#### Topics

##### Number Systems

##### Real Numbers

##### Algebra

##### Pair of Linear Equations in Two Variables

- Linear Equations in Two Variables
- Graphical Method of Solution of a Pair of Linear Equations
- Substitution Method
- Elimination Method
- Cross - Multiplication Method
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Consistency of Pair of Linear Equations
- Inconsistency of Pair of Linear Equations
- Algebraic Conditions for Number of Solutions
- Simple Situational Problems
- Pair of Linear Equations in Two Variables
- Relation Between Co-efficient

##### Arithmetic Progressions

##### Quadratic Equations

- Quadratic Equations
- Solutions of Quadratic Equations by Factorization
- Solutions of Quadratic Equations by Completing the Square
- Nature of Roots
- Relationship Between Discriminant and Nature of Roots
- Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
- Quadratic Equations Examples and Solutions

##### Polynomials

##### Geometry

##### Circles

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

##### Triangles

- Similar Figures
- Similarity of Triangles
- Basic Proportionality Theorem Or Thales Theorem
- Criteria for Similarity of Triangles
- Areas of Similar Triangles
- Pythagoras Theorem
- Similarity Triangle Theorem
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Triangles Examples and Solutions
- Angle Bisector
- Similarity
- Ratio of Sides of Triangle

##### Constructions

##### Trigonometry

##### Heights and Distances

##### Trigonometric Identities

##### Introduction to Trigonometry

##### Statistics and Probability

##### Probability

##### Statistics

##### Coordinate Geometry

##### Lines (In Two-dimensions)

##### Mensuration

##### Areas Related to Circles

##### Surface Areas and Volumes

#### notes

The mode of a list of data values is simply the most common value. Eg. find the mode of the ungrouped data 2, 3, 4, 4, 3, 9, 6, 3, 5, 3

Here the mode is 4 because the highest frequently occured number is 4.

But this was about ungrouped data. In this concept we will learn to find mode of a grouped data. The mode of a grouped data is found with the help of formula.

Mode= `l+ [(f1-fo)/ (2f1-fo-f2)] xx h`

where, l= lower limit of modal class

f1= frequency of the modal class

fo i.e f not= frequency of the class preceeding the modal class

f2= frequency of the class succeeding the modal class

h= Class size= Upper limit- Lower limit

Let's take a example for better understanding,

Find the mode of the given data:

Family size |
1-3 |
3-5 |
5-7 |
7-9 |
9-11 |

No. of families |
7 |
8 |
2 |
2 |
1 |

Solution:

The maximum frequency is 8

Therefore, Modal class= 3-5,

then l= 3, h=2, f1=8, fo=7, f=2

`Mode= l+ [(f1-fo)/ (2f1-fo-f2)] xx h`

= `3+ [(8-7)/ (16-7-2)] xx 2`

= `3+ (1 xx 2)/7`

= `3+ 0.285`

Mode= 3.285