Class 12 – Mathematics

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CLASS 12 – MATHEMATICS

Unit I. Relations and Functions 

1. Relations and Functions

 Relations, Functions

2. Inverse Trigonometric Functions        

Inverse Trigonometric Functions

Unit II. Algebra 

1. Matrices 

Types of Matrices, Operations on Matrices, Matrix Multiplication

2. Determinants 

Determinants, Inverse of a Matrix, Solution of System of Linear Equations by  Matrix Method, Properties of Determinants

Unit III. Calculus 

1. Continuity and Differentiability 

Continuity at a point, Continuity in an Interval, Derivative of Parametric Functions, Derivative of Implicit Functions, Logarithmic Differentiation, Second Order Derivative of a Function, Rolle’s Theorem, Lagrange’s Mean Value Theorem

2. Applications of Derivatives  

Equation of Tangent and Normal at any point, Approximations, Local Maxima and Minima, Absolute Maximum and Minimum of a Function, Applied Problems in Maxima and Minima

3. Integrals 

Integration as Antiderivative, Integration by Substitution-I, Integration by Substitution – II, Integration by substitution – III, Some standard Integrals – I, Some standard Integrals – II, Some standard Integrals – III, Some standard Integrals – IV, Some Standard Integrals of Trigonometric Functions – I , Some Standard Integrals of Trigonometric Functions – II, Some Standard Integrals of Trigonometric Functions – III, Integration by parts, Special Types of Integrals, Integration by Partial Fractions, Definite Integral as Limit of Sum, Fundamental Theorem of Integral Calculus, Properties of Definite Integrals.

4. Applications of the Integrals 

Equation of parabola, Equation of ellipse in the standard form, General equation of ellipse, Equation of hyperbola

5. Differential Equations

General Equation of Second Degree, Differential as Rate Measure, Formation of Differential Equations, Solution of Differential Equation by Separating Variables, Second Order Differential Equations, Homogeneous Differential Equations of First Order, Linear Differential Equations of First Order

Unit IV. Vectors and Three-dimensional Geometry

1. Vectors

Direction cosines, Laws of vector addition, Properties of vector addition, Position vector of a point, Linear Combination of Vectors, Dot Product, Cross Product, Scalar triple product, Vector triple product

2. Three-dimensional Geometry 

Equations of Line, Angle between two lines, Equations of Plane in Normal and  Intercept Forms, Equations of Plane Passing through a Point, Equation of Plane Containing Two Lines, Equation of Plane through the Intersection of Two Planes, Angle between two planes

Unit V. Probability 

Multiplication rule of probability, Conditional probability, Baye’s theorem, Random variable and probability distribution, Binomial Distribution