Program of lessons

Principles of analytic geometry

Lesson 1.  Arithmetic

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Lesson 2.  Algebraic transformations

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Lesson 3.  Algebraic equations

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Lesson 4.  Logarithmic and exponential equations

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Lesson 5.  Inequalities

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Lesson 6.  Problems on composition of equations

Theory: A successful selection of unknowns is the main moment at solving of problems on composition of equations. It is not essential to select as unknowns the values that would be found according to a problem formulation. Sometimes it is advantageous to select some other values as unknowns, to solve the received equations and after this to find the required values using the problem formulation.

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Lesson 8.  Planimetry (Plane geometry)

Problems: .

Lesson 9. Stereometry (Solid geometry)

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Lesson 10.  Trigonometric functions and transformations

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Lesson 11. Trigonometric equations

Problems: .

Lesson 12.  Trigonometric inequalities

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Lesson 13.  Vectors and complex numbers

Lesson 14.  Functions and graphs

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Lesson 15.  Limits

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Lesson 16.  Derivative

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Lesson 17.  Integral

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Lesson 18.  Sets

Theory: Basic notions. Examples of sets .

Problems: Sets .

Lesson 19.  Theory of combinations and Newton’s binomial

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Lesson 20.  Principles of probability theory

Theory: . . .

Problems:

Lesson 21.  Principles of analytic geometry

1. Theory (analytic geometry in a plane) : . Straight line. Circle. Ellipse. Hyperbola . Parabola.

2. Theory (analytic geometry in a space) : Transformations of coordinates. Plane. Straight line. Sphere.

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Lesson 22.  Miscellaneous problems

Theory: Any notions from any section of elementary mathematics may be used here.

Problems: .

Tests

The each test fulfillment is 3 hours. Solving tests note the "pure" time used to fulfill the test. It's necessary to check will you get through the examination time or not.

Tests: Select test