## Class 12th

###### Personalised Session
• Personal tutor
• Two way interaction
• No risk of travel (Learn at Home)
• Learn at your convenient time
• No hassle for parents to monitor their kids
• Real time doubt clearance
###### Complete Course

Class XII Mathematics

Class Schedule

Monday, Wednesday, Friday
4:20 - 5:20 PM

commence from 5th April 2021

Taken by Vishwajeet Sir

###### Class 12th Course Detail
This course contains full syllabus of class 12 according to NCERT syllabus. A student will able to do all questions related to class 12, JEE Main (engineering entrance) and NDA entrance. It is also benefitted to do any Olympiad based questions. You can join live session or take recorded lectures by expert faculties. You can see demo before joining. You can join live class batch with few students or can schedule one to one class also.

#### Syllabus

1. Relations and Functions

• Definition of Reflexive, Symmetric and Transitive relations, Equivalence relation
• Types of functions, injective(one-one), surjective(onto) and bijective functions
• Composition of functions, invertible functions, inverse of a function

2. Inverse Trigonometric Functions

• Domain and range of inverse trigonometric functions, principal values
• Properties of inverse trigonometric functions
• Derivation of properties of inverse trigonometric functions and its application
• Simplification and its application of inverse trigonometric functions
• Solution of Inverse trigonometric equations

3. Matrices

• Definition, Order and Formation of Matrices
• Equality, addition and subtraction of matrices
• Matrix Equation, word problems on addition and subtration of matrices
• Multiplication of matrices
• Types of matrices and its application
• Problems based on Principle of mathematical induction (PMI)
• Transpose, symmetric and skew symmetric matrices

4. Determinants

• Minors and cofactors of matrices and determinants, expansion of determinants
• Properties of determinants and its application
• Solution of determinants equations
• Application of determinants
• Adjoint and inverse of a matrix, properties of adjoint and inverse
• To solve the system of linear equations using matrix method, consistency and inconsistency
• To find the inverse of a matrix by elementary transformations

5. Continuity and differentiability

• Basis concept of Continuity and problems based on continuity
• Properties of continuous functions and its applications
• Differentiability and problems on differentiability
• Basic formulae of differentation, product rule, quotient rule and chain rule of differentiation
• Differentiation of implicit functions and problems based on implicit functions
• Differentiation of Inverse trigonometric functions
• Differentiation of logarithmic functions
• Differentiation of infinite series
• Differentiation of parametric functions
• Differentiation of a function with respect to another function
• Higher order derivatives (second order derivative, third order derivatives)
• Parametric functions in higher order derivatives

6. Application of derivatives

• Basic concept of application of derivatives, Rate of change
• Important problems on rate of change, Marginal revenue and marginal cost
• Slope of tangents and normals, equation of tangents and normals
• Increasing and decreasing functions
• Maxima and minima introduction, first order derivative test
• Higher order derivative test
• Word problems related to two dimensional figures
• Absolute maxima and absolute minima
• Approximations and errors
• Rolle's Theorem and its applicability
• Lagrange's Mean Value Theorem and its applicability

7. Integrals

• Indefinite integrals introduction, formulae
• Basic Integration of trigonometric functions
• Indefinite integrals by substitution method
• Standard form of indefinite integrals
• Integration by parts
• Problems in the form of e^x(f(x)+f'(x))
• Problems in the form of e^x sinx and e^x cosx
• Integrals of some special form
• Integrals using partial fractions
• Miscellaneous problems based on indefinite integrals
• Definite integrals introduction, substitution method
• Properties of definite integrals and its applications (f(x)=f(a-x))
• Properties of definite integrals and its applications (modulus functions)
• Properties of definite integrals and its applications (odd and even functions)
• Integrals by limit of a sum

8. Application of Integrals

• Area under curves (Circles and circle with straight line)
• Area under curves (Parabolas and parabolas with circle)
• Area under curves (Inequality based problems)
• Area under curves (Modulus functions and Ellipse based problems)
• Area under curves (Straight lines)Area under curves (Trigonometric functions and Miscellaneous problems)

9. Differential Equations

• Order and degree of differential equations
• Formation of differential equations
• Solution of differential equations by variable seperable method
• Solution of homogeneous differential equations
• Solution of linear differential equations
• Word problems on solution of differential equations

10. Vectors

• Vector introduction, types of vectors and resultant of vectors, triangle law, addition and subtraction of vectors
• Position vectors, component of vectors, magnitude of vector and unit vector
• Section formula and its application
• Scalar or dot product of vectors, projection of vectors
• Cross or vector product of vectors, Application of cross product, area of parallelogram and triangle by vector method
• Scalar triple product
• Properties and application of scalar triple product

11. Three Dimensional Geometry

• Introduction of three dimensional geometry, direction ratios and direction cosines
• Equation of straight line in vector and cartesian forms
• Angle between two straight lines
• Length of perpendicular, foot of perpendicular and coordinate of image
• Point of intersection of intersecting lines
• Distance between two skew lines, distance between two parallel lines
• Equation of plane cartesian forms (three point form and intercept form)
• Vector equation of plane and normal form
• Angle between two planes, Angle between a line and a plane
• Foot of perpendicular, coordinates of image
• Intersection of line and plane
• Equation of plane containing two coplanar lines
• Equation of plane passing through the line of intersection of two planes

12. Linear Programming

• Manufacturing problems
• Diet problems
• Transportation problems
• Miscellaneous problems

13. Probability

• Conditional probability
• Multiplication theorem, Independent events
• Problems on independent events
• Total probability, Baye's theorem
• Probability distribution, its mean, variance and standard deviation
• Problems on probability distribution