DIDACTIC UNITS
Mathematics for Academic Studies 4º E.S.O.
Last updated 23 Enero, 2023
| DIDACTIC UNIT : | CONTENTS: |
|---|---|
| Real numbers | Operations with fractions. Hierarchy. Representation and comparison of fractions. Classification of real numbers. Intervals. Aproximations and errors. |
| Powers | Laws and operations with powers. Scientific notation. |
| Radicals | Definition of nth root. Powers of fractional exponents. Equivalent roots. Simplification of roots. Properties of radicals. Rationalizing denominators. |
| Logarithms | Definition of base-a logarithm. Common and natural logarithms. Logarithmic calculus: logarithm of a product, quotient, power and root. Exercises (with solutions). |
| Equations and simultaneous equations | 1st degree equations and systems of equations. 2nd degree equations. Biquadratic equations. Irrational equations. Systems of 2nd degree equations. |
| Polynomials and algebraic fractions | Operations with polynomials. Notable products. Power of a binomial: the binomial theorem. Division of P(x) by x-a: Ruffini's rule. Polynomial remainder theorem. Factorization of polynomials using Ruffini's rule. Simplification of algebraic fractions. Operations with algebraic fractions. |
| Inequations | 1st degree inequations. 2nd degree inequations. Systems of linear inequalities in one variable. Rational inequations. |
| Trigonometry | Degrees and radians. Definition of the trigonometric ratios. Use of the calculator for Trigonometry: inverse trigonometric ratios. Trigonometric ratios of 30º, 45º & 60º. Trigonometric identities. Resolution of triangles (right-angled & oblique triangles). Finding the sine and cosine on the unit circle. Trigonometric ratios in 4 quadrants. Historical overview on Trigonometry. Exercises (with solutions). |
| Vectors | Definitions: length and direction of a vector, zero vector, opposite vector, etc. Vectors in component form. Operations on vectors: sum, difference, scalar multiplication, linear combination. Length of a vector. Straight lines and vectors.. Exercises (with solutions). |
| Functions | Concept of function. Graph of a function. Domain of the most common functions. Properties deduced from the graph of a function: continuity, symmetry, increasing intervals, M & m, intersection points with the axes. Straight lines review. Parabola. Hyperbola. Piecewise functions. 60 exercises (with solutions). |
| Statistics | Frequencies and tables, statistical graphs, central and dispersion parameters, etc. 24 exercises (with solutions). |
| Probability | Definitions. Types of events. operations with events: U and ∩. Laws of the operations among events. Laplace’s Rule. Laws of probability: probability of the U of two mutually exclusive events, probability of the complementary events, probability of the U of two non-mutually exclusive events. Compound events: tree diagrams. Probability of independent & dependent events. ANEX I: Vocabulary about probability. ANEX II: Steps required to solve probability problems. Exercises (with solutions). |
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