NEW! Mathematics course, 8th grade

Lesson 1: Reducing rational fractions

• Rational fractions
• The main property of a fraction
• Reducing Fractions

Lesson 2: Multiplying and dividing rational fractions

• Multiplying fractions
• Division of fractions

Lesson 3: Adding and Subtracting Rational Fractions

• Adding and subtracting fractions with the same denominator
• Adding and subtracting fractions with different denominators

Lesson 4: Polygon. Quadrangle. Parallelogram

• Properties of a parallelogram
• Signs of a parallelogram

Lesson 5: Rectangle. Rhombus. Square

• Properties and characteristics of a rectangle
• Properties and signs of a rhombus
• Properties and signs of a square

Lesson 6: Thales' Theorem. The middle line of the triangle. Medians of a triangle

• Sign and properties of the midline of a triangle
• Property of medians of a triangle

Lesson 7: Trapezoid. Midline of trapezoid

• Properties of the midline of a trapezoid
• Trapezium midline sign

Lesson 8: Square Roots

• Arithmetic square root
• Calculating the square root

Lesson 9: Properties of Square Root

• Expressions with square roots
• Transforming expressions with square roots

Lesson 10: Irrational Equations

• Simplifying Irrational Expressions
• Irrationality

Lesson 11: Concept of area. Area of ​​a rectangle and square

• Formula for finding the area of ​​a square
• Formula for finding the area of ​​a rectangle

Lesson 12: Area of ​​a parallelogram, rhombus, triangle

• Formulas for calculating the area of ​​a parallelogram and triangle
• Formulas for calculating the area of ​​a rhombus

Lesson 13: Solving incomplete quadratic equations. Complete quadratic equations

• Types of incomplete quadratic equations and methods for solving them
• Standard form of complete quadratic equation
• Methods for solving complete quadratic equations

Lesson 14: Formulas for the roots of a quadratic equation. Vieta's theorem

• Discriminant formula
• Formulas for finding the roots of a complete quadratic equation
• Solving quadratic equations using Vieta's theorem

Lesson 15: Fractional rational equations. Biquadratic equations

• Equations reducing to quadratic
• Solving equations using substitution

Lesson 16: Solving Problems Using Quadratic Equations

• Drawing up equations according to the problem conditions
• Movement tasks
• Tasks for work

Lesson 17: Area of ​​a trapezoid

• Trapezoid area formula
• Additional constructions in trapezoid problems

Lesson 18: Pythagorean Theorem. Theorem converse to the Pythagorean theorem

• Finding the lengths of the legs and hypotenuse of a right triangle
• Solving problems about right triangles

Lesson 19: Quadratic function. Graphing a Function

• Constructing a parabola
• Properties of a quadratic function
• Building graphs with shifts

Lesson 20: Quadratic function. Transformations of function graphs

• All types of quadratic functions
• Plan for graphing a quadratic function

Lesson 21: Similar triangles. Signs of similarity of triangles

• The first sign of similarity of triangles
• The second sign of similarity of triangles
• The third sign of similarity of triangles

Lesson 22: Bisector Property of a Triangle

• Bisector in a right triangle
• Finding the sides of a triangle

Lesson 23: Proportional Lines in a Right Triangle

• Projections of the legs of a right triangle
• Properties of segments
• Formulas for calculating segments

Lesson 24: Relationships between sides and angles of a right triangle

• Sine, cosine, tangent of an acute angle of a right triangle
• Values ​​of sine, cosine, tangent of angles 30, 45, 60 degrees

Lesson 25: Solving Linear Inequalities

• Numeric intervals
• Solving double inequalities

Lesson 26: Solving systems of inequalities

• Translation of double inequality into the system
• Set of inequalities

Lesson 27: Inequalities with modulus. Equations with modulus

• Types of equations with modulus
• Module Expansion Rules

Lesson 28: Tangent to a circle. Mutual arrangement of circles

• Tangent properties
• Solving problems on tangent properties

Lesson 29: Angles in a Circle

• Inscribed angles
• Central angles
• Relationships between arcs and angles of a circle

Lesson 30: Proportional segments in a circle

• Property of intersecting chords
• Property of tangent and secant segments
• Property of secant segments