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。

 

 


A-Level Further Math进阶数学课本


A-Level Further Math进阶数学真题


 

翰林学院Alevel Further Math进阶数学辅导大纲

 

Topic Subtopics Hours* Homework
Roots of quationsCoefficients of Equations
Algebraic Combinations
Substitution
Recurrence Relations
Rational functionsPartial Fractions
Vertical Asymptote
Horizontal Asymptote
Oblique Asymptotes
Sign Tables
Curve Sketching
Polar coordinatesDefinitions
Converting between Cartesian and Polar
Sketching Polar Curves
Extremes – Maxima, Minima & Tangents
Calculus in Polar Curves
Mathematical inductionProof by Induction
Standard Results of Sums
General Summation Rules
Method of Differences
Convergence
Finding a Formula
DifferentiationSecond Derivative of Implicit Expressions
Second Derivative of Implicit Equations
Second Derivative of Parametric Equations
Applying Differentiation Skills
IntegrationReduction 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 equationsHomogenous Equations
Non-Homogenous Equations
Method Summary
Complex numbersRepresenting Compl+ex Numbers
De Moivre’s Theorem
Finding Roots
Binomial Expansions
Trigonometric Identities
VectorsVector 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
MatricesEigenvalues, 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 spacesDefinition
Axioms
Liner Independence
Spanning Sets
Base Vectors
Matrix Transformations
The Rank of a Matrix
Subspaces
Special Subspaces
Solving Linear Equations
Total

*计划课时仅供学霸级学员参考,实际用时依学员具体情况会有调整。
*翰林学院原创内容,谢绝转载。课程咨询/商务合作请联系小助手linstitute。

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