CBSE Mathematics

Quadratic equation Chapter 4 Class 10 Basic concepts on Quadratic Equation class 10, chapter 4,  Nature of roots, Discriminant, Quadratic Formula, method of completing the square. Complete explanation of quadratic equations QUADRATIC EQUATION :-  An equation whose degree is 2 is called a quadratic equation. General Quadratic Equation is  ax 2 + bx + c = 0  Here "a" is the coefficient of x 2  ,  "b" is the coefficient of x and  "c" is the constant term.  Difference between the quadratic equations and quadratic polynomials. Quadratic equations are very similar to the quadratic polynomials. But they are different from each other because of the following reasons. Quadratic Equations Quadratic Polynomials General Quadratic Equations is    ax 2  + bx + c = 0 General Quadratic Polynomial is  P(x) = ax 2  + bx + c Solutions of quadratic equations are called its roots. Sol

DIVISIBILITY TEST INMATHEMATICS Short cut method of checking the divisibility of numbers. Divisibility test for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 with examples and explanation Divisibility Test : Divisibility tests are the short-cut methods of checking whether the given number is divisible by the another given digit or number. Here in this topic we will discuss the divisibility test by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 with examples for more understanding. Divisibility Test by 2:  If unit digit of a number is even ( 0, 2, 4, 6, 8) then that number is divisible by “2” All even numbers are divisible by “2”. Example 1: Let given number is 258694 Unit digit of this number is “4” it is even. Therefore 258694 is also divisible by “2” Example 2: Let given number is 2586947 Unit digit of this number is “7”, it is odd. So the number 2586947 is not divisible by “2”. Divisibility Test by 3:   If sum of the digits of a given number is divisible by “3” then that number is also divisible by “3”.

Limits and Continuity   Basic concepts and formulas based on limit and continuity important for the students of classes 11 and 12. Important formulas of chapter 13 class 11 and important formulas necessary for the students of class 12 chapter 5 Introduction Limit and continuity is the introduction of calculus. Calculus is that branch of Mathematics which mainly deals with the study of change in the value of a function as the point in the domain changes.   Definition:  Suppose f is a real function on a subset of the real numbers and let c be a point in the domain of f. Then f is continuous at c if \[\lim_{x\rightarrow c}f(x)=f(c)\] ALGEBRA OF LIMITS \[Let \; f(x)\; and\; g(x)\; be\; two\; functions \; such\; that\; \lim_{x\rightarrow 0}\; f(x)\; and\; \lim_{x\rightarrow 0}\; g(x) \; exists\]\[1)\; \lim_{x\rightarrow a}\left [ f(x)+g(x) \right ]=\lim_{x\rightarrow a}\: f(x)+\lim_{x\rightarrow a}\: g(x)\]\[2)\; \lim_{x\rightarrow a}

Statistics  Formulas & Basic Concepts Statistic formulas for class 8th, 9th, 10th, Calculation of mean, mode, median, mean deviation  about mean & median, standard deviation, variance. Statistics For Class 10 MEAN FOR UNGROUPED DATA \[Mean=\frac{Sum \; of \; all \; observations}{Number\; of \; observations}\] \[Mean\left ( \overline{X} \right )=\frac{\sum x_{i}}{n}\] MEAN FOR A GROUPED DATA  There are three methods for this 1) DIRECT METHOD \[Mean\left ( \overline{X} \right )=\frac{\sum f_{i}x_{i}}{\sum f_{i}}\; \; or\; \; \; \; \frac{\sum f_{i}x_{i}}{n}\] \[Where:\; \; x_{i} = Mid \; values,\; \; x_{i} = \frac{Lower\: limit+Upper\: limit}{2}\] \[\sum f_{i} = sum \; of\; all \; frequencies\] Table for finding Mean by Direct Method C-I \[x_{i}\] \[f_{i}\] \[f_{i}x_{i}\] - - - - - - - - - - - - - - - - - - - -