Author name: chandan sharma

Probability Probability is the study of mathematics which calculates the degree of uncertainty. There are two types of approaches to study probability- 1. Experimental or Empirical Probability The result of probability based on the actual experiment is called experimental probability. In this case, the results could be different if we do the same experiment again.

Statistics Statistics is one of the parts of mathematics in which we study about the collecting, organizing, analyzing, interpreting and presenting data. Statistics is very helpful in real life situations as it is easy to understand if we represent a data in a particular number which represents all numbers. This number is called the measure of central

Surface Areas and Volumes Surface Area is the area of the outer part of any 3D figure and Volume is the capacity of the figure i.e. the space inside the solid. To find the surface areas and volumes of the combination of solids, we must know the surface area and volume of the solids separately. Some of the formulas of

Perimeter and Area of a Circle The perimeter of all the plain figures is the outer boundary of the figure. Likewise, the outer boundary of the circle is the perimeter of the circle. The perimeter of circle is also called the Circumference of the Circle. Circumference = 2πr = πd (π = 22/7) r = Radius

Circle A figure made by all the points which are at the same distance from a fixed point is called a Circle. 1. Center The fixed point is known as the centre of the circle. 2. Radius The distance from any point on the circle to the fixed point is the radius. Any line segment

Some Applications of Trigonometry Trigonometry can be used in many ways in the things around us like we can use it for calculating the height and distance of some objects without calculating them actually. Heights and Distances To find the height of an object or to find the distance of an object to the other

Trigonometry To find the distances and heights we can use the mathematical techniques, which come under the Trigonometry. It shows the relationship between the sides and the angles of the triangle. Generally, it is used in the case of a right angle triangle. Trigonometric Ratios In a right angle triangle, the ratio of its side and

Cartesian Coordinate System In the Cartesian coordinate system, there is a Cartesian plane which is made up of two  number lines which are perpendicular to each other, i.e. x-axis (horizontal) and y-axis (vertical) which represents the two variables. These two perpendicular lines are called the coordinate axis. The intersection point of these two lines is known as the center

Triangles Any polygon which has three sides and three vertices is known as Triangle. Types of Triangles 1. There are three types of Triangles on the basis of the length of the sides. 2. There are three types of Triangles on the basis of angles. Centers of the Triangle There are four different centers of the

Arithmetic Progressions An Arithmetic Progression is a sequence of numbers in which we get each term by adding a particular number to the previous term, except the first term. Each number in the sequence is known as term. The fixed number i.e. the difference between each term with its preceding term is known as common difference. It can be

Quadratic Polynomial A polynomial, whose degree is 2, is called a quadratic polynomial. It is in the form of p(x) = ax2 + bx + c, where a ≠ 0 Quadratic Equation When we equate the quadratic polynomial to zero then it is called a Quadratic Equation i.e. if p(x) = 0, then it is known as

Linear Equations A Linear Equation is an equation of straight line. It is in the form of ax + by + c = 0 where a, b and c are the real numbers (a≠0 and b≠0) and x and y are the two variables, Here a and b are the coefficients and c is the

Polynomials A polynomial is an expression consists of constants, variables and exponents. It’s mathematical form is- anxn + an-1xn-1 + an-2xn-2 + a2x2 + a1x + a0 = 0 where the (ai)’s are constant Degree of Polynomials Let P(y) is a polynomial in y, then the highest power of y in the P(y) will be the degree of polynomial P(y).

Euclid’s Division Lemma It is basically the restatement of the usual division system. The formal statement for this is- For each pair of given positive integers a and b, there exist unique whole numbers q and r which satisfies the relation  a = bq + r, 0 ≤ r < b, where q and r can also be Zero. where ‘a’ is