Topics
Mathematical Logic
- Statements and Truth Values in Mathematical Logic
- Logical Connectives
- Tautology, Contradiction, and Contingency
- Quantifier, Quantified and Duality Statements in Logic
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Algebra of Statements
- Application of Logic to Switching Circuits
- Overview of Mathematical Logic
Matrices
Trigonometric Functions
Pair of Straight Lines
Vectors
Line and Plane
Linear Programming
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Derivative of Composite Functions
- Geometrical Meaning of Derivative
- Derivative of Inverse Function
- Logarithmic Differentiation
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Higher Order Derivatives
- Overview of Differentiation
Applications of Derivatives
- Applications of Derivatives in Geometry
- Derivatives as a Rate Measure
- Approximations
- Rolle's Theorem
- Lagrange's Mean Value Theorem (LMVT)
- Increasing and Decreasing Functions
- Maxima and Minima
- Overview of Applications of Derivatives
Indefinite Integration
- Indefinite Integration with Standard Indefinite Integral Formulae
- Methods of Integration> Integration by Substitution
- Methods of Integration> Integration by Parts
- Methods of Integration> Integration Using Partial Fraction
- Overview of Indefinite Integration
Definite Integration
- Definite Integral as Limit of Sum
- Integral Calculus
- Methods of Evaluation and Properties of Definite Integral
- Overview of Definite Integration
Application of Definite Integration
- Application of Definite Integration
- Area Bounded by Two Curves
- Overview of Application of Definite Integration
Differential Equations
- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equations
- Homogeneous Differential Equations
- Linear Differential Equations
- Applications of Differential Equation
- Solution of a Differential Equation
- Overview of Differential Equations
Probability Distributions
- Random Variables
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Variance of a Random Variable
- Expected Value and Variance of a Random Variable
- Overview of Probability Distributions
Binomial Distribution
- Bernoulli Trial
- Mean and Variance of Binomial Distribution
- Probability using Binomial Distribution
- Overview of Binomial Distribution
Estimated time: 5 minutes
Maharashtra State Board: Class 12
Formula: Angle Between Lines
For equation: ax² + 2hxy + by² = 0
\[\Theta=\tan^{-1}\left\{\frac{2\sqrt{(h^{2}-ab)}}{\mid a+b\mid}\right\}\]
or \[\Theta=\sin^{-1}\left\{\frac{2\sqrt{h^{2}-ab}}{\sqrt{\left(a-b\right)^{2}+4h^{2}}}\right\}\]
or \[\Theta=\cos^{-1}\left\{\frac{|a+b|}{\sqrt{\left(a-b\right)^{2}+4h^{2}}}\right\}\]
Maharashtra State Board: Class 12
Formula: Bisectors of Angle
\[\frac{x^2-y^2}{a-b}=\frac{xy}{h}\]
Maharashtra State Board: Class 12
Key Points: Pair of Straight Lines
Lines are perpendicular if: a + b = 0
Lines are parallel (coincident) if: h² = ab
Perpendicular Pair:
- Equation: bx² − 2hxy + ay² = 0
Parallel Lines through (x₁, y₁):
- Equation: a(x − x₁)² + 2h(x − x₁)(y − y₁) + b(y − y₁)² = 0
