CBSE Class 12 Mathematics Exam 2019: Chapter-wise Important Topics, Concepts & More

→ Types of relations:

• Reflexive Symmetric

• Transitive

• Equivalence relations (Very important)

→ One to one and onto functions

→ Composite functions

→ Inverse of a function

→ Binary operations (Very important)

→ Range, domain and principal value branch

→ Graphs of inverse trigonometric functions (Very important)

→ Elementary properties of inverse trigonometric functions (Very important)

Understanding of notation, order, equality of matrix, types of matrix, zero and identity matrix

Types of matrices, zero and identity matrix

Questions based on transpose of a matrix, symmetric and skew symmetric matrices, operation on matrices (i.e. Addition and multiplication and multiplication with a scalar)

Invertible matrices and proof of the uniqueness of inverse, if it exists

→ Determinant of a square matrix (up to 3 × 3 matrices)

→ Properties of determinants (Very important)

→ Adjoint and inverse of a square matrix

→ Consistency, inconsistency and number of solutions of system of linear equations (very important)

→ Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix (very important)

→ Questions based on continuity & differentiability  (very important)

→ Students must know  how to differentiate:

• Composite functions

• Inverse trigonometric functions

• Implicit functions

• Concept of exponential & logarithmic functions

→ Derivative of functions expressed in parametric forms

→ Second order derivatives

 → Questions based on Rolle's and Lagrange's Mean Value Theorems (very important)

→ Rate of change of bodies

→ Increasing/decreasing functions (very important)

→ Tangents and normals (very important)

→ Use of derivatives in approximation

→ Maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool) very important

→ Simple problems that illustrate basic principles and understanding of the subject as well as real-life situations

→ Integration of a variety of functions

• by substitution

• by partial fractions

• by parts

→ Evaluation of simple integrals of the following types and problems based on them

→ Definite integrals as a limit of a sum

→ Fundamental Theorem of Calculus (without proof)

→ Basic properties of definite integrals and evaluation of definite integrals

→ Applications in finding the area under simple curves (very important)

→ Especially lines, circles/parabolas/ellipses (in standard form only)

→ Area between any of the two above said curves (the region should be clearly identifiable)

→ Order and degree (very important)

→ General and particular solutions of a differential equation (very important)

→ Formation of differential equation whose general solution is given (very important)

→ Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree (very important)

→ Solutions of linear differential equation of the type: (very important)

• (dy/dx) + py = q, where p and q are functions of x or constants

• (dx/dy) + px = q, where p and q are functions of y or constants

→ Vectors and scalars (magnitude and direction of a vector)

→ Direction cosines and direction ratios of a vector (very important)

→ Position vector of a point dividing a line segment in a given ratio (very important)

→ Properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors (very important)

→ Direction cosines and direction ratios of a line joining two points

→ Cartesian equation and vector equation of a line

→ Coplanar and skew lines

→ Shortest distance between two lines

→ Cartesian & vector equation of a plane

→ Angle between

 • two lines

 • two planes

 • a line and a plane

→ Distance of a point from a plane

→ Mathematical formulation of L.P. problems (very important)

→ Graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded)

→ Conditional probability (very important)

→ Multiplication theorem on probability (very important)

→ Independent events (very important)

→ Baye's theorem (very important)

→ Random variable & its probability distribution (very important)

→ Mean and variance of random variable (very important)

→ Repeated independent (Bernoulli) trials and Binomial distribution (very important)

→ These are some important topics from complete CBSE Class 12th Maths Syllabus 2018.