12th Grade Math

• Math

  What is math? Math is a language from which most of the students gets fear. It can define, as the study of measurement, properties and relationship of quantities using Numbers and symbols. More precise, we can say that it is the study of numbers ... Read More

  • Geometry

    Geometry is defined as the branch of mathematics which is concerned with the studies of the problems related to shape, size, position of figures, construction, measurement of angles sides, etc. In other words, it can be said as a science conc... Read More

    • Math Unit Conversions
      Math unit conversions include inter conversion of units of length, mass volume, are time etc. One unit can be converted into other unit by use of conversion factor. This conversion factor is actually a constant value. When we multi... Read More
  • Analytical Geometry

    Analytical Geometry is the part of the Algebra. It is basically concerned with the points, lines, circles, and other shapes that are the part of the geometry. In analytical geometry points are defined as the coordinate of (x,y) and... Read More

    • Tangents and Normals

      Tangent is a straight line which passes through the curve or we can say the line touching the edge of a Circle or curve at a single Point, and never crosses it, there can be infinite number of Tangent to a circle or a curve.

      ... Read More

    • Hyperbola
      Hyperbola definition states that a line which has curve shape is known as hyperbola or we can say that both focus (a fix Point) and directrix are always in the same ratio. It is just like a conic section. Conic section looks like a cone shape ... Read More
    • Distance From a Point to a Line
      The Distance between two points is given by
         D = √ (dp² + dq²);
      Where ‘D’ is the distance;
      ‘P’ is the coordinates of x – axis;
      ‘Q’ is the coordinates of y – axis;
      ‘dp’ is the difference between the x – coordinates ... Read More
    • Coordinate of a Point
      A number pair which represents the location of a Point in two - dimensional space is known as coordinates of a point.
      Suppose we have coordinate of a point R (5, -9) then it defines the location of points.
      Where ‘R’ is the name a... Read More
    • Area of Polygon in Coordinate Geometry
      Polygon can be defined as packed or closed shape made by joining more than two line segments end to end. The sides of a Polygon never bisect each other. The Point where two lines meet is known as vertex of polygon.... Read More
    • Cartesian Coordinates in Space
      If any figure has three dimensions than it has three co-ordinates i.e. X, Y and Z axis. Cartesian coordinates in space is denoted by Point ‘P’ which contains three Real Numbers that indicate the positions of the perpendicu... Read More
    • Line in a Coordinate Geometry
      In the coordinate Geometry two lines are present one is known as vertical line and other is defined as horizontal line. Now, we will see what is vertical and horizontal line in a coordinate geometry? If the x- coordinate of... Read More
  • Discrete Math

    Discrete Math has a wide application in the modern mathematics. Discrete mathematics is generally used in decision mathematics. In this mathematics, we study about objects, set and graphs. Before studying discrete mathematics you must ha... Read More

    • Functions in Discrete Mathematics
      A function in discrete Math named ‘g’ from the Set ‘P’ to ‘Q’ is a relation from P to Q that satisfies the below conditions-
      For each value of ‘a’ belonging to ‘P’, there will exist a unique value ‘b’ which belongs to ... Read More
    • Permutations and Combinations
      The terms permutations and combinations both have different meanings. The Permutation is an arrangement of items where its order matters. For example we can prove ML ≠ LM. For instance take any three names of your friends s... Read More
    • Mathematical Induction
      In Mathematical induction we find whether a given statement is true for all the natural Numbers or not. So the answer to What is Mathematical Induction is that it is basically a technique used to prove a statement or a theorem, or... Read More
      • Recursion
        Recursion is the process of repeating it-self in its own way. The term is very vast and has many implications. If we are taking about practical implementation of recursion we can take two parallel mirrors facing each other, now we will see so ... Read More
        • Solve Recurrence Relation
          Solving recurrence Relations is the method of analyzing the whole relationship of the terms with each other, tracking the sequence of Recursion and observing the progress. In mathematics there are many different ways of solving... Read More
  • Trigonometry

    Trigonometry is that branch of mathematics which deals with the real life problems related to angles. Trigo means three sides, so trigonometry is basically a branch of mathematics which relates to the study of three sided figures i.e. tri... Read More

    • Trigonometric Equations
      An equation which contains Trigonometric Functions is known as trigonometric equations.
      For example: Cos p = ½.
      When we solve trigonometric equations using different Relations then the equation is converted to form through whic... Read More
    • Applications of Trigonometry
      Trigonometry is the branch of mathematics which deals with Triangles and the relationship between the angles and sides of triangles.
      Now we will see some applications of Trigonometry:
      Some of the applications of trigonomet... Read More
    • Graphs of Circular Functions
      The equation x² + y² = 1 forms the Circle in Rectangular Coordinate System. This graph is known as Unit Circle it has radius one with the center at its origin i.e. (0, 0). The Domain of the trigonometric function is the Set ... Read More
  • Algebra

