翰林國(guó)際教育Alevel Further Math進(jìn)階數(shù)學(xué)輔導(dǎo)

Further Math進(jìn)階數(shù)學(xué)課程

進(jìn)階數(shù)學(xué)課程屬于英國(guó)數(shù)學(xué)的下一階段課程，數(shù)學(xué)和高等數(shù)學(xué)在申請(qǐng)大學(xué)時(shí)分別考試，并作為兩門成績(jī)被全球認(rèn)可。高等數(shù)學(xué)考察純數(shù)學(xué)、力學(xué)和統(tǒng)計(jì)學(xué)，在向量、矩陣、微積分方程、動(dòng)靜力學(xué)、統(tǒng)計(jì)模型等方面考察的內(nèi)容較深，多為國(guó)內(nèi)大學(xué)級(jí)別的高等數(shù)學(xué)課程，含金量與認(rèn)可度很高。高數(shù)學(xué)習(xí)的時(shí)間一般是學(xué)生A2年級(jí)進(jìn)行，也有極少數(shù)數(shù)學(xué)天賦出類拔萃的少年選擇即完成部分或全部高等數(shù)學(xué)的學(xué)習(xí)。各大考試局對(duì)于A*的定義不完全一致，但通?？偡衷?0%以上為A*。英國(guó)名校的理工科、金融類、經(jīng)濟(jì)類、心理學(xué)類等專業(yè)往往對(duì)申請(qǐng)者高等數(shù)學(xué)的學(xué)習(xí)有相關(guān)要求。

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Further Math進(jìn)階數(shù)學(xué)課本

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Further Math進(jìn)階數(shù)學(xué)真題

翰林國(guó)際教育 Further Math進(jìn)階數(shù)學(xué)輔導(dǎo)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
Total

*計(jì)劃課時(shí)僅供學(xué)霸級(jí)學(xué)員參考，實(shí)際用時(shí)依學(xué)員具體情況會(huì)有調(diào)整。

Further Math進(jìn)階數(shù)學(xué)相關(guān)國(guó)際學(xué)術(shù)活動(dòng)

國(guó)際課程+國(guó)際學(xué)術(shù)活動(dòng)更具競(jìng)爭(zhēng)力

AMC10 每年2月
難? ? 度： 含金量： American Mathematical Competition 10，10年級(jí)及以下學(xué)生參加，前2.5%可以晉級(jí)AIME

AMC12 每年2月
難? ? 度： 含金量： American Mathematical Competition 12，適合12年級(jí)及以下學(xué)生參加，全球前5%可以晉級(jí)AIME

AIME 每年3月
難 ? ?度： 含金量： American Invitational Mathematics Examination, AMC10和AMC12優(yōu)勝者參加的數(shù)學(xué)邀請(qǐng)賽

HiMCM 每年10月27日開賽
難 ? ?度： 含金量： High School Mathematical Contest in Modeling，美國(guó)高中生數(shù)模學(xué)術(shù)活動(dòng)，歷史悠久，每年超千支隊(duì)伍，Outstanding特等獎(jiǎng)不足1%

Euclid數(shù)學(xué)學(xué)術(shù)活動(dòng) 每年4月12日
難 ? ?度： 含金量： Euclid Mathematics Contest,滑鐵盧大學(xué)歐幾里德數(shù)學(xué)學(xué)術(shù)活動(dòng)，參賽對(duì)象12年級(jí)學(xué)生

丘成桐數(shù)學(xué)獎(jiǎng) 每年9月-12月
難 ? ?度： 含金量： Yau Science Awards (Mathematics),每年一屆，研究報(bào)告的形式參賽。旨在發(fā)現(xiàn)有前途的全球華人年輕科學(xué)天才。