#### Topics

##### Linear equations in two variables

- Linear Equations in Two Variables
- Linear Equations in Two Variables Applications
- Cross - Multiplication Method
- Substitution Method
- Elimination Method
- Graphical Method of Solution of a Pair of Linear Equations
- Determinant of Order Two
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Simple Situational Problems
- Inconsistency of Pair of Linear Equations
- Cramer'S Rule
- Consistency of Pair of Linear Equations
- Pair of Linear Equations in Two Variables

##### Quadratic Equations

- Quadratic Equations Examples and Solutions
- Quadratic Equations
- Roots of a Quadratic Equation
- Nature of Roots
- Relation Between Roots of the Equation and Coefficient of the Terms in the Equation Equations Reducible to Quadratic Form
- Solutions of Quadratic Equations by Factorization
- Solutions of Quadratic Equations by Completing the Square
- Formula for Solving a Quadratic Equation

##### Arithmetic Progression

- Introduction to Sequence
- Geometric Mean
- Arithmetic Progressions Examples and Solutions
- Arithmetic Progression
- Geometric Progression
- General Term of an Arithmetic Progression
- General Term of an Geomatric Progression
- Sum of First n Terms of an AP
- Sum of the First 'N' Terms of an Geometric Progression
- Arithmetic Mean - Raw Data
- Terms in a sequence
- Concept of Ratio

##### Financial Planning

##### Probability

- Basic Ideas of Probability
- Probability - A Theoretical Approach
- Type of Event - Elementry
- Type of Event - Complementry
- Type of Event - Exclusive
- Type of Event - Exhaustive
- Equally Likely Outcomes
- Probability of an Event
- Concept Or Properties of Probability
- Addition Theorem
- Random Experiments
- Sample Space
- Basic Ideas of Probability

##### Statistics

- Tabulation of Data
- Inclusive and Exclusive Type of Tables
- Median of Grouped Data
- Mean of Grouped Data
- Graphical Representation of Data as Histograms
- Frequency Polygon
- Concept of Pie Graph (Or a Circle-graph)
- Concept of Pie Graph (Or a Circle-graph)
- Ogives (Cumulative Frequency Graphs)
- Applications of Ogives in Determination of Median
- Relation Between Measures of Central Tendency
- Introduction to Normal Distribution
- Properties of Normal Distribution
- Graphical Representation of Data as Histograms
- Mode of Grouped Data

#### notes

Let us think of a simple experiment. A bag contains 4 balls of the same size. Three of them are white and the fourth is black. You are supposed to pick one ball at random without seeing it. Then obviously, possibility of getting a white ball is more.

In Mathematical language, when possibility of an expected event is expressed in number, it is called ‘Probability’ . It is expressed as a fraction or percentage using the following formula.

For a random experiment, if sample space is ‘S’and ‘A’ is an expected event then probability of ‘A’ is P(A). It is given by following formula.

`P(A)="Number of sample points in event A"/"Number of sample points in sample spaces"="n(A)"/"n(S)"`

In the above experiment, getting a white ball is event A. As there are three white balls n(A) = 3, As the number of balls is 4, n(S) = 4

probability of getting a white ball is, `P(A)="n(A)"/"n(S)"=3/4`

Similarly, if getting black ball is event B, then n(B) = 1

`therefore P(B)="n(B)"/"n(S)"=1/4`

**Ex.** Find the probability of the following, when one coin is tossed.

(i) getting head (ii) getting tail

**Solution** : Let ‘S’ be the sample space.

S = {H, T} n(S) = 2

(i) Let event A be getting head

A = {H} ∴ n(A) = 1

`P(A)="n(A)"/"n(S)"=1/2`

(ii) Let event B be getting tail

B={T} ∴n(B)=1

`P(B)="n(B)"/"n(S)"=1/2`