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ALGEBRA 3 : Analysis, vectors, trigonometry, probabilities is known as a useful and convenient mathematics program intended for High School pupils (age 15-17).This Title comprises 20 chapters of complete courses completed with exercises covering every subject undertaken. The exercises are corrected step by step using the Evalutel Teaching Method which reconciles the struggle against failure in school and the valorisation of the most talented students. Among the subjects covered: Homogeneous polynomials, homographic functions, Derivative of functions, Taylor's theorem for polynomials, Barycenter.Major Features:Identity which factorizes an - bn and its applications.Definition and properties of polynomials: multiplication, division and divisibility by (x-a).Examples of a polynomial's factorizations.Permutations and combinations. Pascal's triangle and Newton's binomial.Polynomial functions: recalling of the second, third and fourth degree polynomials.The square root function. Inversely proportional and homographic functions.Derivative at a point. The derivative function and tangent to the graph. Derivation formulas.Functions defined as rational powers and their derivatives.Direction of variation of a function. Extremums. Third and fourth degree polynomials.Derivation of a compound function. Absolute value, oblique asymptotes.Vectors on a plane. Properties and applications of Thales's theorem.Definition and properties of the barycenter. Point and vector notations. Applications.Trigonometric functions: definitions and properties.Relations between trigonometric functions. Inverse trigonometric functions.Scalar product and norm. Applications to geometry.Scalar product and norm in an orthonormal base. Basic formulas of trigonometry.Distance between two points. Metric relations in a triangle. Equation of a circle.Sets, counting, and probabilities.Conditional probabilities, total probablities. The use of trees.Random variable and function. Mean expectation value and variance. Binomial distribution.
