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
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`
