上海AMC10圣诞节集训班

课程大纲

 Algebra

i). Polynomials

Including Fundamental Theorem of Algebra, Euclidean Division, Remainder Theorem, Rational Roots test, Vieta’s Theorem ... and more.

ii). Techniques with variables Including Techniques dealing with sets of equations, fraction of variables, completing of squares, expansion and simplification... and more.

iii). Inequalities Including linear inequalities, quadratic inequalities, modular inequalities, AM -GM ... and more.

Geometry 1

i). Triangles Including the Theorems of areas, Segments, Law of Sines and Cosines, and several centres in Triangles.

ii). Circles Including the Theorems of Angles, Power of a point, and Two classic figures: Fact 5 and Radical Axis.

iii). Transformation and rotation.

Geometry 2

i). Polygons

ii). A very important figure in solid geometry —-Tetrahedron Explain the relations between lines, planes, angles, spheres in 3 dimensional geometry using one model —-Tetrahedron.

iii). Other 3D figures pyramids, cylinders, spheres ... and more.

iv). Past paper

Number Theory

i). Terminology and fundamental theorems of Number Theory Basic Divisibility Rules and Analysis with Odd, even numbers.

ii). Prime factorisation LCM and GCD and Number of Divisors.

iii). Modular Arithmetic Basic rules of Modular Arithmetic, Chinese remainder Theorem.

 Combinatorics

i). Sets and Vein’s Diagrams.

ii). Permutation and combination

iii). Balls and Urns

 Functions.

i). Linear function, quadratic function, hyperbolic function, trigonometric function, exponential function loga-rithmic function

ii). Inverse function and composite function

iii). Complex Number

 Comprehensive

i). Series and Sequences

ii). Classic comprehensive problems

Revision