2023AMC12考前沖刺班
該AMC12考前沖刺班輔導(dǎo)旨在幫助學(xué)生備戰(zhàn)AMC12數(shù)學(xué)競(jìng)賽，提高他們的數(shù)學(xué)思維和解題能力。該課程將涵蓋AMC12數(shù)學(xué)競(jìng)賽中的常見題型和解題技巧，包括代數(shù)、幾何、概率等方面，并為學(xué)生提供模擬測(cè)試和個(gè)性化反饋，以強(qiáng)化他們的技能和自信心。該課程將為參與者提供全面的指導(dǎo)和支持，幫助他們克服難關(guān)，順利完成AMC12數(shù)學(xué)競(jìng)賽的考試。
- 課時(shí)：30小時(shí)
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項(xiàng)目介紹
AMC全稱American Mathematics Contest，前身為美國(guó)中學(xué)數(shù)學(xué)考試American High School Mathematics Examination（AHSME），是美國(guó)數(shù)學(xué)協(xié)會(huì)MAA（Mathematics Association of America）管理下的最熱門，歷史最悠久的學(xué)術(shù)比賽之一。
課程大綱
| Fundamentals | Advanced?Complementaries |
| Prime?factorization,?Number?of?divisors,?LCM?and?GCD | Sum/Product?of?divisors,?Euclidean?Algorithm?and?its?extensions,?Bezout's?Theorem |
| Congruence?and?Divisibility | Euler’s?function?and?theorem,?Fermat’s?little?theorem,?Wilson's?Theorem,
Chinese?remainder?theorem(CRT) |
| Character?of?digits,?Base-n?representation | Infinite?decimal,?Advanced?Base-n?representation?problems |
| Arithmetic?and?geometric?sequences,
periodic?sequence |
Recursive?sequence?and?Characteristic?Equation?Method |
| Algebraic?Manipulations?and?Polynomials | Fundamental?Theorem?of?Algebra,?Remainder's?Theorem,?Rational?Root?Theorem,
Generalized?Vieta's?Theorem |
| Inequalities?and?Extreme?Value?Problems | Fundamental?inequalities,?Cauchy's?inequality,?other?advanced?inequalities |
| Complex?Numbers | DeMoivre'?Theorem,?Roots?of?unity,?Vector?Transformation |
| Logarithm | Complicated?Logarithmic?calculation |
| Trigonometry | Advanced?trigonometry?identities |
| Basics?in?Geometry | The?law?of?sines,?The?Law?of?Cosines;?Heron's?formula |
| Triangles | Centers?of?triangle,?Menelaus's?theorem,?Ceva's?theorem,?Stewart?Theorem |
| Circles?(chord,?angles,?area) | Inscribed?and?circumscribed?polygon/circle,?Cyclic?Quadrilateral,?Ptolemy's?theorem |
| Solid?Geometry | Theorem?of?three?perpendiculars,?Euler's?Polyhedron?Formula |
| Sum?rules?and?product?rules | Advanced?problems?in?sum?rules?and?product?rules |
| Permutations?and?combinations | Advanced?problems?in?combinatorics |
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