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Mathematics and geometry reference

This section contains reference materials on the main topics of mathematics and geometry: formulas, tables, theorems, and definitions. The materials are organized into sections and are suitable for preparing for lessons, tests, the EGE, and the OGE.

Reference sections

  • Quick facts — Sine values for 30, 45, 60 degrees, the inscribed angle theorem, 8th-grade geometry essentials, comparison of descent rates.
  • Tables — Multiplication table, tables of squares, cubes, powers, factorials, the Bradis table, tables of sines, cosines, tangents, cotangents, logarithms, prime numbers, and instructions on how to use them.
  • Formulas — Abbreviated multiplication formulas, properties of powers and roots, formulas and properties of logarithms, trigonometric formulas, formulas of arithmetic and geometric progressions.
  • Geometry formulas — Areas and volumes of figures, perimeters, surface areas, properties of a regular polygon and a triangle, the Pythagorean theorem.
  • Math theory — Natural numbers, the Gaussian method, Vieta's theorem, Fermat's Last Theorem — with examples and proofs.

About this reference

The materials in this reference were prepared by Alexey Pavlov, a mathematics teacher. All formulas, tables, and theorems have been tested in practice while preparing students for the EGE and OGE.

  • Quick facts
  • Tables
  • Formulas
  • Geometry formulas
  • Math theory
  1. Sine values for 30, 45, 60 degrees.
  2. Geometry essentials for 8th grade. Module 1.
  3. Preparation for a geometry test in 8th grade.
  4. Inscribed angle theorem.
  5. Comparison of descent rates for a parachute jump and a jump from a window.
  1. Multiplication table (1 to 10).
  2. How to quickly learn the multiplication table.
  3. Extended multiplication table (1 to 20).
  4. Table of squares (1 to 10).
  5. Table of cubes (1 to 10).
  6. Table of powers (1 to 10).
  7. Table of factorials (1 to 10).
  8. Bradis table (with corrections).
  9. How to use the Bradis table. Visual guide.
  10. Table of sines.
  11. Table of cosines.
  12. Table of tangents.
  13. Table of cotangents.
  14. Table of prime numbers.
  15. Table of trigonometric functions.
  16. Table of function values.
  17. Table of natural logarithms.
  18. Table of decimal logarithms.
  19. Table of logarithms by base.
  1. Abbreviated multiplication formulas (2nd, 3rd, 4th and nth powers).
  2. Formulas and properties of powers.
  3. Formulas and properties of roots.
  4. Formulas and properties of logarithms.
  5. Formulas and properties of arithmetic progression.
  6. Formulas and properties of geometric progression.
  7. Trigonometric formulas.
  8. Inverse trigonometric functions.
  1. Areas of figures.
  2. Volumes of figures.
  3. Perimeters of figures.
  4. Surface areas of figures.
  5. Regular polygon.
  6. Triangle.
  7. Pythagorean theorem.
  1. Natural numbers.
  2. Gaussian method.
  3. Vieta's theorem.
  4. Fermat's Last Theorem.
  5. Number and digit.
  6. Divisibility of numbers.
  7. Decimal numbers.
  8. Classes of numbers.
  9. GCD and LCM.
  10. Rounding numbers.
  11. Prime and composite numbers.
  12. Place values of numbers.