Ripetizioni di AnalisiPrecalculusUnlockedITSearch

The exam topics

Precalculus

The mathematics you need before Mathematical Analysis 1: logic, polynomials, equations and inequalities of every kind, analytic geometry.

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  1. Elementary logic

    What a proposition is, how propositions are combined with connectives, how statements with quantifiers are negated, and how proofs are built.

  2. Powers and roots

    Powers with integer, rational and real exponents and their properties, n-th roots with their domain conditions, rationalization, and the comparison of powers and of roots.

  3. Factorization, Ruffini’s rule and polynomial division

    What a polynomial is, how special products are expanded and recognized, how polynomial division is carried out and how a polynomial is factored with Ruffini's rule.

  4. Polynomial and rational equations and inequalities

    How to solve first- and second-degree equations, how to lower the degree by factorization, and how to study inequalities with the sign of the parabola, the sign chart and systems.

  5. Equations and inequalities with absolute value

    The piecewise definition of absolute value, its properties, and the systems that solve equations and inequalities with one or more absolute values.

  6. Irrational equations and inequalities

    The domain conditions of roots and the systems that solve equations and inequalities with roots of even and odd index.

  7. Logarithmic equations and inequalities

    The logarithm as an exponent, its properties and its function, and the methods for solving logarithmic equations and inequalities starting from the domain conditions.

  8. Exponential equations and inequalities

    The function a^x and its properties, and the methods for solving equations and inequalities in which the unknown appears in the exponent.

  9. Trigonometric equations and inequalities

    Sine, cosine and tangent on the unit circle, the identities that relate them, and the solution methods for every type of trigonometric equation and inequality.

  10. Analytic geometry and conic sections

    Points and lines in the Cartesian plane, then parabola, circle, ellipse and hyperbola, with the method for recognizing a conic from its equation and drawing it.

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