Maths : Types of Sums

## Matrices

1. Elementary Transformations
2. ..
	1. Minors & Co-factors
	2. Finding Adjoint of Matrices
	3. Inverse by Transformation Method
	4. Inverse by Adjoint Method
3. Linear Equations in 3 Variables
	1. Solve using Method of Inversion
	2. Solve by Reduction Method

## Trigonometry

1. Principle & General Solutions
2. Polar Co-ordinates
3. sine rule , cosine rule , projection rule .
4. Half Angle Formulae , Area of Triangle , Hero's Formula
5. Principle Solutions of Inverse Trigonometric Equations
6. Properties of Inverse Trigonometric Functions

## Pair of Straight Lines

1. Pair of Straight Lines through Origin
	1. Joint Equation of Line
	2. Separate Equations
	3. Auxillary Equation
	4. Conditions for Nature of pair of Lines
	5. Acute Angle between Pair of Straight Lines
2. Pair of Straight Lines not passing through Origin
	1. Joint Equation
	2. Acute Angle between pair of lines
	3. Separate Equations
	4. Condition for Pair of Lines

## Vectors

1. Conditions for Collinearity & Coplanarity
2. Section Formulae
3. Scalar Triple Product
	1. Simplifications
	2. Volume of Parallelopiped
	3. Volume of Tetrahedron
4. Geometric Applications of Vectors
	1. Finding Centroid
	2. Proofs in Geometry

## 3D Geometry

1. Direction Cosines , Direction Ratios
2. Angle between two lines in Space

## Lines

1. ..
	1. Vector Equation of Line & Cartesian Form
	2. Conditions for Parallel and perpendicular Lines
	3. Collinearity & Coplanarity of two lines
2. ...
	1. Distance from a point
	2. Finding Foot of Perpendicular
	3. Shortest Distance between Skew Lines

## Planes

1. Vector Equation of a Plane
2. .
	1. Acute Angle between two planes
	2. Acute Angle between Plane and Line
	3. Conditions for coplanarity

## Linear Programming Problems

1. Formation of LPP
2. Maximize / Minimize
3. Finding Feasibility (Special Cases of LPP)

## Continuity

1. ...
	1. Check for Continuity , using limits
	2. Given the function is continuous , find the unknown value 'k'
	3. Removable & Irremovable Discontinuity
	4. Continuity and Conditions
	5. Checking Continuity in at border of intervals
2. Continuity in Intervals

## Differentiation

1. Differentiability & Continuity
2. Composite Functions
3. Inverse Trigonometric Functions
4. Logarithmic Differentiation
5. Implicit Functions
6. Parametric Functions
7. Higher Order Derivatives

## Application of Derivatives

1. .
	1. Tangents & Normals
	2. Rate Measurer
2. Approximations
3. Increasing / Decreasing Functions
4. LMVT & Rolle's Theorem
5. Maxima & Minima

## Integration

1. Basic Functions
2. Substitution Method
3. sine-cosine or ex in numerator as well as in denominator
4. Completing the Squares
5. Substitutions for achieving C.T.S.
6. Substitutions for achieving C.T.S.
7. Special Substitutions
8. Integration by Parts (u.v)
9. ex [ f(x) + f'(x) ]
10. Root of a2 - x2
11. Partial Fractions

## Definite Integration

1. Integrals as Limit of Sum
2. Basic Definite Integration
3. By Substitution
4. by Integration by parts
5. By Partial Fractions
6. Properties of Definite Integrals

## Differential Equations

1. ..
	1. Degree & Order of a Differential Equation
	2. Verification of Differential Equation (Prove that sums)
2. Formation of Differential Equations
3. ..
	1. Solution of Differential Equations (by integrating)
	2. Solution of Differential Equation when x & y are inseparable
	3. Solution of Differential Equation (Reduction to variable separation form)
4. Homogenous Differential Equations
5. Linear Differential Equations
6. Application of Differential Equations

## Probability Distribution

1. Random Variables : Identify Discrete or Continuous
2. Probability Mass Function
	1. Identification
	2. Find unknown 'k'
	3. Finding Probability Distribution and sketching Graph
	4. Finding Cumulative Distribution
3. Expected Value , Variance & Deviation
4. Probability Density Function
	1. Identification
	2. Find unknown 'k'
	3. Finding Probability Distribution and sketching Graph
	4. Finding Cumulative Distribution

## Binomial Distribution

1. Probability based on Binomial Distribution
2. Mean , Variance and Deviation
3. Word Problems