Precalculus

       
           

Precalculus is the basic introduction about mathematical analysis. First we will know about Pre-calculus. Pre-calculus is required to understand concepts which are used in calculus.
Precalculus covers large number of concepts which are mentioned below.
Sets, real numbers, complex numbers, composite and polynomial Functions, trigonometry, limits, vectors, metrics, binomial theorem, mathematical induction, sequence, series, conic section, logarithm function, basic graphs, roots and rational exponents, quadratic functions, inverse functions, inequality involving Rational functions, Algebraic simplification and many more. Let's discuss some of them here.

Set: - It is a collection of different types of objects in a well defined manner. Sets involve basic operations like union, intersection, complements and cardinality product. In sets we also study cardinality of a set. As we know that if set 'P' has 'n' distinct elements for Natural Numbers 'n', then 'n' is the cardinality of set ‘P’ and ‘P’ is also a finite set. Cardinality of a set is denoted by |P|.
For example: Cardinality of set 4, 3, 2 and 1 is 4.
There are different types of sets which are shown below:
Empty set, Universal set etc:
If no element is present in a set then it is called as empty set, and a set in which all elements are present in universe of discussion is known as universal set.
Empty set is represented by symbol ‘∅’ and universal set is represented by ‘U’.

Real number:- Real numbers involve all numbers that may be Rational and Irrational Numbers, whole numbers etc.
For example: 1, 2, 5, 8, 9 these are Whole Numbers. Sometimes number 0 is also included in whole numbers.
Rational numbers – 4/5, 0.126, 0.4444…2.2 etc are Rational Numbers.

Irrational numbers – (⊼, √ 3, etc are irrational number).
If we have √ -3, this given number is not real because it contains imaginary value and ‘∞’ is also not a Real Number.

Function: - Function is used to illustrate the property between input and respective outputs.

Conic sections: - Conic section is a special type of curve, which is of three types that are hyperbola, parabola and ellipse, and circle. Circle is considered as special type of ellipse.

Limits: - In mathematics limits are initial part of calculus and limits are helpful when we define continuity, derivatives and integrals.

Mathematical induction: - Mathematical induction is used for mathematical proofs, by use of mathematical induction we can determine whether given statement is true or false for given Natural Numbers.

Trigonometry: - It deals with study of angles of triangle and its sides, trigonometry represents relation between sides and angles of a triangle.
This is all about precalculus.

Topics Covered in Precalculus

  • Binomial Theorem

    The binomial theorem formula is given in order to make it easy to expand the complex values that have powers. It is based on the arrangement of Pascal’s triangle that means all the values of the expressed theorem can be arranged to form...Read More

  • Relations and Functions

    Relations can be defined as set of ordered pairs of input values with output values, such that ‘P’ and ‘Q’ be two sets, a binary relation from P to Q is a subset of P´Q.

    It is a rule that produces one or more output numbers f...Read More

  • Mathematical Reasoning
    In mathematics we have to assume many things and mathematical reasoning is the part of assumption mathematics. In mathematical reasoning or math reasoning if we are performing some calculation like checking of inequalities, performin...Read More
  • Rotation Math
    With reference of mathematics, rotation is defined as motion of an object around a fixed point. Rotation is a transformation in plane of an object.  We can say that, rotations in math are transformation where an object rotates about a fixed p...Read More
  • Vectors Math
    Line is a geometrical shape that extends to infinity. Part of line with specific measure is called as line segment .These line segments are of a fixed length and can be used to symbolize vector magnitudes. We have studied the representation of...Read More
  • Introduction to Precalculus
    Pre calculus introduction involves sets, real and complex numbers, solving inequalities and equations, functions and their properties, composite, polynomial, rational, and trigonometric functions, sequences and series, binomial ...Read More
  • Translation Math
    Translation math, is kind of transformation math. In translation, object’s shape is not supposed to change but location of quadrants can change according to translation factor. New coordinates may lie in any of four quadrants and so result...Read More
  • Complex Number
    Complex number definition can be given as numbers that are formed by combination of real numbers and imaginary numbers. It is represented in form of a +ib. Here, ‘a’ is part of real set of numbers and b is  part of imaginary set of numbers. ...Read More
  • Precalculus Functions
    Precalculus functions are based on concept of dependence. For example total surface area of a circle can be determined if we know radius of circle. Thus area of circle is a function of radius and varies with value of radius. Mathemati...Read More
  • Reflection in Math
    Reflections math basically arise from the concept of transformations. Transformations in maths includes altering of geometrical forms by means of different methods like: reflection, translation, turning and resizing. Reflection geometry ...Read More
  • Plane Curve
    Plane curves in maths are those which are plotted using two axes only. For instance, all conics, lines etc. kind of shapes come in category of plane shapes. Points lying on these curves are formed using a pair of x and y values such as (x, y). ...Read More
  • Exponents and Logarithms
    Exponent is used to describe how many times a number is multiplied by itself. Example 2 * 2 * 2 here 2 is multiplied three times so we can represent it as 23. Here 3 is the exponent of number 2. So we can say that exponent is the p...Read More
  • Spherical Coordinates

    Spherical coordinate system is a coordinate system in three dimensional space. 3 dimensional objects can be described using spherical coordinates. Three parameters are used to describe these objects and these three parame...Read More

  • Rational Function

    Rational function can be described as ratio of two polynomial functions or we can say that when we divide a polynomial function by another polynomial function then it will be called as rational function. We can describe a rat...Read More

  • Parametric Equations

    Parametric equations can be defined as equations which are expressed using some parameters or we can say that the parametric equation is used to define a relation using parameters. For Example: Equation of circle in Cartes...Read More

  • Reflection in Math

    Reflections math basically arise from the concept of transformations. Transformations in maths includes altering of geometrical forms by means of different methods like: reflection, translation, turning and resizing. Reflect...Read More

  • Asymptote

    Asymptote definition states that it is a line for a given curve such that curve approaches infinity, the distance between the curve and line tends to zero. In other words, an it can be defined as a line which is normally tangent (tou...Read More

Math Topics