10th 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

  • Number Sense

    As a child many have difficulty to understand maths. It may be due to the lack of common sense. There is a way through which the children can love maths by providing it the knowledge of numbers using real world examples. This is all about th... Read More

    • Fractions
      A fraction is a number expressed in form of $\frac{a}{b}$, where the numerator is 'a' and the denominator is 'b'. Fractions are of two kinds: like fractions and unlike fractions. If the denominators of the two fractions are same, then it is... Read More
    • Absolute Value Function
      Absolute value is defined as the value which is equals to both positive value and negative value. Absolute value makes the negative number into a positive number. In absolute value both the real number and its negative have th... 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

    • Polygons
      Polygons are the closed figures, which are formed by three or more line segments.  We say that the Line Segment is the part of the line which has the fixed length and the fixed end points. In polygon Geometry, we will learn about the different ... Read More
      • Special Quadrilaterals
        Quadrilaterals are the special type of polygons which are the closed figure formed by joining 4 line segments, sometimes they may be equal and sometimes not, depending upon the type of quadrilateral it is. Here we are talking abou... Read More
        • Trapezoid
          Trapezoid is a type of quadrilateral which is having at least one pair of parallel sides. Other definition a trapezoid is a quadrilateral which is having four sides, out of four, one pair of sides are parallel. Other definition, in a quadrilat... Read More
    • Geometric Solids
      Geometric solid is a three dimensional space or geometric solids are three dimensional figures, which includes polyhedral, pyramids, prism, cylinder, cones, sphere, ellipsoids etc. It also includes the points, lines, shapes, and regions... Read More
      • Prisms
        A prism is a collection of 3 or more cross section objects like triangular prism is a collection of 3 cross section objects; square prism is a collection of 3 cross section objects. Now we discuss prism Geometry of all kind of prisms–
        Triangular... Read More
    • Perimeter and Area of Similar Figures
      Perimeter is defined as the total of the peripheries of any figure that is the sum total of all sides of a figure. Perimeter is defined for almost every figure that is triangle, rectangle, square and others. For a R... 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

    • Introduction to Analytical Geometry
      The concept of Analytical Geometry was given by Mr. Percey F. Smith and Mr. Arthur Sullivan Gale. Mr. Percey F. Smith was a professor of mathematics in Sheffield scientific school, Yale University and Arthur Sullivan ... Read More
      • Angles between two lines
        The Angles between two lines is defined as shown below:
        If the lines are parallel then the angles between both lines is zero.
        Suppose we have angle ‘∅’in between two lines then it always satisfy the inequalities condition.
        =>... Read More
    • Polar Coordinates
      Polar coordinate is a method of presentation of points in the plane with use of Ordered Pair. This polar coordinate system comprises of an origin, pole, a Ray of specific angle and a polar axis. The polar axis is any line which initiat... Read More
    • Surface, Curves and Equations

      If we talk in mathematical terms, the surface Geometry deals with the plane and smooth surfaces. “Carl Friedrich Gauss” gave this concept. In this field the vital role has been played by the Lie groups. Lie groups defin... Read More

    • Ellipse

      Euclid first propounded the ellipse and the name ellipse in Math was given by Apollonius. In the year 1602, Kepler believed that the mars’s orbit is of oval shape, later he noticed that it was forming an ellipse with the sun as focus. We ca... Read More

    • Parabola
      Parabola can be defined as the conic section created by Intersection of a plane which is parallel to the generator line of surface and a Right Circular Cone. The other definition of parabola: A Plane Curve obtained by the moving a Point which i... Read More
    • Equation of a Line
      The equation of a line in Slope Intercept Form is written as shown as: y = m x + c,
      Where ‘m’ is the Slope of the line which is also named as gradient of a line and ‘c’ is named as the y- intercept of the line.
      The parameters used i... Read More
      • Intercept of a line
        The intercept of a line is a Point in a graph which intersects either x axis or y axis. It can not cut both axes at a time.
        Now we will see how to find the line intercept with the help of formula:
        If we have a point on the line and... 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
    • Rectangular Coordinate System
      The coordinate system containing two axes that is vertical and horizontal with center as origin is known as rectangular coordinate system. These two axes also form four quadrants. In Rectangular Coordinate System axes are r... 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
    • Triangular Coordinate System
      A packed figure which has three sides is known as triangle. Here we will see some properties of triangle. In a triangle the corner Point is known as the vertex of a triangle. In a triangle three vertices are present.
      The di... Read More
      • Heron's Formula
        Heron’s formula is used for calculating the Area of Triangle, it uses semi perimeter for calculation of area. Semi perimeter is given by:
        S = ½ (p + q + r)
        The area of the triangle by the heron s formula is given as:
        A = √ s (s – p) (... 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

