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Preparation course for the OGE in mathematics for grade 8 - free course from Foxford, training 32 lessons, Date: December 4, 2023.
Miscellaneous / / December 06, 2023
Who will benefit from the course?
The course is suitable for students who want to repeat and systematize topics from grades 5-7, as well as begin preparing for the OGE in mathematics.
What knowledge does the course provide?
The course briefly and systematically examines the theory and tasks of the school mathematics curriculum: plotting graphs, transforming expressions, solving equations, and much more.
What skills does the course provide?
The classes will help you remember and work through all the necessary theory to prepare for the OGE in mathematics, and practice solving problems in algebra and geometry.
Getting ready for the OGE in advance
Be sure to repeat and structure the entire program for grades 5-8 in mathematics
No panic or stress
All the necessary topics for passing the OGE are in one program
We manually check samples and homework
We do not leave the written part assignments for self-testing - this is done by OGE experts.
We check “for real”, like in an exam, and as a result you receive detailed feedback. All this is for the sake of speed of preparation and your results.
The lesson lasts 2 academic hours.
Teacher of mathematics, preparation courses for the Unified State Exam and Unified State Exam. Expert OGE 2021.
Teacher of mathematics, preparation courses for the Unified State Exam and Unified State Exam.
Expert OGE 2021.
Master's degree at Moscow Pedagogical State University, Faculty of Mathematics, direction - methods of teaching mathematics using information technology.
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
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