Preparation course for the OGE in mathematics for grade 8 - free course from Foxford, training 32 lessons, Date: December 4, 2023.

7th grade review
Let's review the main topics of grade 7 algebra and geometry
- Linear equations
- Systems of linear equations
- Linear function
- Polynomials
- Abbreviated multiplication formulas
- Factorization
- Adjacent and vertical corners
- Signs of equality of triangles
- Isosceles triangle
- Parallel lines
- Sum of triangle angles
- Middle line of the triangle

Algebraic fractions
Let's learn how to divide polynomials, and also study operations on algebraic fractions
- Column division of polynomials
- Horner scheme
- Application of polynomial division to solving equations
- Algebraic fractions
- Reduction
- Addition and subtraction
- Multiplication and division of algebraic fractions
- Converting rational expressions

Powers and roots
We will explore a power with an integer exponent and its properties, and also find out what an arithmetic square root is and what properties it has
- Degree with natural and integer exponent
- Standard number view
- Irrational numbers
- Arithmetic square root
- Properties of roots
- Converting expressions with roots

Quadratic equations
Let's get acquainted with quadratic equations and ways to solve them. We will learn which equations can be reduced to quadratic equations, and also learn how to solve more complex word problems
- Quadratic equations
- Incomplete quadratic equations
- Selecting a complete square
- Discriminant of a quadratic trinomial
- Factoring a quadratic trinomial
- Vieta's theorem
- Problems on the application of Vieta's theorem
- Equations reducing to quadratic
- Variable change method and biquadratic equations
- Equations reducing to quadratic
- Fractional rational equations
- Problems involving movement in a straight line and on water

Functions
Let's explore the quadratic function and the inverse proportionality function and learn how to build their graphs. We’ll also learn how to transform graphs and build graphs of piecewise continuous functions.
- Function y=k/x
- Quadratic function
- Convert graphs
- Piecewise continuous functions
- Repetition. Algebra

Triangles
Let's deepen our knowledge of right triangles, learn how to calculate the area of ​​a triangle, and also explore similar triangles
- Right triangle
- Pythagorean theorem
- Sine, cosine, tangent and cotangent of an acute angle in a right triangle
- Area of ​​a triangle
- Ratio of areas of triangles
- Property of the bisector of a triangle
- Similar triangles
- Signs of similarity

Quadrilaterals
Let's get acquainted with various convex quadrilaterals, their properties and area formulas
- Parallelogram
- Properties and signs
- Area of ​​a parallelogram
- Trapezoid
- Midline of trapezoid
- Area of ​​the trapezoid
- Rhombus, rectangle and square
- Squares

Circle
Let's find out what angles there are in a circle, as well as what an inscribed and circumscribed circle is.
- Circumference
- Tangent to a circle
- Inscribed and central angles
- Circle circumscribed about a triangle
- Circle inscribed in a triangle
- Inscribed quadrilateral
- Circumscribed quadrilateral
- Repetition
- Geometry

Word problems

 -Let's get acquainted with the main types of word problems and learn how to solve them. Let's learn how to solve problems with the plot "Oven", "Local plan"
 -Text tasks for movement
 -Text task productivity and collaboration
 -Text problems percentages, mixtures and alloys
 -Tasks with practical content. Scene "Oven", "Plan of the area"

Functions and graphs
 -Let's learn how to build and read graphs of functions. We will learn how to build graphs of piecewise given functions and analyze the main types of transformation of function graphs
 -Function y=k/x
 -Quadratic function
 -Transform graphs
 -Piecewise continuous functions