    • Sets and Relations
      The collection of perfectly defined objects is a Set. Sets and Relations according to their name bear different properties. Set theory was given by “Georg Cantor”. The collection of definite Numbers is termed as elements of Sets. Lett... Read More
      • Binary Relations
        A binary relation is a collection of Sets between two Sets ‘M’ and ‘N’ which is the subset of M * N, or we can say that it is a Set of Ordered Pair m, n Є M*N. Here set of ‘M’ and ‘N’ are known as Domain.
        Binary Relations can be used ... 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 Functions
      Trigonometric Functions are also known as circular Functions; trigonometric functions are the functions of angles. These functions are helpful to form a relation between the angle and sides of triangle. Sine, cosine, tangent, are... Read More
    • Angles and their Measurements
      The angle is a structure formed with the help of two rays by sharing a common endpoint known as vertex of the angle. There are also trig identities which involves the angles and their measurements. The Trigonometric Identit... Read More
    • Radian Measure
      The proportionate Ratio between the length of an arc and its radius is used to define radian measure. In most areas of mathematics radian is considered as its standard unit for the measurements of the angle. “rad” is the symbol which is u... 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
    • Trigonometric Identities
      If we have an equation which contains one or more variables and it is valid for replacement of the values in which both sides of equation is defined then the equation is said to be an identity. The equalities that include the Tr... Read More
    • Unit Circle
      Trigonometry unit Circle is a circle which has radius one. The equation of unit circle is x² + y² = 1. The graph of the unit circle is shown below:
       
      Following steps will help us to draw the circle:
      
      As it is already described in the def... Read More
    • Right Triangles Trigonometry
      In a Right Triangle the side opposite to the Right Angle is called the hypotenuse and side opposite to the angle is opposite side and other side is adjacent side.
       
       
      Fig:-  Right triangle, right angled at ‘C’.
       
      Trigon... Read More
      • Solutions of Right Triangles
        Solving right Triangles means we need to find the measures of other two angles (as one angle is of 90⁰) or the measures of sides of the Right Triangle.
        Figure shown below is a right triangle, right angled at ‘C’ i.e. angle ... 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

    • Algebraic Equations
      Algebra is the study of mathematics, which helps us to find the value of the unknown variables, which are written in the combinations of the terms. Here in Algebraic Equations, we say that the left side and the right side of the equa... Read More
    • Mathematical Expressions
      By mathematical expression, we Mean the series of Numbers which are joined together with different mathematical operators. In order to solve the series of these numbers, we need to know a particular order which is to be followed... Read More
    • Pre-Algebra
      In study of Pre Algebra, we come across the following types of problems and then we follow certain rules and patters to solve the Set of Pre Algebra, problems. Prealgebra includes the study of solving the mathematical expressions and getting... Read More
      • Quadratic Equations
        The polynomial which can be expressed in the form of ax² + bx + c = 0, then we say that the equation is in the form of quadratic polynomial. Here we say that a, b, c are the real Numbers and we must remember that a <> 0, since if we ... Read More
        • Applications of Quadratic Equations
          Quadratic equations means an equation which is written in form of ax² + bx + c = 0. In real life we come across many practical problems which are related to applications of our life. If we know area of Rectangle, and ... Read More
    • Rationalization
      Rationalization in Math is a process that is undertaken to make the fraction denominator real especially in the cases where we may find surds or complex numbers in denominator. Dividing any number by a Complex Number is not likely to be ... 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

    • Polynomials

      If the exponent of a variable in an algebraic expression is a Whole Number then it is called a polynomial. A function p(x) of the form: p(x) = an x₀ + a₁ x + a₂ x₂ + …. + a_n, where all a₀ , a₁, a₂ , an are real Numbers and n is non zero ne... 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

