NEW! Mathematics course, 10th grade

Lesson 1: Spatial figures. Straight lines and planes

• Polyhedra
• Prism, parallelepiped, pyramid, tetrahedron
• Area of ​​the lateral and total surface of a polyhedron

Lesson 2: Axioms of stereometry. Corollaries from the axioms

• Three axioms of stereometry and consequences from them
• Application of axioms in solving problems

Lesson 3: Polyhedra. Construction of sections of polyhedra

• Prism, parallelepiped, pyramid, tetrahedron
• Types of prisms, parallelepipeds, pyramids
• Solving problems on constructing sections of polyhedra

Lesson 4: Introduction to Trigonometry

• Relationships between sides and angles of a right triangle
• Degree and radian measure of angles and arcs
• Sine and cosine of an arbitrary angle
• Tangent and cotangent of an arbitrary angle

Lesson 5: Properties of the expressions sin α and cos α, tan α and ctg α. Inverse trigonometric expressions

• Many values ​​of sine, cosine, tangent and cotangent
• Signs of sine, cosine, tangent and cotangent
• The concept of arcsine and arccosine
• The concept of arctangent and arccotangent

Lesson 6: Relationships between sine, cosine, tangent and cotangent of the same angle

• Fundamental trigonometric identity
• Formulas for sine, cosine, tangent and cotangent
• Simplifying trigonometric expressions

Lesson 7: Reduction formulas. Addition formulas

• Rules for reduction formulas: rule of sign and name
• Addition theorems for sine and cosine
• Addition theorems for tangent and cotangent

Lesson 8: Double and half angle formulas

• Converting product to sum (difference)
• Converting a sum (difference) into a product
• Using double and half angle formulas to simplify trigonometric expressions

Lesson 9: Relative position of lines in space

• Parallel lines in space
• Crossing lines
• Sign of crossing lines

Lesson 10: The relative position of a straight line and a plane in space

• Parallelism of a line and a plane
• Crossing lines
• Angle between straight lines

Lesson 11: Relative arrangement of planes in space

• Parallelism of planes
• Sign of parallel planes
• Parallel plane theorems

Lesson 12: Functions y = sin x, y = cos x, y = tg x, y = ctg x. Properties and graphs

• Periodicity
• Plotting graphs of sine, cosine, tangent and cotangent functions
• Description of the properties of trigonometric functions

Lesson 13: Trigonometric Equations

• The simplest trigonometric equations
• Solving equations of the form sin x = a, cos x = a
• Solving equations of the form tg x = a, ctg x = a
• Special cases

Lesson 14: Trigonometric Equations

• Solving trigonometric equations using the substitution method
• Solving trigonometric equations using the factorization method
• Homogeneous trigonometric equations

Lesson 15: Trigonometric equations. Trigonometric inequalities

• Solving trigonometric equations using various methods
• Solving trigonometric inequalities using the trigonometric circle
• Solving systems of trigonometric equations

Lesson 16: Perpendicularity of a line and a plane

• Perpendicular and oblique
• Sign of perpendicularity of a line and a plane
• Theorem on oblique lines drawn from one point
• Three Perpendicular Theorem

Lesson 17: Distance from a point to a plane. Angle between a straight line and a plane

• Perpendicular and oblique
• Three Perpendicular Theorem
• Constructing a linear angle between a straight line and a plane

Lesson 18: Perpendicularity of planes. Angle between planes. Dihedral angle

• Distance between crossing lines
• Linear dihedral angle
• Sign of perpendicularity of planes

Lesson 19: Power with an integer exponent. nth root. Identities with roots containing one variable

• Properties of actions on powers with integer exponents
• Roots of even and odd powers
• Simplifying Expressions with Radicals

Lesson 20: Actions with nth roots

• Actions with roots of odd degree
• Actions with roots of even degree
• Periodic fractions

Lesson 21: Power with rational exponent. Actions with powers with rational exponents

• Theorem on actions over powers with rational exponents
• Properties of powers with rational exponents
• Comparing degrees with rational exponents

Lesson 22: Irrational equations. Solving irrational equations

• Method of replacing the original equation with an equivalent equation (a system or set of equations and inequalities)
• Method of replacing the original equation with its consequence
• Solving irrational equations using properties of functions

Lesson 23: Irrational inequalities

• Statements about equivalence in inequalities
• Methods for replacing the original inequality with an equivalent inequality (a system or set of inequalities)

Lesson 24: Degree with real exponent. Exponential function

• Determining the power of a number with an irrational exponent
• Theorems on actions on powers with arbitrary real exponents
• Definition of Exponential Function
• Theorem on the properties of the exponential function

Lesson 25: Exponential function. Exponential equations

• Methods for solving exponential equations
• Using Power Properties to Solve Exponential Equations
• Variable replacement and factorization methods

Lesson 26: Exponential Inequalities

• Methods for solving exponential inequalities
• Using power properties to solve exponential inequalities
• Variable substitution methods for solving exponential inequalities

Lesson 27: Logarithms. Basic properties of logarithms

• Logarithm
• Basic logarithmic identity
• Decimal logarithms
• Theorems about logarithms

Lesson 28: Logarithmic function. Logarithmic equations

• Graphing a Logarithmic Function
• Properties of the logarithmic function
• Solving logarithmic equations

Lesson 29: Logarithmic Inequalities

• Solving logarithmic inequalities
• Variable change method for solving logarithmic inequalities
• Factorization method for solving logarithmic inequalities

Lesson 30: Review. Generalization and systematization of the material covered