Dictionary Rank of a Word | Permutations & Combinations

 PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

Lesson Plan Math Class X (Ch-4) | Quadratic Equations

E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10
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Board - CBSE

CLASS –X

SUBJECT- MATHEMATICS

CHAPTER 4  :- Quadratic Equations

TOPIC:-
Chapter 4 Quadratic Equations

DURATION:-  
This chapter is divided into seven modules and it is completed in fifteen class meetings.

PRE- REQUISITE KNOWLEDGE:-
TEACHING AIDS:- 
Green Board, Chalk,  Duster, Charts, smart board, laptop, projector  etc.

METHODOLOGY:- 
Demonstration and Lecture method.

OBJECTIVES:-
  • Introduction explanation and definition of quadratic equations.
  • Difference between the quadratic equations and quadratic polynomials.
  • Relationship between roots and coefficients of quadratic polynomials.
  • Method of finding the roots by factor method, by the method of completing the square and by quadratic formulas.
  • Discuss the nature of roots by using discriminant.
PROCEDURE :-
Start the session by checking their previous knowledge, by asking the questions of quadratic polynomials, its general equation, its degree and zeroes. After this explain the topic to the students. 

S.No.

TOPIC 

[FOR COMPLETE EXPLANATION OF THE TOPIC]

1

Introduction

Teacher should write the quadratic equation on the board and then explain all the components of quadratic equations like coefficient, variable and constant term.

General Quadratic Equation is :  

ax2 + bx + c = 0

a is the coefficient of x2,

b is the coefficient of  x,

c is the constant term.

Now teacher will introduce the definition of quadratic equations and explain the difference between the quadratic equations and quadratic polynomials.

2

Roots of a Quadratic Equation

Solutions of the quadratic equations are called its roots.

Roots are the values of x for which the given quadratic equation become equal to zero.

Now teacher will explain the relationship between the roots and coefficients of quadratic equations.

Teacher will also explain the method of making the quadratic equation from the roots.

x2 – Sx + P = 0

Where S is the sum of roots and P is the product of roots

x2 – (Sum of roots)x + Product of roots = 0

3

Factor Method to solve Q.E.

Now teacher will introduce the factor method of finding the roots of the quadratic equations. Teacher will also provide sufficient number problems to the students so that students will understand the concept properly.

4

Discriminant and Nature of roots

Now teacher will introduce the Discriminant(D) and explain its relation with the general Q.E.

D = b2 – 4ac

Now teacher will explain the Nature of Roots with different conditions of  D. i.e.  for D > 0,  D = 0, D < 0  and  D ≥ 0

5

Method of Completing the Square

Now teacher will write general quadratic equation and step by step explain the method of completing the square. Teacher will also explain the method by taking 2 - 3 examples so that students will completely understand the concept.

6

Quadratic Formula

Now teacher will explain to the students that the last result that we get in the method of completing the square is called the Quadratic formula.\[x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\]Students can also solve the quadratic equations by directly applying the quadratic formula

7

Applications

It is important for the students to have the ability to apply all the methods of solving the quadratic equations in different situations (word problems).

Teacher will provide different situations to the students and help then to solve the problems by using different methods.

Teacher can also introduce some practice worksheets to the students.


EXPECTED OUTCOMES:-
After studying this lesson students should know 
  • All formulas and all important concepts related to the quadratic equations.
  • Students should know the nature of solutions by using Discriminant.
  • Students should know the  factor method, method of completing the squares, and quadratic formula for solving the Q.E. 
  • Students should also know the method of implementation of these formulas in simple and complex problems.
STUDENTS DELIVERABLES:-
  • Students should review the questions given by the teacher. 
  • Students should prepare the presentation on the different methods of solving quadratic equations.
  • Students should Solve the  N.C.E.R.T. problems with examples, 
  • Students should solve assignment on Multiple Choice Questions (MCQ) given by the teacher.
EXTENDED LEARNING:-

Students can extend their learning through the RESOURCE CENTRE and can find more valuable and interesting concepts on mathematics at  cbsemathematics.com

ASSESSMENT TECHNIQUES:-
Assignment sheet will be given as home work at the end of the topic. Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.
Class Test , Oral Test , worksheet and Assignments can be made the part of assessment.
Re-test(s) will be conducted on the basis of the performance of the students in the test.

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