    • 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
    • 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
    • Graphing Linear Relations and Functions
      A Set of Ordered Pair is known as relation.
      Suppose we have (2, 5), (-3, 4), (12, -5), (5, 7), (0, 5), (6, 9), (1, 6);
      The value lies on x – axis and it is known as Domain of given set and the value of y – axis ... Read More
    • Arithmetic Mean
      Arithmetic Mean, or Arithmetic Average is the value obtained by dividing the sum of various values  of series by number of items in series.
      So to Define Arithmetic Mean, we say that Arithmetic mean is the tool to measure central tendenc... Read More
    • Investigating Sequences and Series
      Three types of sequences are there i.e. A.P. (Arithmetic Progression), G.P. (Geometric Progression) and Harmonic Progression (H.P.), here we will be investigating sequences of these three types.
      Progression is defined... 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

    • Vectors Math
      A Scalar quantity is a quantity which only has a magnitude like mass, temperature, light, etc. On the other hand, vectors in Math are objects that have both magnitude and direction. To represent math vectors we use an arrow having a line of... Read More
    • Rational Function
      Ratio of two polynomial Functions is defined as a rational Function, where, a Polynomial is a finite length expression, made up of 3 basic mathematical operations( addition, subtraction and multiplication and non-negative exponents) wh... 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
    • Parametric Equations
      In plane, parametric equation is a pair of Functions which is given by:
      ⇒x = f (s) and y = g (s); which is used to define the ‘x’ and ‘y’ coordinate graph of the given curve in the plane.
      In mathematics, a Set of equations which i... Read More
    • Asymptote
      An asymptote is basically a line in which a graph approaches, but it never intersects the line. For example: In the following given graph of P =1 / Q, (here the x axis is denoted by ‘P’ and y axis is denoted by Q) the line approaches the p-axi... Read More
      • Horizontal Asymptote
        Asymptote of a curve can be defined as a line in such a way that the distance between curve and line reaches to value zero as they tends to infinity. In coordinate Geometry generally there are two type of Asymptote.
        -> Horizontal 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
    • Rotation Math
      In English, Rotation means to turn around an object around a center. When an object rotates around a centric Point then it is called as rotation. When any object rotates in three dimensional space about an imaginary line we call it as rota... Read More
      • Rotation Matrix
        Matrix is a Set of similar type of values. In mathematics, matrix is used in various applications like engineering mathematics, trigonometry, geometry, differential equation, etc. We can convert an object in 3D matrix into translate matr... Read More
    • Translation math
      In general language translation means to translate the code or language in other language for better communication. Translation is mainly used to convert an object from a form to another form. We can see this term Translation in various... Read More
    • Plane Curve
      In Geometry, we deal with many types of shapes and figures like lines, circles, ellipses, curve and many more. They all come under the family of curves. In geometry, there are two types of curve:
      1. Open curve: In open curve, we consider th... Read More
    • Reflection in Math
      By the term Reflections Math, we Mean the line where two halves of any figure are exactly equal. Then we say that one side of the figure is reflection half of the other. While we study Reflection Geometry, we draw the line in between ... Read More
    • Spherical Coordinates
      In three dimensional spaces Spherical Coordinate is used to find the location of a Point that depends on the distance ρ which is measured from the origin and two angles θ and ϕ. When we are going to define a spherical coordinate s... 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

      • Differentiation Formulas

        Differentiation Formulas are useful in finding a derivative of Functions and we use them in solving differentiation problems. Here, we will discuss useful differentiation formulas and other properties:-

        Derivative of const... Read More

        • Rules of Differentiation

          Differentiation is a process used to find a derivative of function where derivative means rate of change with respect to some variable like derivative of f(x) with respect to 'x' is - 

          d  (f(x)

          dx

          There are some ru... Read More

          • Power Law, Polynomials, Quotients and Reciprocals in Calculus

            Calculus is used for counting and it contains many procedures and methods,

            Power law-: we use power law in those situations where we are showing a special kind of mathematical relationshi... 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

      • Multiplication Theorems on Probability
        Probability is the branch of mathematics which deals with the occurrence of samples. The basic form of Multiplication theorems on probability for two events ‘X’ and ‘Y’ can be stated as,
        p ( x . y ) = p ( x ) . p ... Read More
      • Conditional Probability
        Whenever we deal with conditional Probability we need to have knowledge about the word probability. Generally people have a rough idea about its meaning. In our day-to-day life we came across statement like, probably it may rain ... 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 Histogram
          In the statics, the information can be represented by the help of a frequency histogram. In the histogram graph the rectangles are used to show the frequency of data items in form of successive intervals. The independent variables of... Read More