#### 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

`|[a,b],[c,d]|` is a determinant. (a, b), (c, d) are rows and `([a],[c]), ([b],[d])` are columns.

Degree of this determinant is 2, because there are 2 elements in each column and 2 elements in each row. Determinant represents a number which is (ad-bc).

ad-bc is the value of determinant `|[a,b],[c,d]|`

Determinants, usually, are represented with capital letters as A, B, C, D, . . . . . etc.

**Example:** Find the values of the following determinant.

`A=|[5,3],[7,9]|`

**Solution: **

`A=|[5,3],[7,9]| = (5xx9)-(3xx7)=45-21=24`

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