翰林國際教育Alevel Further Math進階數學輔導

Category: A-level課程, 國際課程 Date: 2018年1月3日下午9:36

Further Math進階數學課程

進階數學課程屬于英國數學的下一階段課程，數學和高等數學在申請大學時分別考試，并作為兩門成績被全球認可。高等數學考察純數學、力學和統計學，在向量、矩陣、微積分方程、動靜力學、統計模型等方面考察的內容較深，多為國內大學級別的高等數學課程，含金量與認可度很高。高數學習的時間一般是學生A2年級進行，也有極少數數學天賦出類拔萃的少年選擇即完成部分或全部高等數學的學習。各大考試局對于A*的定義不完全一致，但通常總分在90%以上為A*。英國名校的理工科、金融類、經濟類、心理學類等專業往往對申請者高等數學的學習有相關要求。

Further Math進階數學課本

Further Math進階數學真題

翰林國際教育 Further Math進階數學輔導大綱

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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