#### Topics

##### Linear equations in two variables

- Linear Equation in Two Variables
- Simultaneous Linear Equations
- Elimination Method
- Substitution Method
- Cross - Multiplication Method
- Graphical Method of Solution of a Pair of Linear Equations
- Determinant of Order Two
- Cramer’s Rule
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Simple Situational Problems
- Pair of Linear Equations in Two Variables

##### Quadratic Equations

- Quadratic Equations
- Roots of a Quadratic Equation
- Solutions of Quadratic Equations by Factorization
- Solutions of Quadratic Equations by Completing the Square
- Formula for Solving a Quadratic Equation
- Nature of Roots of a Quadratic Equation
- The Relation Between Roots of the Quadratic Equation and Coefficients
- To Obtain a Quadratic Equation Having Given Roots
- Application of Quadratic Equation

##### Arithmetic Progression

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

##### Financial Planning

##### Probability

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

##### Statistics

- Tabulation of Data
- Inclusive and Exclusive Type of Tables
- 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
- Concepts of Statistics
- Mean of Grouped Data
- Method of Finding Mean for Grouped Data: Direct Method
- Method of Finding Mean for Grouped Data: Deviation Or Assumed Mean Method
- Method of Finding Mean for Grouped Data: the Step Deviation Method
- Median of Grouped Data
- Mode of Grouped Data
- Concept of Pictograph
- Presentation of Data
- Graphical Representation of Data as Histograms
- Frequency Polygon
- Concept of Pie Graph (Or a Circle-graph)
- Interpretation of Pie Diagram
- Drawing a Pie Graph

## Notes

a and b are the roots of the equation ax^{2} + bx + c = 0 then,

(1)`alpha+beta=(-b+sqrt(b^2-4ac))/(2a)+(-b-sqrt(b^2-4ac))/(2a)`

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

`=-(2b)/(2a)`

`therefore alpha+beta=-b/a`

(2) `alphaxxbeta=(-b+sqrt(b^2-4ac))/(2a)xx(-b-sqrt(b^2-4ac))/(2a)`

`=((-b+sqrt(b^2-4ac))xx(-b-sqrt(b^2-4ac)))/(4a^2)`

`=(b^2-(b^2-4ac))/(4a^2)`

`=(4ac)/(4a^2)`

`=c/a`

`therefore alpha beta=c/a`

Ex. (1) If a and b are the roots of the quadratic equation 2x^{2} + 6x - 5 = 0, then find (a + b) and a × b.

Solution : Comparing 2x^{2} + 6x - 5 = 0 with ax^{2} + bx + c = 0.

∴a = 2, b = 6 , c = -5

∴a + b = -b/a = -6/2 = -3

and a × b =c/a =−5/2

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