# 翰林学院Alevel Further Math进阶数学辅导

### A-Level Further Math进阶数学课程

A-Level进阶数学课程属于英国A-Level数学的下一阶段课程，数学和高等数学在申请大学时分别考试，并作为两门成绩被全球认可。高等数学考察纯数学、力学和统计学，在向量、矩阵、微积分方程、动静力学、统计模型等方面考察的内容较深，多为国内大学级别的高等数学课程，含金量与认可度很高。高数学习的时间一般是学生A2年级进行，也有极少数数学天赋出类拔萃的少年选择AS即完成部分或全部高等数学的学习。各大考试局对于A*的定义不完全一致，但通常总分在90%以上为A*。英国名校的理工科、金融类、经济类、心理学类等专业往往对申请者高等数学的学习有相关要求。

### 翰林学院Alevel 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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## A-Level 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

Dongrun-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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