Synopsis:
• Modification of algebraic expressions. The basic formulas for counting with powers
and roots. The factorizations of algebraic expressions. Goniometrical formulas. The
rules for calculating with complex numbers.
• Basic properties of elementary functions. The graph of elementary functions and
their domain and range. Even, odd, inverse, periodic, increasing, decreasing and
bounded function. Maximum and minimum of the function.
• Sequences and series. In particular, arithmetical and geometrical sequence. Infinite
geometric series and its sum.
• Basic types of equations and inequalities. In particular, linear, quadratic, irrational,
logarithmic, exponential and goniometrical equations, resp. inequalities.
• Combinatorics and probability. Permutations, variations, combinations. Classical
probability.
• Geometry - planimetry and solid geometry. In particular, the areas and volumes of
basic formations in the plane and in the space.
• Analytic geometry in the plane and in the space. Analytical equations of conic
sections , lines and planes. Scalar and vector product.