Tag: Class 10 Mathematics Notes
-
Introduction to Probability
Basic Terms of Probability Random Experiments Any fair experiment whose consequence cannot be pre-determined is known as random experiment. Let us imagine the tossing of a coin. As long as a fair coin is used, no person can accurately predict the occurence of a Head or a Tail. Thus, it is known as a random…
-
Area of Triangles
There are so many formulae to find the Area of a Triangle. Here, we have the formuale of area of the following triangles.
-
Mensuration: Area of Plane Surfaces
In this chapter, we will have an overview of the Formulae of Area and Perimeter of Some Basic Plane Surfaces.
-
Compound Depreciation
Introduction When we buy products like machineries, vehicles, furniture, etc from the shop for the first time, we say those items are first hand. When we sell those items to someone else, they become second hand items. When they sell them again to someone else, they become third hand items. And, you will notice that the cost of…
-
Compound Interest
Let us consider that we deposit certain sum \$ 1000 in a bank at 10% rate of interest. The bank allows its customer to withdraw their money at regular interval of time. Instead of receiving simple interest on the money for 10 years, we will now play a trick to multiply our money quickly. So,…
-
Simplification of Rational Expressions
Expressions that do not contain surds and can be expressed in the form of p/q where q is not equal to 0 are called rational expressions. Simplification of Rational Expressions is only possible if the denominators of the given expressions are identical or same or equal. Rational Expressions: An expression in the form of p/q…
-
Cramer’s Rule: Solution of a System of Linear Equations
Cramer’s Rule is used to solve the system of linear equations in two variables using determinants. Analytical Geometry and Cramer’s Rule Let us consider the following two linear equations: i) $a_1x + b_1y + c_1 = 0$ ii) $a_2x + b_2y + c_2 = 0$ The values of x and y which satisfy both the…
-
Solution of a System of Linear Equations – Matrix Method
Introduction By notating the linear equations in matrix form and using the Inverse of Matrices, we can find the solution of the system of linear equations. Linear Equation: Any equation in the form of ax + by = c is called linear equation. Some examples of linear equations are: $6\text{x} + 5\text{y} = 1$ $9\text{x}…
-
Inverse of 2×2 Matrix
Introduction If A be a square matrix of order mxm then the inverse matrix of A is another matrix of the order mxm, denoted by A-1 and defined as $\text{AA}^{-1} = \text{A}^{-1}\text{A} = \text{I}_m$ where $\text{I}m$ is a identity matrix of the same order as of the matrix A. In order to find out the…
-
Determinant of 2×2 Matrix
Introduction In a 2×2 square matrix, the determinant is obtained by subtracting the product of the elements of the secondary diagonal by the product of the elements of the leading diagonal. Determinant of a matrix is written as |A| or |A+B| or |B|. The name of the the matrix should be written inside ‘||’. In…