Style: The class is interactive. Students may ask questions at any time, the instructor will explain and will not move on unless everyone is ready. The class is designed to help with the majority of standardized tests, including the SAT, which means we will go into details and types of questions that may be somewhat different from school assignments. In general, we do not promote learning by rote and we do not assign 'busy homework'. This class is harder and more detailed than the usual school class - the student must be willing to take on a challenge! Our class is close in difficulty and style to what is currently taught in Eastern Europe, Russia and some Western European countries, yet does not explore all the nooks and crannies that the AMC12 class goes into. If things are done properly, this class should be taken before the AMC12 class.

Credit: There is no credit for this class. Our goal is to help students understand logically, memorize for the long term and enjoy the control they acquire over the subject matter. We believe there is a conflict of interest between selling knowledge and selling credits, therefore we do not grade students' performance and we do not give credit. For parents' information, we send a progress report based on classroom observations and homework completion.

Set Theory: definitions, operations, introduction to sets of numbers, interval notation.

Functions: definition, domain, range, graph, piecewise definitions, how to graph by hand, how to graph using a graphing calculator.

Properties of functions: onto, one-to-one, inverse function, monotony, increasing, decreasing, restrictions, symmetries (odd, even, neither).

Function composition: composition, properties of inverses.

Function transformations: translation, scaling, reflection.

Specific functions: linear, ceiling, floor, step, absolute value, power functions, rational functions, radicals.

Aymptotes: introduction to limits, types of asymptotes, how to graph by hand, how to graph using graphing calculator.

Linear functions: properties of linear functions, graphing, graphical interpretation of linear systems of 2 equations with 2 unknowns.

Quadratic functions: definition, transformations, symmetry, intercepts, vertex, roots, complex roots, how to graph, functions and equations with parameters.

Polynomials: definition, equality, operations with polynomials, divisibility, fundamental theorem of algebra, remainder theorem, factoring, Viete's relations, roots, rational root theorem, Descartes rule of signs, real roots, complex roots.

Exponential functions and equations: definition, properties, graphs, equations, inequalities, systems of equations.

Logarithmic functions: definition, properties, graphs, equations, inequalities, systems of equations.

Unit circle trigonometry: radians, unit circle, trigonometric functions of common angles.

Trigonometric functions: definitions, domain, range, period, symmetry, transformations, graphing.

Inverse trigonometric functions: principal period, invertibility, inverses.

Trigonometric identities: geometric derivation, sum and difference, double angle, half-angle, tangent ot half arc, product to sum, sum to product.

Trigonometric equations:

Law of sines: law of sines, area of a triangle.

Law of cosines: law of cosines, solving triangles.

Polar coordinates: definition, properties, conversion to Cartesian.

Complex numbers: definition, operations, complex plane, trigonometric form, exponential form, de Moivre's formula, complex number equations (cyclotomic).

Conic sections: parabolas, ellipses, hyperbolas.

Linear algebra: matrices, operations with matrices, determinants, linear systems, Cramer's rule, solving linear systems in matrix notation, Gaussian elimination, inverse matrices.

Sequences and Series: arithmetic, geometric.

Mathematical induction: principle of mathematical induction and applications in algebra and geometry.

Binomial Theorem: binomial theorem, combinations, properties of combinations, combinatorial sums, applications of the binomial theorem.

We send GOTM lecture notes and homework at each lesson. Answer keys and full solutions are sent before the next lesson.