Mathematics courses 11th grade - course 30,800 rub. from Online school TutorOnline, training 70 ac. hours, Date: December 5, 2023.
Miscellaneous / / December 08, 2023
70 lessons.
The applied focus of the course is ensured by systematic use of examples that reveal the possibilities of using mathematics in the study of reality and solving practical problems.
The teaching of the course is structured as a study of issues provided for in the training program for methods and techniques for solving mathematical problems. tasks that require the use of high logical and operational culture, developing scientific, theoretical and algorithmic thinking students.
The topics of the tasks do not go beyond the scope of the main course. A special place is occupied by tasks that require students to apply knowledge in an unfamiliar (non-standard) situation.
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Algebra
Antiderivative
- Review: derivative and its applications. Definition of antiderivative
- The main property of the antiderivative
- Three rules for finding an antiderivative
Area of a curved trapezoid
- Area of a curved trapezoid lesson 1
- Area of a curved trapezoid lesson 2
- Integral
- Newton-Leibniz formula
- Applications of the integral lesson 1
- Applications of integral lesson 2
Generalization of the concept of degree
- The nth root and its properties lesson 1
- The nth root and its properties lesson 2
- Root nth degree and its properties lesson 3
- Irrational equations lesson 1
- Irrational equations lesson 2
- Exponent with rational exponent lesson 1
- Exponent with rational exponent lesson 2
- Exponent with rational exponent lesson 3
Exponential and logarithmic functions
- Exponential function
- Solving exponential equations and inequalities lesson 1
- Solving exponential equations and inequalities lesson 2
- Logarithms and their properties lesson 1
- Logarithms and their properties lesson 2
- Logarithmic function
- Solving logarithmic equations and inequalities lesson 1
- Solving logarithmic equations and inequalities lesson 2
Derivative of exponential and logarithmic functions
- Derivative of an exponential function
- Derivative of a logarithmic function
- Power function lesson 1
- Power function lesson 2
- Concept of differential equations lesson 1
- Concept of differential equations lesson 2
- Solving problems on the topic “Derivative of exponential and logarithmic functions” lesson 1
- Solving problems on the topic “Derivative of exponential and logarithmic functions” lesson 2
Elements of probability theory
- Probability of event
- Probability of the sum of incompatible events
- Probability of the opposite event
- Independence of random events
- Total probability formula
- Solving practical problems using probabilistic methods. Newton's binomial formula
Geometry
Coordinates method in space
- Rectangular coordinate system in space. Vector coordinates
- Relationship between vector coordinates and point coordinates
- The simplest tasks in coordinates
- Angle between vectors. Dot product of vectors
- Calculation of angles between straight lines and planes
- Central symmetry. Axial symmetry
- Mirror symmetry. Parallel transfer
- Problem solving
Cylinder, cone and ball
- The concept of a cylinder. Cylinder surface area
- Concept of cone
- Surface area of the cone
- Frustum
- Sphere and ball
- Sphere equation
- The relative position of the sphere and the plane
- Tangent plane to the sphere
- Area of the sphere
- Problem solving
Volumes of bodies
- The concept of volume
- Volume of a rectangular parallelepiped
- Volume of a straight prism
- Cylinder volume
- Calculation of volumes of bodies using a definite integral
- Inclined prism volume
- Volume of the pyramid
- Cone volume
- Ball volume
- Volume of the spherical segment, spherical layer and spherical sector
- Area of the sphere
- Problem solving lesson 1
- Problem solving lesson 2