Euclid比賽規(guī)則

1、比賽時(shí)長(zhǎng)共2.5個(gè)小時(shí)，150分鐘

2、Euclid共有10道題，無(wú)選擇題，均為簡(jiǎn)答題，每題都有2-3小題：

一些題目只需寫出最后的答案，一些題目需要寫出計(jì)算過程，一些題目需要寫出完整證明過程。評(píng)分標(biāo)準(zhǔn)不光是以最終結(jié)果正確與否給分，也會(huì)根據(jù)答題步驟及思路和技巧來給分。如果答題步驟或方式過為散亂，即使最終結(jié)果是正確的也不會(huì)給予滿分。

3、可使用計(jì)算器，且大部分計(jì)算器均可使用，但還有以下功能的除外：

（1）網(wǎng)絡(luò)功能
（2）與其他設(shè)備溝通功能
（3）存儲(chǔ)功能
（4）電腦代數(shù)系統(tǒng)
（5）動(dòng)態(tài)幾何軟件

Euclid備賽

University of Waterloo滑鐵盧大學(xué)官方建議為：

1、Grade 12 open courseware：

這是一個(gè)Center for Education in Mathematics and Computing（CEMC）開設(shè)的網(wǎng)課，有數(shù)學(xué)和計(jì)算機(jī)的課程。滑鐵盧大學(xué)推薦參賽者上Advanced Functions and Pre-Calculus（高端方程與預(yù)備微積分）和Calculus and Vectors（微積分與向量）兩門課程

2、Mathematics Resource Manual for High School Students and Undergraduate Studies：

這本書盤點(diǎn)了高中數(shù)學(xué)的主要內(nèi)容，不僅能成為準(zhǔn)備學(xué)術(shù)活動(dòng)的利器，也能幫助同學(xué)們由高中更好地進(jìn)入大學(xué)數(shù)學(xué)的學(xué)習(xí)

3、Euclid eWorkshop：

這是CEMC為Euclid打造的準(zhǔn)備材料，類似于一個(gè)帶有例題的概念表，盤點(diǎn)了參加Euclid Contest所需要的知識(shí)點(diǎn)

4、往屆比賽題目：

往屆比賽題目是很珍貴的準(zhǔn)備學(xué)術(shù)活動(dòng)的資源，做這些題目不僅能幫助參賽者復(fù)習(xí)知識(shí)點(diǎn)，也能讓他們更加熟悉Euclid的出題方式和套路，更好地應(yīng)對(duì)比賽

課程大綱

（具體內(nèi)容根據(jù)學(xué)生的情況調(diào)整）

	Main?Topics	Selected?Essential?Details?(Materials?with?*?are?aimed?for?the?potential?last?Problems)
Number?Theory	Prime?factorization	Number?of?factors,?Sum/Product?of?factors
		LCM?and?GCD,?*Euclidean?Algorithm?and?Bézout's?Theorem
	Congruence?and?Modular?Algebra	Principles?of?Modular?Calculations
		*Euler’s?Theorem/Fermat's?Little?Theorem
		*Chinese?Remainder?Theorem(CRT)
	Digits?and?Base-n?Representation	Mutual?Conversion?between?different?bases
	Diphantine?Equations	Estimation?and?Molular?Method
Algebra	Sequences	Arithemetic?and?Geometric?Sequences
		Periodic?Sequences,?*Recursive?Sequences?and?Characteristic?Equation?Method
		*Conjecture?and?Mathematical?Induction?Proof
	Functions?and?Equations	Elementary?Functions?(Linear,?Quadratic,?Exponential,?Logarithmic,?Trigonometric)?and?their?properties
		Functional?Equations
		*Gaussian/Floor?function
	Inequalities?and?Extreme?Value?Problems	Simple?Polynomial?Inequalities
		AM-GM?Inequality,?*Cauchy?inequality
	Polynomials	Division?Algorithm?of?Polynomials?and?the?Remainder's?Theorem
		Fundamental?Theorem?of?Algebra?(Polynomial?Factorization)?and?Vieta's?Theorem
		The?Rational?Root?Theorem
Geometry	Triangles?and?Polygons	The?Law?of?Sines,?The?Law?of?Cosines
		Area?Method?and?Heron's?formula
		*Menelaus's?theorem,?Ceva's?theorem,?Stewart?Theorem
		Centers?of?triangle
	Circles	Chords,?Arcs,?Tangents,?Inscribed?and?Central?accepted?angles
		Cyclic?Quadrilateral
		Power?of?a?Point?Theorem,?*Ptolemy's?theorem
	Basic?Coordinate?Geometry	Coordinate?System?and?Equations?of?lines,?Circles
	Basic?Solid?Geometry	Lines?in?space,?Planes;?Rectangular?Box,?Pyramids,?Prisms,?Sphere?and?Cones,Frustums
Combinatorics	Basic?Counting?Principle	Sum?Rules?and?Product?Rules
	Permutations?and?Combinations	Combinatorics?numbers?and?*Combinatorics?identities
		Grouping?Theorems,?Boards?Method?and?the?Problem?of?Balls?into?Boxes
	Logic?reasoning	*Pigeonhole?principle

學(xué)員成績(jī)

2019Euclid歐幾里得數(shù)學(xué)學(xué)術(shù)活動(dòng), 75-80分部分2人，分布于武外英中等學(xué)校, 84-87分部分5人，分布于武外英中，Bedstone college等學(xué)校，上海大同中學(xué)等 ?90%以上優(yōu)秀獎(jiǎng)

2021Euclid歐幾里得數(shù)學(xué)學(xué)術(shù)活動(dòng)，90分+有4人，分布于Oversea international school ，西安鐵一中 ，深圳國(guó)際交流學(xué)院，南京外國(guó)語(yǔ)等學(xué)校，80分+有12人，共計(jì)33位學(xué)生獲得DISTINCTION ,翰林學(xué)員參賽獲獎(jiǎng)率達(dá)50%。