Mathematics RU

Mathematics

Exams

Tasks of the Russian state exams (ЕГЭ, ОГЭ), Kazakhstan's UNT and first-year calculus. Each comes with a guide to solving it, a live example, and a trainer: the tasks never run out, the answer is checked at once, and if you get stuck there are hints and a worked solution.

Russian state exam, profile level The tasks with equations, inequalities, values of expressions, the derivative and a parameter. Each task comes with a guide to the method and a trainer that never runs out of tasks. No. 6 · Simple equations No. 7 · Values of expressions No. 12 · The greatest and least value of a function No. 13 · An equation with roots on a segment No. 15 · Inequalities No. 18 · A problem with a parameter To the tasks Russian state exam, grade 9 Equations, inequalities, calculations and part 2: systems, fractions, factoring. No. 8 · Calculations with powers No. 9 · Equations No. 13 · Inequalities No. 20 · Systems of equations No. 20 · Fractions and factoring To the tasks UNT (Kazakhstan), mathematics Kazakhstan's Unified National Testing: equations, inequalities, values of expressions, systems, extrema and integrals. Equations Inequalities Values of expressions Systems of equations The greatest and least value Antiderivatives and integrals To the tasks First-year calculus The first-year exam: limits, derivatives, integrals, differential equations and series. Limits Derivatives Antiderivatives Definite integrals Differential equations Series To the tasks
Mathematics

Chapters

Introduction

  1. 0 What mathematics is

I Numbers

  1. 1 Counting
  2. 2 Zero and minus
  3. 3 Primes
  4. 4 Divisibility
  5. 5 Fractions
  6. 6 Root two

II Algebra

  1. 7 Letters
  2. 8 Equations
  3. 9 Functions and graphs
  4. 10 Quadratic equations
  5. 11 Systems and inequalities
  6. 12 Powers and logarithms
  7. 13 Sequences
  8. 14 Polynomials
  9. 15 Complex numbers

III Geometry

  1. 16 Euclid's Elements
  2. 17 The triangle
  3. 18 Pythagoras' theorem
  4. 19 The circle and π
  5. 20 Area and volume
  6. 21 Trigonometry
  7. 22 Vectors
  8. 23 Symmetry
  9. 24 Conic sections

IV Calculus

  1. 25 Limits
  2. 26 The derivative
  3. 27 Extrema
  4. 28 The integral
  5. 29 The number e
  6. 30 Series
  7. 31 Differential equations
  8. 32 Several variables
  9. 33 Fourier series
  10. 34 Complex analysis

V Linear algebra

  1. 35 Matrices
  2. 36 Gaussian elimination
  3. 37 Vector spaces
  4. 38 Eigenvectors
  5. 39 Least squares and SVD

VI Structures

  1. 40 Groups
  2. 41 Remainders and ciphers
  3. 42 Rings and fields
  4. 43 Galois theory
  5. 44 Zeta and curves

VII Chance & data

  1. 45 Combinatorics
  2. 46 Graphs
  3. 47 Probability
  4. 48 Random variables
  5. 49 Statistics
  6. 50 Markov and information

VIII Foundations

  1. 51 Logic and sets
  2. 52 Infinities
  3. 53 Rigorous analysis
  4. 54 Measure and integral
  5. 55 Functional analysis
  6. 56 Gödel and Turing

IX Horizons

  1. 57 Topology
  2. 58 Non-Euclidean geometries
  3. 59 Chaos and fractals
  4. 60 The frontier