Topics
Linear Equations in Two Variables
- Foundation of Linear Equations in Two Variables
- Simultaneous Linear Equations
- Graph of a Linear Equation in Two Variables
- Methods of Solving Linear Equations in Two Variables > Graphical Method
- Methods of Solving Linear Equations in Two Variables > Determinant method (Cramer’s Rule)
- Equations Reducible to Linear Equations
- Application of Simultaneous Equations
Quadratic Equations
- Concept of Quadratic Equations
- Factorisation Method
- Completing the Square Method
- Quadratic Formula (Shreedharacharya's Rule)
- Nature of Roots of a Quadratic Equation
- Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
- Formation of a Quadratic Equation with Given Roots
- Application of Quadratic Equation
Arithmetic Progression
- Patterns and Sequences
- Arithmetic Progression (A.P.)
- General Term (nth) of an Arithmetic Progression
- Sum of First ‘n’ Terms of an Arithmetic Progressions
- Application of an Arithmetic Progression (A.P)
Financial Planning
Probability
Statistics
Definition: Linear Inequations in Two Variables
An equation which contains two variables and the degree of each term containing a variable is one is called a linear equation in two variables.
General Form:
ax + by + c = 0
Definition: Linear Inequations in One Variables
A linear inequality or inequation, which has only one variable, is called a linear inequality or inequation in one variable.
e.g. ax + b < 0, where a ≠ 0, 3x + 4 > 0
Definition: Linear Inequations
An inequality or inequation is said to be linear if each variable occurs in the first degree only and there is no term involving the product of the variables.
e.g. ax + b ≤ 0, ax + by + c > 0, x ≤ 4
Definition: Convex Set
A set of points in a plane is called a convex set if the line segment joining any two points in the set lies entirely within the set.
Definition: Non-Convex Set
If the line segment joining any two points in the set does not completely lie in the set, then it is a non-convex set.
