Mathematics courses for grade 11 - course RUB 63,360. from SkySmart, training 9 months, Date: December 5, 2023.

My favorite book is Harry Potter, and I am Professor McGonagall in it. I’ll teach you how to bottle actions with numbers, how to cook a problem using a formula, and even how to seal the root of an equation. But as long as you ask questions and do your homework!

My signature learning method is through association: the rule of inheritance for rounding numbers, the rule of friendship for numbers with different signs, and much more. In my free time I play chess and volleyball

I always try to find a common language with students and gain their trust, I am in touch 24/7. In my free time I study English and German, I like to read, mainly English classics

1. Basic topics to study in algebra

The mathematics course for grade 11 is devoted to preparing high school students for the state final certification in the form of a unified state exam.

By the 11th grade, teenagers have come a long way in learning and can now independently solve problems using the properties of numbers and number systems, divisibility, shares and parts, percentages, modules of numbers, as well as apply knowledge of the properties of powers and roots, polynomials, transformations of polynomials and fractional rationals expressions.

In mathematics classes in the eleventh grade, schoolchildren solve problems on the following topics:

• arithmetic and geometric progression,
• many numerical and geometric figures,
• module of number and its properties,
• circles and Euler functions,
• Euclidean algorithm,
• Chinese Remainder Theorem,
• Fermat's little theorem,
• radian angle measure and trigonometric circle,
• trigonometric functions y = sinx, y = cosx, y = tgx, y = ctgx,
• the largest and smallest value of a function,
• periodic functions and the smallest period,
• logarithm and its properties,
• logarithmic function and its properties and graph,
• power function and its properties and graph,
• interval method for solving inequalities,
• Newton's binomial formula,
• Vieta's theorem,
• Bezout's theorem,
• Fermat's theorem on the sum of squares,
• Fermat's theorem on the sum of squares,
• Cauchy-Bunyakovsky inequality,
• Jensen's inequality
• properties of continuous functions,
• Weierstrass's theorem,
• geometric and physical meaning of derivative,
• Newton-Leibniz formula,
• methods for solving functional equations and inequalities,
• axioms of probability theory,
• discrete random variables and distributions,
• Chebyshev's theorem,
• Bernoulli's theorem.

In a mathematics course for the eleventh grade, students will have to solve many problems in the following ways:

• using numerical inequalities and systems of inequalities with one variable, using the image of numerical intervals,
• graphical method for solving equations and inequalities,
• finding extrema of functions of several variables,
• finding extrema of functions of several variables,

In individual lessons, the tutor will help the student develop a mathematical style of thinking: induction, deduction, generalization, specification, analysis, synthesis, classification, systematization.

2. Basic topics to study in geometry

The geometry section of the 11th grade mathematics course will help students develop spatial concepts and improve their skills in using graphical methods.

In the process of individual learning, schoolchildren solve problems:

• using the properties of figures on a plane,
• to prove and construct counterexamples,
• using the simplest logical rules,
• using triangle theorem, relations in right triangles, facts related to quadrilaterals,
• using facts related to circles,
• for measurements on a plane, calculations of lengths and areas,
• using vectors and coordinates.

The eleventh grade program involves studying the following topics:

• prism, parallelepiped, pyramid, tetrahedron,
• Menelaus' theorem,
• intersecting lines in space and the angle between them,
• theorems on the parallelism of lines and planes in space,
• types of tetrahedrons - orthocentric, frame, isohedral, rectangular,
• Euler's theorem,
• bodies of rotation - cylinder, cone, ball and sphere,
• plane equation,
• proving theorems using vectors and the coordinate method,
• volumes of polyhedra and bodies of rotation,
• movements in space: parallel translation, relative symmetry
• planes, central symmetry, rotation relative to a straight line.

Homework for the 11th grade math course involves using tables and charts to present data.

3. Working with additional information

At the Skysmart online school, teachers strive to support students and not burden them with unnecessary information that will not be useful for the Unified State Exam.

If the student copes with the program, he can dive into the study of propositional algebra, learn the basic rules of logic and solve logic problems. Schoolchildren can learn more in individual lessons about types of proofs, mathematical induction and what kinds of statements there are: the inverse of a given, the opposite, the inverse of the opposite given.