Russian Mathematics Education

Equations and inequalities.

Equations with one variable. Roots

of equations. Linear equations. Quadratic equations: the quadratic

formula. Solving rational equations. Examples of solutions to higher-

degree equations; methods of variable substitution, factorization.

Equations with two variables; solving equations with two variables.

Systems of equations; solving systems of equations. Systems of two

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Russian Mathematics Education: Programs and Practices

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Russian Mathematics Education: Programs and Practices

linear equations with two variables; solving by substitution and

algebraic addition. Equations with several variables. Examples of

solutions to nonlinear systems. Examples of solutions to equations

in integers.

Inequalities with one variable. Solving such inequalities. Linear

inequalities with one variable and systems of such inequalities.

Quadratic inequalities. Examples of solutions to fractional–linear

inequalities.

Numerical inequalities and their properties. Proving numerical and

algebraic inequalities.

Transposing verbal formulations of relations between magnitudes

into algebraic formulations. Solving word problems algebraically.

Representing numbers using points on the number line. The

geometric meaning of the absolute value of a number. Numeric

intervals: interval, segment, ray.

Cartesian coordinates in the plane; the coordinates of a point.

The equation of a straight line, the slope of a line, conditions for

parallelism. The equation of a circle centered at the origin and at any

given point.

Graphically interpreting equations with two variables and systems

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

inequalities.