Topics
Linear equations in two variables
- Introduction to linear equations in two variables
- Methods of solving linear equations in two variables
- Simultaneous method
- Simultaneous method
- Substitution Method
- Cross - Multiplication Method
- Graphical Method
- Determinant method
- Determinant of Order Two
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Simple Situational Problems
- Pair of Linear Equations in Two Variables
- Application of simultaneous equations
- Simultaneous method
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 ax2 + 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 2x2 + 6x - 5 = 0, then find (a + b) and a × b.
Solution : Comparing 2x2 + 6x - 5 = 0 with ax2 + bx + c = 0.
∴a = 2, b = 6 , c = -5
∴a + b = -b/a = -6/2 = -3
and a × b =c/a =−5/2
If you would like to contribute notes or other learning material, please submit them using the button below.
