Mathematics courses 9th grade - course 30,705 rub. from Online school TutorOnline, training 69 ac. hours, Date: December 5, 2023.
Miscellaneous / / December 08, 2023
Mastering the apparatus of equations and inequalities as the main means of mathematical modeling of applied problems, studying the properties of functions. We will continue to solve geometric problems, relying on the studied properties of figures and relationships between them, using additional constructions.
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Algebra
Properties of functions. Quadratic function
- Function
- Function properties
- Square trinomial
- Factoring a quadratic trinomial
- Function y = ax 2+ bx + c, its properties and graph
- Inequalities of the second degree with one variable. Interval method
Equations and inequalities with one variable
- Whole equations
- Equation with two variables and its graph lesson 1
- Equation with two variables and its graph lesson 2
- Systems of equations of the second degree lesson 1
- Systems of equations of the second degree lesson 2
- Solving problems using systems of second degree equations lesson 1
- Solving problems using systems of second degree equations lesson 2
Equations and inequalities with two variables
- Equation with two variables and its graph lesson 1
- Equation with two variables and its graph lesson 2
- Solving systems of equations of the second degree lesson 1
- Solving systems of equations of the second degree lesson 2
- Solving word problems using systems of second degree equations lesson 1
- Solving word problems using systems of second degree equations lesson 2
- Solving word problems using systems of second degree equations lesson 3
Power function nth root
- Even and odd function lesson 1
- Even and odd function lesson 2
- Even and odd function lesson 3
- Function y = x n lesson 1
- Function y = x n lesson 2
- Determination of the nth root
- Calculation of nth roots.
Sequences
- Types of number sequences and examples
- Arithmetic and geometric progression lesson 1
- Arithmetic and geometric progression lesson 2
- Formulas of the nth term and the sum of the first n terms of the progression lesson 1
- Formulas of the nth term and the sum of the first n terms of the progression lesson 2
- Infinitely decreasing geometric progression
Elements of combinatorics and probability theory
- Combinatorial multiplication rule lesson 1
- Combinatorial multiplication rule lesson 2
- Permutations, placements, combinations lesson 1
- Permutations, placements, combinations lesson 2
- Relative frequency and probability of a random event
Geometry
Vectors. Coordinate method
- The concept of a vector. Equality of vectors
- Addition and subtraction of vectors
- Multiplying a vector by a number. Decomposition of a vector into two non-collinear vectors
- Vector coordinates. The simplest problems in coordinates
- Equations of a circle and a line
- Application of vectors and coordinates in solving problems
Relationships between sides and angles of a triangle. Dot product of vectors
- Sine
- cosine
- tangent of the angle
- Theorems of sines and cosines lesson 1
- Theorems of sines and cosines lesson 2
- Solving triangles
- Dot product of vectors and its application in geometric problems
Circumference and area of a circle
- Regular polygons
- Circle circumscribed about a regular polygon and inscribed in it lesson 1
- Circle circumscribed about a regular polygon and inscribed in it lesson 2
- Construction of regular polygons
- Circumference
- Area of a circle
Movements
- Mapping the plane onto itself
- Concept of movement
- Axial and central symmetry
- Parallel transfer
- Rotate
- Overlays and movements
Basic information from stereometry
- Subject of stereometry
- Geometric bodies and surfaces
- Polyhedra: prism, parallelepiped, pyramid, formulas for calculating their volumes lesson 1
- Polyhedra: prism, parallelepiped, pyramid, formulas for calculating their volumes lesson 2
- Bodies and surfaces of revolution: cylinder, cone, sphere, ball, formulas for calculating their volumes lesson 1
- Bodies and surfaces of revolution: cylinder, cone, sphere, ball, formulas for calculating their volumes lesson 2