    Algebra is an important branch of mathematics in which we deal with several types of problems. These problems may either related to constants or variables. It is an interesting part of Math, and in this we mainly concentrate on "how to solve Numb... Read More

    • Algebra and Functions
      If we have two Sets, and the elements of one Set is associated with the element of other set is known as Functions. Algebra and functions are very important for finding the Relations in the given sets. We can say Algebra is a branc... Read More
    • Boolean Algebra
      A function in the form of f: P^k ⇢ P, where the values of P = 0, 1 and value of ‘k’ is non- negative Integer is known as Boolean function. Now we will see what is Boolean Algebra? Both Boolean algebra and Boolean logic are same terms. I... Read More
      • Boolean Operators
        A function in the form f: R^k ⇢ S, where values of ‘R’ are equals 0 or 1 and value of ‘k’ is non negative Integer is known as Boolean function.
        Now we will see the Boolean operators.
        There are three types of Boolean operators which ... Read More
  • Algebra 1

    Algebra 1 is part of algebraic mathematics which can be define as Algebra 1 is a branch of mathematics in which we represent the components of a specified Set or the numbers by use of symbols, alphabetical letters to express general relation... Read More

    • Solving Inequalities

      An inequality is defined as the expression that does not have equality sign joining the terms, but has the less than or greater than signs combining them. The objective of solving inequality is to find all the possible solutions ... Read More

    • Linear Equations

      A linear equation is a very important topic of Algebra. It is necessarily an algebraic equation which may consist of a single variable and constant or product of two or more constants. It may consist of more than one variable.
       

      ... Read More
  • Algebra 2

    Algebra 2 consists of many topics which are especially included for students who are weak in maths as they are quiet easy. The topics under Algebra 2 are:

    1.  Equations and inequalities which consist of many principles like:

    Adding p... Read More

    • Exploring Rational Expressions
      We know that all the mathematical operations can be performed on the Rational Numbers. We say that the Rational expression is the Mathematical Expression in which we can find the rational numbers combined together with the... Read More
    • Solving Systems of Linear Equations and Inequalities
      When we plot a graph then if equation makes a straight line then the equation is known as linear equation. For example:  y = mx + c; where ‘m’ is the Slope of a line and ‘c’ is Y- intercept where the ... Read More
    • Using Matrices
      Matrices are a Set of Numbers or we can say it is a collection of number which is arranged in rows and column. The numbers which we are using in matrices are Real Numbers. Generally in the matrices the complex numbers are used. With the h... Read More
    • Exploring Polynomial Functions
      Any polynomial function is said to be an expression of the form p(x) = a₀ + a₁*x + a₂ * x² + a₃* x³ . . . . + a_n * xⁿ , where we have a_n< > 0, is called the polynomial Functions, ‘x’ in the degree of ‘n’. While exploring p... Read More
    • Exploring Polynomials and Radical Expression
      An expression which consists of constant, variables and exponent values is known as polynomial expression. The polynomial expression is combined with the addition, subtraction, and multiplication.
      Like 5x² +... Read More
  • Precalculus

    Precalculus is a vast concept as it covers large number of topics and other concepts. Precalculus does not include topics from Calculus but it covers the topics and concepts which will be useful in calculus. Precalculus is studied from pri... Read More

    • Scalar
      Scalar Math is studied in linear Algebra where real number is considered as scalar and we can also relate the term scalar math with the vectors in vector space by using the operation known as Scalar Multiplication. In this operation a scalar or a... Read More
    • Precalculus Functions
      In Precalculus we study many topics which are Sets, real Numbers, complex numbers, composite and polynomial Functions, trigonometry, limits, vectors, metrics,  conic section, logarithm function, basic graphs, binomial theorem, math... Read More
  • Calculus

    Calculus! many students get fear with this branch of mathematics as it is consider as one of the difficult branch of Math. The word Calculus is derived from Latin word, which means calculating something and used for counting anything. Calculu... Read More

    • Differential Calculus

      When we talk about study of differential calculus, our primary objective is to study about the Derivatives of the function. Differential Calculus is the important part of calculus, in which we deal with the change of rate of quan... Read More

      • Differential Equations

        Differential equations are those types of equations that have some Derivatives of certain Functions. The derivatives can either be ordinary derivatives or partial derivatives. If there are only ordinary derivatives in the equati... Read More

