翰林国际教育Alevel Further Math进阶数学辅导

Category: A-level课程, 国际课程 Date: 2018年1月3日下午9:36

Further Math进阶数学课程

进阶数学课程属于英国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。

Further Math进阶数学课本

Further Math进阶数学真题

翰林国际教育 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
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