergence Finding a Formula Differentiation Second Derivative of Implicit Expressions Second Derivative of Implicit Equations Second Derivative of Parametric Equations Applying Differentiation Skills Integration Reduction Formula Mean Value of a Function Arc Length of a Function Surface Area of a Solid Revolution Centroid of a 2-D Shape Centroid of a 3-D Shape Differential equations Homogenous Equations Non-Homogenous Equations Method Summary Complex numbers Representing Compl+ex Numbers De Moivre’s Theorem Finding Roots Binomial Expansions Trigonometric Identities Vectors Vector Product Equation of a Plane Finding the Equation of a Plane Distance from a Point to a Plane Line of Intersection of Two Planes Intersection of a Line and a Plane Distance between Two Skew Lines Angles Matrices Eigenvalues, Eigenlines and Eigenvectors Matrix Decomposition Powers of Matrices Determinant of a Square Matrix Inverse of a 3-by-3 Matrix Eigenvalues and Eigenvectors of 3×3 Matrices Vector spaces Definition Axioms Liner Independence Spanning Sets Base Vectors Matrix Transformations The Rank of a Matrix Subspaces Special Subspaces Solving Linear Equations Total

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## Further Math进阶数学相关国际竞赛

AMC10

American Mathematical Competition 10，10年级及以下学生参加，前2.5%可以晋级AIME

AMC12

American Mathematical Competition 12，适合12年级及以下学生参加，全球前5%可以晋级AIME

AIME

American Invitational Mathematics Examination, AMC10和AMC12优胜者参加的数学邀请赛

HiMCM

High School Mathematical Contest in Modeling，美国高中生数模竞赛，历史悠久，每年超千支队伍，Outstanding特等奖不足1%

Euclid数学竞赛

Euclid Mathematics Contest,滑铁卢大学欧几里德数学竞赛，参赛对象12年级学生

Yau Science Awards (Mathematics),每年一届，研究报告的形式参赛。旨在发现有前途的全球华人年轻科学天才。

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