Topics
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
11th Std
Matrices
12th Std
Straight Line
Circle
Trigonometric Functions
Conic Sections
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
Pair of Straight Lines
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
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
Applications of Derivatives
Indefinite Integration
Continuity
Conics
Definite Integration
- Definite Integral as Limit of Sum
- Fundamental Theorem of Integral Calculus
- Properties of Definite Integrals
- Method for Finding Definite Intergrals
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
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.)
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
Determinants and Matrices
- Minors and Cofactors of Elements of Determinants
- Properties of Matrix Multiplication
Binomial Distribution
Estimated time: 2 minutes
Maharashtra State Board: Class 12
Formula: Foundation of Coordinate Geometry
| Sr. No. | Name | Condition | Formula |
|---|---|---|---|
| i. | Distance Formula | Two points P(x₁, y₁), Q(x₂, y₂) | \[\mathrm{d(PQ)}=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\] |
| a. | Internal Division | P divides AB in the ratio m: n | \[\mathrm{P\equiv\left(\frac{mx_{2}+nx_{1}}{m+n},\frac{my_{2}+ny_{1}}{m+n}\right)}\] |
| b. | Midpoint Formula | P is the midpoint of AB | \[\mathrm{P}\equiv\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)\] |
| c. | External Division | P divides AB externally in m: n | \[\mathrm{P\equiv\left(\frac{mx_{2}-nx_{1}}{m-n},\frac{my_{2}-ny_{1}}{m-n}\right)}\] |
| iii. | Centroid Formula | Triangle with vertices A, B, C | \[\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)\] |
