項目介紹

課程大綱

Number?theory

TOPIC

Divisor?Problems?of?integers

Remainder?Problems?of?integers

Digit?Problems?in?different?base?representations

Divisibility?Problems

Details

Exponents,?Prime?factorization,?Number?of?divisors,?LCM?and?GCD

Modulus,?Congruence?and?its?properties,?simple?Modular?algebra

Base-10?representation,?Base-2?representation,?Different?base?conversion

Divisibility?rules;?Venn?diagram,?Sets,?*Union?formula?for?two/three?sets

 

Algebra

TOPIC

Sequences

Algebraic?Operations?and?Polynomials

Functions?and?Graphs

Solving?Equations

Inequalities?and?Extreme?Value?Problems

Details

Arithmetic?Sequences,?Geometric?sequences,?Simple?Repeating?Sequence

Expansion?and?Factorization?Formulas;?*Binomial?theorem,?Pascal?Triangle;?Polynomials,?Division?Algorithm,?Remainder?Theorem

Linear?Functions,?Quadratic?Functions,?*Rational?Functions,?Absolute?Value?Functions

Linear?equations?and?quadratic?equations,?Vieta’s?theorem?for?quadratic?equations

Linear?inequalities?and?System?of?linear?inequalities;?AM-GM?inequality,?Absolute?value?inequality

 

Geometry

TOPIC

Triangles

Polygons

Circles

Simple?Solid?Geometry

Details

Similar?and?Congruent;?Angle?bisector?and?the?Angle?Bisector?Theorem,?Median?and?the?Centroid;?Pythagorean?Theorem,?*Heron's?formula

Trapezoid,?Parallelogram,?Rhombus,?Rectangle,?Square

Chords,?Arcs,?Angles?and?Areas;?Inscribed?Circles?and?Circumscribed?Circles;?*Four?Concyclic?Points

Rectangular?Box,?Prisms,?and?Pyramids;?Sphere?and?Cones;?Lines?and?Planes?in?Space

Geometry?Total:

 

Combinatorics

TOPIC

Counting?Problems

Permutation?Problems?and?Combination?Problems

Simple?Probability?Problems

Details

Sum?rules?and?Product?rules

Permutation?Numbers?and?Combination?Numbers;?Balls?into?Boxes?Problems

The?Concept?of?Probability?and?basic?Properties;?Simple?Geometric?Probability