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
Key Points: Tangents and Conditions of Tangency for Conic Sections
| Conic sections | Eccentricity | Equation of the curve | Equation of the tangent at a point (x₁, y₁) on it | Equation of tangents with slope m | Point of contact | Condition of tangency |
|---|---|---|---|---|---|---|
| Circle | – | x² + y² = a² | xx₁ + yy₁ = a² | \[y=\mathrm{mx}\pm\sqrt{\mathrm{a}^{2}\mathrm{m}^{2}+\mathrm{a}^{2}}\] | \[\left(\frac{-\mathbf{a}^2\mathbf{m}}{\mathbf{c}},\frac{\mathbf{a}^2}{\mathbf{c}}\right)\] | c² = a²m² + a² |
| Parabola | e = 1 | y² = 4ax | yy₁ = 2a(x + x₁) | \[y=\mathrm{m}x+\frac{\mathrm{a}}{\mathrm{m}}\] | \[\left(\frac{\mathrm{a}}{\mathrm{m}^{2}},\frac{2\mathrm{a}}{\mathrm{m}}\right)\] | \[c=\frac{a}{m}\] |
| Ellipse | 0 < e < 1 | \[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\] (a > b) | \[\frac{xx_{1}}{a^{2}}+\frac{yy_{1}}{b^{2}}=1\] | \[y=\mathrm{mx}\pm\sqrt{\mathrm{a}^{2}\mathrm{m}^{2}+\mathrm{b}^{2}}\] | \[\left(\frac{-a^{2}m}{c},\frac{b^{2}}{c}\right)\] | c² = a²m² + b² |
| Hyperbola | e > 1 | \[\frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{b}^2}=1\] | \[\frac{xx_1}{a^2}-\frac{yy_1}{b^2}=1\] | \[y=\mathrm{mx}\pm\sqrt{\mathrm{a}^{2}\mathrm{m}^{2}-\mathrm{b}^{2}}\] | \[\left(\frac{-\mathbf{a}^{2}\mathbf{m}}{\mathbf{c}},\frac{-\mathbf{b}^{2}}{\mathbf{c}}\right)\] | c² = a²m² − b² |
