Analytic Geometry and Unit
his unit goes from natural numbers to solving everyday problems and the need to gradually increase the numerical sets shown. Operations with real numbers are formalized and the existence of imaginary and complex numbers is mentioned. Operating with absolute value, scientific notation and logarithms begins. At the end of this unit we will be moving from numerical to symbolic representation to generalize the operational rules of the mathematical representation. There are also significant problems for the student to solve.
Fourth unit: operations with monomials and polynomials. In this unit the fundamental operations with monomials and polynomials are reviewed giving them a greater scope than in previous years. Through the development of the content of this unit, we achieve the mechanization of the fundamental operations of algebra, which systemize and simplify the development of the next unit, which is highly encouraged. Fifth Unit: remarkable and factoring products. This unit is a complete study of the remarkable products and their respective factorization.
Factorizations of greater difficulty are addressed. The acquisitions of knowledge outlined in this unit, together with the last unit are used as needed to solve the problems. Sixth unit: operations with fractions and radicals. In this unit factor theorems and residue are addressed, and are operated with synthetic division by simplifying fractions to their lowest terms. Operations with radicals are discussed. At the end of this unit the student will be in a position to apply the acquired knowledge in algebraic problems that model various situations.
Seventh unit: equations and inequalities. In this unit, methods for solving equations and inequalities are studied. Problems as an equation or an inequality of first or second degree with one variable are resolved, pretending that the students infer that there are situations in your environment that are expressed in terms of one variable with one or more possible solutions, but also that there are events that need to be represented, with more than one variable as it is in the next unit. Eighth unit: systems of equations and inequalities.
In this unit algebraically systems two and three linear equations in three variables are resolved, also expressed as such problems. Systems two and three linear equations with three variables resolve themselves, as well as such problems expressed. Resolve two first-degree inequalities with two variables and problems expressed as a system of inequalities. Structuring the program listed. First Unit: relations and functions. In this unit Cartesian product, relation and function are defined.
The function is classified by the operations that define the way that it is expressed and properties presented. Second Unit: trigonometric functions. In this unit we review trigonometric reasons; direct and inverse trigonometric functions are defined. The domain, range and graph are plotted and defined for each one of the Cartesian planes. Third Unit: exponential and logarithmic functions. In this unit exponential and logarithmic functions and inverse functions are defined; the domain, range and the corresponding graph are defined.
Exponential and logarithmic equations are solved. At the end of this unit the operational part of the course will be introduced. Fourth Unit: coordinated systems and some basic concepts. In this unit the dimensions one, two and three are localized. The distance between two points and the coordinates of the point that divides a segment into a given reason are calculated. Polar coordinates are defined, trigonometric reasons are reviewed, and polygons are classified by sides and by their angles. Perimeters and areas thereof are determined.
Some of the notable lines of a triangle and their points of intersection are defined. The slope of a line and the analytical conditions of parallelism and perpendicularity are established, as well as angle between two intersecting lines. Unit Five: Discussion of algebraic equations. In this unit, the fundamental problems of analytic geometry: given an equation, and graphic representations are addressed. That is, the intersections with the coordinate axes, the tria in respect to the axes and origin, the extent, the asymptotes and graph are defined. Sixth Unit: equation of the first degree.
In this unit your equation is obtained from the definition of a straight line as your equation locus. This is determined as a function of two conditions. It is expressed in the general forms, simplified as symmetrical and normal. The distance from a point to a line, the distance between the parallel lines is also calculated. Equations of the medians, the bisectors of the heights, as well as their respective points of intersection are obtained. Seventh Unit: General equation of the second degree. This unit is defined generally as the chronicles locus.
The general equation of second degree sets criteria that are discussed to determine the curve represented by it. Translation concepts and rotation of coordinated axes are introduced. Unit Eight: Circumference. In this unit, from its definition as a locus, the equation of the circle is obtained in the ordinary and generally forms. Center coordinates and radius lengths are determined; circumferences are considered specific and distinguished between circumference and circle. Application problems are resolved in other disciplines Ninth Unit: Parabola.
In this unit, from its definition as a locus, the parabola with COMAPS rule is constructed, its equation is obtained in the ordinary and generally forms when the vertex is in the orgy and the focal axis coincides with one of the axes coordinated, the vertex is any point on the plane but the focal axis is parallel to one of the coordinated axes. The equation is obtained when some elements are known. These are determined and the graph is plotted if the corresponding equation is known. The equation of parabola passing through three points is determined, knowing the position of the focal axis.
The equation is finally determined when the focal axis is oblique with respect to the coordinate axes. It solves application problems in other disciplines. Tenth Unit: ellipse. In this unit, from its definition as a locus, the ellipse is constructed with a ruler and a compass, its equation is obtained in the ordinary and generally forms when the center is at the origin and the focal axis coincide with any of the coordinate axes, the center is any point on the plane, but the focal axis is parallel to one of the coordinate axes. Equation is obtained when some elements are known.
Their equations known its elements are determined and plotted the corresponding graph. The equation of an ellipse passing through four points is determined. Application problems are resolved in other disciplines. Eleventh Unit: hyperbola. In this unit from its definition as the locus, a hyperbola is built by ruler and compass, its equation is obtained in the ordinary and generally forms when the center is at the origin and the focal axis coincides with one of the coordinate axes, the center is any point on the plane but the focal axis is parallel to one of the coordinate axes.
The equation you can get when you know some of their elements. The equation of the hyperbola passing through four points is obtained. Equilateral hyperbolae and conjugated are considered. Application problems resolve themselves in other disciplines. Structuring the program listed. First Unit: functions. This unit will review and deepen the concept of function with their properties and graphs. Second Unit: Limit of a function. In this unit the concept of limit is defined.
Setting forth the theorems to determine the limits of algebraic and transcendental functions, limits of functions were calculated when the independent variable tends to a constant, zero to plus infinity and minus infinity. Unit Three: The derivative. In this unit the derivative of algebraic and non-algebraic, explicit, implicit and function using LVM function boards are otendra drifts; successive derivatives of a function will be calculated. The meaning of the derivative will be studied in different contexts. The concept of the maximum and minimum of function, also inflection points and concavity be addressed.
Fourth Unit: applications of the derivative. In this unit application to problems of physics, the chemistry, the economy and other disciplines, whose solution involves the use of a derivative is considered. Unit Five: The integral. In this unit the concepts of definite and indefinite integral is addressed. Comprehensive proposals shall be calculated by applying the methods of integration: by parts, by substitution, by change of variable and by rational fractions, also some of numerical integration methods. Sixth Unit: applications of integrals. In this unit problems at other disciplines will be resolved in terms of an integral.