Topics
11th Std
Mathematical Logic
- Statements and Truth Values in Mathematical Logic
- Logical Connectives
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Logical Equivalence
- Tautology, Contradiction, and Contingency
- Quantifier, Quantified and Duality Statements in Logic
- Algebra of Statements
- Application of Logic to Switching Circuits
Trigonometry - II
- Trigonometric Functions of Allied Angels
- Trigonometric Functions of Compound Angles
- Trigonometric Functions of Sum and Difference of Three Angles
- Trigonometric Functions of Multiple Angles
- Trigonometric Functions of Sub-Multiple Angles
- Conversion Formulae in Trigonometry
- Trigonometric Functions of Angles of a Triangle
- Important Identities and Standard Results
Matrices
Straight Line
12th Std
Circle
Trigonometric Functions
Conic Sections
Pair of Straight Lines
Measures of Dispersion
- Range, Variance and Standard Deviation
- Coefficient of Variation
- Standard Deviation for Combined Data
- Meaning and Definition of Dispersion
- Measures of Dispersion
- Quartiles and Range in Statistics
- Variance
- Standard Deviation
- Change of Origin and Scale of Variance and Standard Deviation
- Standard Deviation for Combined Data
- Coefficient of Variation
- Mean Deviation
Probability
Vectors
- Vector Algebra: Representation and Types
- Algebra of Vectors
- Collinearity and Coplanarity of Vectors
- Vector in Two Dimensions (2-D)
- Three Dimensional (3-D) Coordinate System
- Components of Vector
- Position Vector of a Point P(X, Y, Z) in Space
- Component Form of a Position Vector
- Vector Joining Two Points
- Section Formula in Vectors
- Product of Vector in Algebra (Dot Product)
- Direction Ratios, Direction Cosine & Direction Angles
- Vector Product of two vectors in Algebra (Cross Product)
- Scalar Triple Product
- Vector Triple Product
Complex Numbers
- Concept of Complex Numbers
- Algebraic Operations of Complex Numbers
- Equality of Two Complex Numbers
- Conjugate of a Complex Number
- Square Root of a Complex Number
- Fundamental Theorem of Algebra
- Argand Diagram or Complex Plane
- Modulus of a Complex Number
- Argument of a Complex Number
- DeMoivre's Theorem
- Cube Root of Unity
- Set of Points in Complex Plane
Line and Plane
Permutations and Combinations
Linear Programming
Functions
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Algebra of Differentiation
- Derivative of Composite Functions
- Geometrical Meaning of Derivative
- Derivative of Inverse Function
- Logarithmic Differentiation
- Derivative of Implicit Functions
- Derivative of Parametric Functions
- Higher Order Derivatives
- Successive Differentiation
Applications of Derivatives
Limits
- Concept of Limits
- Methods to Find Limit of Rational Function>Factorization Method
- Algebra of Limits
- Methods to Find Limit of Rational Function> Rationalization Method
- Methods to Find Limit of Rational Function> Substitution Method
- Limits of Exponential and Logarithmic Functions
- Limits of Trigonometric Functions
- Limits of Algebraic Functions
Indefinite Integration
Continuity
Definite Integration
- Definite Integral as Limit of Sum
- Fundamental Theorem of Integral Calculus
- Properties of Definite Integrals
- Method for Finding Definite Intergrals
Conics
Application of Definite Integration
Sets and Relation
- Concept of Sets
- Classification of Sets
Differential Equations
Sequences and Series
- Sequence, Series, and Progression
- nth Term of A.G.P
- Expressing Recurring Decimals as Rational Numbers
- Arithmetic Progression (A.P.)
- Geometric Progression (G. P.)
- Sum to' n' Terms of a Geometric Progression
- Harmonic Progression (H. P.)
- Types of Means
- Arithmetico Geometric Series
- Power Series
Methods of Induction and Binomial Theorem
- Principle of Mathematical Induction
- General Term in Expansion of (a + b)n
- Middle term(s) in the expansion of (a + b)n
Probability Distribution
- Random Variables
- Probability Distribution of Discrete Random Variables
- Probability Mass Function (P.M.F.)
- Cumulative Distribution Function (c. d. f. )
- Expected Value and Variance of a Random Variable
- Probability Distribution of a Continuous Random Variable
- Probability Density Function (P.D.F.)
- Cumulative Distribution Functions (c. d. f.)
Binomial Distribution
Determinants and Matrices
- Minors and Cofactors of Elements of Determinants
- Properties of Matrix Multiplication
Estimated time: 3 minutes
Maharashtra State Board: Class 12
Definition: Logical Equivalence
If two statement patterns have the same truth values in the respective columns of their joint truth table, then these two statement patterns are logically equivalent.
Maharashtra State Board: Class 12
Key Points: Logical Equivalence
| Concept | Key Point |
|---|---|
| Symbol |
≡ |
| Contrapositive Rule | \[p\to q\equiv\sim q\to\sim p\] |
| Converse & Inverse | \[q\rightarrow p\equiv\sim p\to\sim q\] |
| Important Idea | Equivalent statements give the same result in the truth table |
