Maths Notes Class XII
As Per CBSE (NCERT) Books
Chapter Wise-Notes PDF ( Board Level )
Chapter 1 - Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.
Chapter 2 -Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
Chapter 3 - Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication.
Download Previous Year Boards Questions & Solutions PDF
Download NCERT Important Questions & Solutions PDF
Chapter 4 - Determinants
Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix.
Chapter 5 - Continuity and Differentiability
Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.
Download Previous Year Boards Questions & Solutions PDF [WILL BE UPLOADED SOON !]
Download NCERT Important Questions & Solutions PDF
Chapter 6 - Applications of Derivatives
Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool).
Download Previous Year Boards Questions & Solutions PDF [WILL BE UPLOADED SOON !]
Chapter 7 : Integrals
Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.
Download Chapter-Notes PDF [INDEFINITE]
Download Chapter-Notes PDF [DEFINITE]
Download Previous Year Boards Questions & Solutions PDF [WILL BE UPLOADED SOON ! ]
Chapter 8 : Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).
Download Chapter-Notes PDF [WILL BE UPLOADED SOON !]
Download Previous Year Boards Questions & Solutions PDF [WILL BE UPLOADED SOON !]
Chapter 9 : Differential Equations
Definition, order and degree, general and particular solutions of a differential equation. formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree.
Solutions of linear differential equation of the type:
(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 constant
Download Previous Year Boards Questions & Solutions PDF [Will be uploaded soon ! ]
Chapter 10 : Vectors
Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.
Chapter 11 : Three - dimensional Geometry
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
(i) two lines,
(ii) two planes,
(iii) a line and a plane. Distance of a point from a plane.
Previous Year Boards Questions & Solutions [Will Be Uploaded Soon !]
NCERT Important Questions & Solutions
Chapter 12 : Linear Programming
Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to 3 non-trivial constraints).
Chapter 13 : Probability
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.
Free Courses
R.k Malik's Newton Classes caters to CBSE and ICSE board from classes 9th to 12th for Maths and Science (Physics, Chemistry & Biology) subjects. Our free reference resources include Interactive Simulations (Enhancing Visual Understanding), Concept Maps , Previous Years Solved Papers ( Upto 12 Years ). textbook detailed solutions (NCERT, R.D Sharma, HC Verma & etc.), Sample papers for CBSE & ICSE board, important questions and much more.
Premium Courses
The R.K. Malik's Newton Classes offers a comprehensive JEE/NEET/OLYMPIADS correspondence courses which is the closest one can get to classroom programme for JEE Main and Advanced preparation. The course also wraps in itself our experience in successfully training thousands of students in classrooms over a decade .
Ready to get started?
Get in touch , create your bright future