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Topos Uranos
English

Level 1 · 54 lessons

Algebra and Geometry I: Numbers, Functions and Plane Geometry

Numbers, algebraic, exponential and logarithmic functions, and analytic geometry of the plane.

Course content

Unit 0Course overview

  1. 01Syllabus of Algebra and Geometry I

Unit 1The natural numbers

  1. 02The natural numbers: introduction
  2. 03Sets, relations and functions
  3. 04The natural numbers and the Peano axiomsWith account
  4. 05Basic operations on natural numbers and order relationsWith account
  5. 06Summations, progressions and inductionWith account
  6. 07Divisibility and division with remainderWith account
  7. 08Prime numbers and the fundamental theorem of arithmeticWith account
  8. 09Greatest common divisor and least common multipleWith account
  9. 10Congruences and modular arithmeticWith account
  10. 11Positional numeral systemsWith account
  11. 12Elementary combinatorics and the binomial theoremWith account
  12. 13The natural numbers: synthesis and challengesWith account

Unit 2Number systems

  1. 14Number systems: introductionSubscriptionWith account
  2. 15Number systems: from the natural to the complex numbersSubscriptionWith account
  3. 16The integers: construction, signs and orderSubscriptionWith account
  4. 17The rational numbers: fractions and their operationsSubscriptionWith account
  5. 18The decimal expansion of rational numbersSubscriptionWith account
  6. 19The real line: order, intervals and absolute valueSubscriptionWith account
  7. 20Powers with rational exponents and radicalsSubscriptionWith account
  8. 21First-degree equations and inequalities, and linear systemsSubscriptionWith account
  9. 22The complex numbers: operations and equationsSubscriptionWith account
  10. 23Number systems: synthesis and challengesSubscriptionWith account

Unit 3Algebraic functions and polynomials

  1. 24Algebraic functions and polynomials: introductionSubscriptionWith account
  2. 25Algebraic functions of a real variableSubscriptionWith account
  3. 26Function operations, inverse functions and graph transformationsSubscriptionWith account
  4. 27The algebra of real polynomialsSubscriptionWith account
  5. 28Factoring quadratic polynomials and trinomials of degree 2nSubscriptionWith account
  6. 29Roots of higher-degree polynomials and synthetic divisionSubscriptionWith account
  7. 30Algebraic fractions and partial fractionsSubscriptionWith account
  8. 31Sign charts and inequalitiesSubscriptionWith account
  9. 32Rational functions: asymptotes and graphsSubscriptionWith account
  10. 33Functions with radicals: domain, signs and graphSubscriptionWith account
  11. 34Algebraic functions and polynomials: synthesis and challengesSubscriptionWith account

Unit 4Analytic geometry of the plane

  1. 35Analytic geometry of the plane: introductionSubscriptionWith account
  2. 36The equation of a line and Cartesian coordinate systemsSubscriptionWith account
  3. 37Vectors in the plane and parametric equations of a lineSubscriptionWith account
  4. 38The equation of the parabola: definitions and propertiesSubscriptionWith account
  5. 39Characterizing parabolas and their graphsSubscriptionWith account
  6. 40The equation of the ellipse and of the circleSubscriptionWith account
  7. 41The circle: tangents, relative positions and power of a pointSubscriptionWith account
  8. 42The equation of the hyperbola and its derivationSubscriptionWith account
  9. 43Conic sections: characterization and graphs of the three conicsSubscriptionWith account
  10. 44Inequalities in the plane and linear programmingSubscriptionWith account
  11. 45Analytic geometry of the plane: synthesis and challengesSubscriptionWith account

Unit 5Exponential, logarithmic and hyperbolic functions

  1. 46Exponential, logarithmic and hyperbolic functions: introductionSubscriptionWith account
  2. 47The exponential function and powers with real exponentsSubscriptionWith account
  3. 48The number e and the natural exponentialSubscriptionWith account
  4. 49The logarithm function and its propertiesSubscriptionWith account
  5. 50Exponential and logarithmic equations and inequalitiesSubscriptionWith account
  6. 51Models of exponential growth and decaySubscriptionWith account
  7. 52The hyperbolic functionsSubscriptionWith account
  8. 53Exponential and hyperbolic functions: synthesis and challengesSubscriptionWith account

Unit 6Course closing

  1. 54Final review of Algebra and Geometry ISubscriptionWith account