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
Definition
A set of numbers where the numbers are arranged in a definite order, like the natural numbers, is called a sequence.
Notes
We write numbers 1, 2, 3, 4, . . . in an order. In this order we can tell the position of any number. For example, number 13 is at 13th position. The numbers 1, 4, 9, 16, 25, 36, 49, . . . are also written in a particular order. Here 16 = 42 is at 4th position. similarly, 25 = 52 is at the 5th position; 49 = 72 is at the 7th position. In this set of numbers also, place of each number is detremined.
In a sequence a particular number is written at a particular position. If the numbers are written as a1,a2,a3,a4,..... then a1 is first, a2 is second, . . . and so on. It is clear that an is at the nth place. A sequence of the numbers is also represented by alphabets f1, f2, f3, . . . and we find that there is a definite order in which numbers are arranged.When students stand in a row for drill on the playground they form a sequence.We have experienced that some sequences have a particular pattern.Complete the given pattern
Look at the patterns of the numbers. Try to find a rule to obtain the next number from its preceding number. This helps us to write all the next numbers. See the numbers 2, 11, -6, 0, 5, -37, 8, 2, 61 written in this order.
Here a1 = 2, a2 = 11, a3 = -6, . . . This list of numbers is also a sequence. But in this case we cannot tell why a particular term is at a particular position ; similarly we cannot tell a definite relation between the consecutive terms.
In general, only those sequences are studied where there is a rule which determines the next term.
For example (1) 4, 8, 12, 16 . . . (2) 2, 4, 8, 16, 32, . . . (3)`1/5,1/10,1/15,1/20,........`