        • First Order Differential Equation
          The general first order differential equation can be expressed as follows:
          dy / dx + p (x) y = q (x) (1)
          Where p (x) and q (x) are continuous Functions of  x. A continuous function is a function having no holes or brea... Read More
      • Application of Differentiation

        The differentiation is the subfield of Calculus and there are various application of differentiation in real world. The differentiation is very important part of Math as it is used in many scientific fields. Differentia... Read More

        • Secant Line
          A secant line is defined as a Straight Line that passes through any two points lying on the curve. Let us assume that a function given as: Y = f(x), where 'Y' is dependent on independent variable 'x'. Thus a function specifies a relationship... Read More
      • Maxima and Minima

        Maxima and minima of a function together can be called as extrema. Maxima and minima can be defined as largest and smallest of a function at a given Point in its Domain or outside its domain. We can calculate the maxima and minima o... Read More

    • Integration

      Integration is widely used in sociology, economy, mathematics, electronics engineering and many other fields. Here, we will discuss integration in terms of mathematics, which is called as integral Calculus or integration calculus. In math... Read More

      • Differential Equations and Mathematical Modelling

        A mathematical model for any system is the description of that system which uses the mathematical concepts related to the differential equation and some of the languages. This process of modeling is c... Read More

        • Antiderivatives

          An antiderivative can be defined as an operation opposite to differentiation operation or we can say that to find antiderivative of a function we have to find the integral of that function. Suppose we have a function f( x ) the we wil... Read More

        • Integration using u-substitutions

          Integration by U substitution is a process used to simplify the integral expressions. U substitution can only be applied to one type of integral, that is.- ∫f(x)*d/dx(f(x)). We can apply this rule only when we have t... Read More

    • Application of Integration

      Anti derivative of function f is the function F whose derivative is function f. We can understand it by an equation as F'=f. This process is also known as anti differentiation. This term is related to the definite integrals... Read More

  • Probability and Statistics

    Probability theory provides a structure or model of certain real world situations that provide very useful understanding and insight about making predictions.
    Here we are talking about the Statistics in mathematics. Statistics is the collecti... Read More

    • Probability

      In statistical mathematics we perform various tasks to accomplish the calculations which are related to the possibility of the event. In general aspect probability is used to describe the process of behavioral or logical estimation, which dep... Read More

      • Probability of Occurrence of an Event

        Let us consider any event E, which is associated to some of the random experiment and is occur if the occurrence of any one of the elementary event is its outcome. If S is a Sample Space and a random experiment i... Read More

        • Addition Theorem
          The addition theorem in the Probability concept is the process of determination of the probability that either event ‘A’ or event ‘B’ occurs or both occur. The notation between two events ‘A’ and ‘B’ the addition is denoted as '∪' and p... Read More
      • Random Variable
        A random variable is a variable which is concerned with random variable Probability Theory or we can say in Probability random variable are used for prediction of occurrence of events. Random variable can be defined as variable which obt... Read More
      • Binomial Distribution
        Binomial distribution is related to the Probability Theory in mathematics. Binomial distribution is discrete Probability distribution and frequently used to model the number of successes in a sample of size ‘n’ that is made by repl... Read More
      • Mathematical Expectation
        Study related to concepts of Probability and Statistics in Math is based on the fact that in a Probability distribution we determine either of the following:
        
        1.       Probability of occurrence of all arbitrary values of a Ran... Read More
    • Statistics

      Statistics is one of the very important and useful fields of mathematics. In statistic we study how to do the collection of data, then how to organize, analyze and interpret data. It is simply concerned with all these things and also involves ... Read More

      • Statistical graphs
        Statistics graphs are a ways to represent Statistics data in pictorial figure because numerical figures are more noticeable and easily intelligible, leaving a more lasting effect on the mind of the observer. With the help of these sta... Read More
        • Frequency Polygon
          A graph which is used for understanding the shapes of distributions is known as a frequency Polygon. A frequency polygon works as histogram; it is useful for comparing the Sets of data. A graph line is drawn by joining all the mid poin... Read More
      • Descriptive Statistics Review
        Descriptive Statistic review helps in describing data in quantitatively form. Mean is the best descriptive form of the Descriptive Statistics .It is one of the most informative and accurate measure of the central tendency. ... Read More
        • Numerical Descriptive Statistics
          Numerical Descriptive Statistics is the collection of different techniques like measures of central tendency, Measures of variability, Measures of relative standing and measures of linear relationship.
          These techniques ... Read More