#### 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

ax^{2} + bx + c, Divide the polynomial by a ( ∵a ≠ 0) to get `x^2+b/ax+c/a`.

Let us write the polynomial `x^2+b/ax+c/a` in the form of difference of two square numbers. Now we can obtain roots or solutions of equation `x^2+b/ax+c/a` which is equivalent to `ax^2 + bx + c = 0 .`

`ax^2 + bx + c = 0` .............(I)

`x^2+b/ax+c/a=0` ..... dividing both sides by a

`therefore x^2+b/ax+(b/(2a))^2-(b/(2a))^2+c/a=0`

`therefore (x+b/(2a))^2-b^2/(4a^2)+c/a=0`

`therefore(x+b/(2a))^2-(b^2-4ac)/(4a^2)=0` `therefore(x+b/(2a))^2=(b^2-4ac)/(4a^2)`

`therefore(x+b/(2a))=sqrt((b^2-4ac)/(4a^2)) or (x+b/(2a))=-sqrt((b^2-4ac)/(4a^2))`

`therefore x=-b/(2a)+sqrt((b^2-4ac)/(4a^2)) or x=-b/(2a)-sqrt((b^2-4ac)/(4a^2))`

`therefore x=(-b+sqrt(b^2-4ac))/(2a) or x=(-b-sqrt(b^2-4ac))/(2a)`

In short the solution is written as `x=(-b+-sqrt(b^2-4ac))/(2a)` and these values are denoted by `alpha,beta`.

`therefore alpha=(-b+sqrt(b^2-4ac))/(2a) , beta=(-b-sqrt(b^2-4ac))/(2a)` ............................(I)

The values of a, b, c from equation ax^{2} + bx + c = 0 are substituted in `(-b+-sqrt(b^2-4ac))/(2a)` and further simplified to obtain the roots of the equation. So `x=(-b+-sqrt(b^2-4ac))/(2a)` is the formula used to solve quadratic equation. Out of the two roots any one can be represented by α and the other by β.

That is, instead (I) we can write `alpha=(-b+sqrt(b^2-4ac))/(2a) , beta=(-b-sqrt(b^2-4ac))/(2a)` .......(II)