Russian Mathematics Education

Grades 10–11

Basic Level

Algebraic expressions.

Roots of power n > 1 and their properties.

Powers with rational exponents and their properties. The concept of

a power with a real exponent. The properties of powers with real

exponents.

The logarithm of a number. The fundamental logarithmic identity.

Logarithms of products, quotients, powers; conversion to a new base.

Common and natural logarithms, the number e.

Transformations of elementary expressions containing arithmetic

operations, powers, and logarithms.

Equations and inequalities.

Solving rational, exponential, logarith-

mic equations and inequalities. Solving irrational and trigonometric

equations.

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Basic techniques for solving systems of equations: substitution,

algebraic addition, introducing new variables. The equivalence

of equations, inequalities, systems. Solving elementary systems of

equations with two unknowns. Solving systems of inequalities with

one variable.

Using the properties and graphs of functions in solving equations

and inequalities. The interval method. Representing the solution sets

of equations and inequalities with two variables, and systems of such

equations and inequalities, in the coordinate plane.

Applying mathematical methods to solve substantive problems

from other areas of science and life. Interpreting results, taking real

limitations into account.