學(xué)員須知：

英國高級(jí)數(shù)學(xué)思維挑戰(zhàn)活動(dòng)（SMC）

活動(dòng)語言：中英文

活動(dòng)時(shí)間：每年11月

參與資格：12年級(jí)（高三年級(jí)）及以下學(xué)生

活動(dòng)形式：筆試，25道單項(xiàng)選擇題

評(píng)分標(biāo)準(zhǔn)：起始分?jǐn)?shù)25分，答對(duì)得4分，答錯(cuò)扣1分

課程大綱

	TOPICS	Details
Number?theory	Divisor?Problems?of?integers	Exponents,?Prime?factorization,?Number?of?divisors,?LCM?and?GCD
	*Remainder?Problems?of?integers	Modulus,?Congruence?and?its?properties,?simple?Modular?algebra
	Digit?Problems?*in?different?base?representations	Base-10?digit?representation,?*Base-2?representation,?*Different?base?conversion
	Divisibility?Problems	Divisibility?rules;?Venn?diagram,?Sets,?*Union?formula?for?two/three?sets
		Number?Theory?Total:
Algebra	Sequences	Arithmetic?Sequences,?Geometric?sequences,?Simple?Repeating?Sequence
	Algebraic?Operations	Expansion?and?Factorization?Formulas;?*Binomial?theorem,?Pascal?Triangle;?Radical?Calculations
	Coodinate?System?and?Functions	Linear?Functions,?Quadratic?Functions,?Rational?Functions,?Absolute?Value?Functions,?Trigonometric?Functions,?Exponential?Functions
	Solving?Equations	Linear?equations?and?quadratic?equations,?Vieta’s?theorem?for?quadratic?equations;?Functional?Equations
	Inequalities?and?Extreme?Value?Problems	Linear?inequalities?and?System?of?linear?inequalities;?Absolute?value?inequality,?*AM-GM?inequality
		Algebra?Total:
Geometry	Triangles	Similar?and?Congruent;?Angle?bisector?and?the?*Angle?Bisector?Theorem,?Median?and?the?Centroid;?Pythagorean?Theorem,?*Heron's?formula
	Polygons	Trapezoid,?Parallelogram,?Rhombus,?Rectangle,?Square
	Circles	Chords,?Arcs,?Angles?and?Areas;?Inscribed?Circles?and?Circumscribed?Circles;?*Four?Concyclic?Points
	Simple?Solid?Geometry	Rectangular?Box,?Prisms,?and?Pyramids;?Sphere?and?Cones;?Lines?and?Planes?in?Space
		Geometry?Total:
Combinatorics	Counting?Problems	Sum?rules?and?Product?rules
	Permutation?Problems?and?Combination?Problems	Permutation?Numbers?and?Combination?Numbers;?*Balls?into?Boxes?Problems
	Simple?Probability?Problems	The?Concept?of?Probability?and?basic?Properties;?Simple?Geometric?Probability
		Combinatorics?Total:

 

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