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Class 12 Syllabus

# Mathematics Class 12 Syllabus

Exam Structure

 Unit Topic Marks I. Relations and Functions 10 II. Algebra 13 III. Calculus 44 IV. Vectors and 3-D Geometry 17 V. Linear Programming 06 VI. Probability 10 Total 100
• Unit I: Relations and Functions
• 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.
• 2. Inverse Trigonometric Functions
• Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
• Unit II: Algebra
• 1. 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. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
• 2. Determinants
• Determinant of a square matrix (up to 3 x 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. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
• Unit III: Calculus
• 1. 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.
• Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.
• 2. 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). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
• 3. 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.
• Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic propertiesof definite integrals and evaluation of definite integrals.
• 4. 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).
• 5. 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 constants.
• Unit IV: Vectors and Three-Dimensional Geometry
• 1. 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.
• 2. 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 and 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.
• Unit V: Linear Programming
• 1. 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 three non-trivial constraints).
• Unit VI: Probability
• 1. Probability
• Conditional probability, multiplication theorem on probability. independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

## Best books for Class 12 CBSE

Reference Book

It is well known that NCERT books are the best and enough for CBSE Class 12 boards preparation. But then again, simply mugging the NCERT books few weeks and days is not going to suffice. You should be thorough with your NCERT books at least 6 months before your boards. This will give you ample time to consider using other reference books.

Listed below are the best books for Class 12 CBSE, subject wise:

• Best books for Class 12 CBSE – Physics
• H C Verma is a must-have and the go-to book for Class 12 Physics. Apart from it, S L Arora, Pradeep’s and Xam Idea are other great options. We would strongly recommend ‘Xam Idea’ as it contains plenty of conceptual questions, which are more frequently asked in CBSE Class 12 boards.
• Best books for Class 12 CBSE – Chemistry
• Pradeep’s Chemistry is really helpful. You can also use O P Tandon as a good and dependable reference. However, do not neglect your NCERT book. Refer to these other books only when you have finished revising the NCERT book thoroughly.
• Best books for Class 12 CBSE – Mathematics
• R S Aggarwal & M L Khanna are strongly recommended. For commerce students, Part 1 and 2 by R D Sharma has a great collection of problems. You could also refer to U-Like papers as Mathematics is one of the most scoring subjects and you certainly don’t want to miss that opportunity.
• Best books for Class 12 CBSE – Biology
• There’s S Chand Publishing by B P Pandey. ‘Pradeep’s – A Textbook for Biology’ is also something you can completely rely on.
• Best books for Class 12 CBSE – English
• First of all, you will be required to read the lessons and be knowledgeable about the theme, characters and value points. NCERT textbooks for English: Flamingo and Vistas are enough for the literature section. You could also refer to U-Like papers, previous year question papers and other sample papers during your preparation.
• Best books for Class 12 CBSE – Economics
• For CBSE Class 12 boards, students mostly opt for textbooks published by NCERT as they are officially recommended by the board. However, to understand different sub-topics, one must also refer to the following books:
• 1. Introductory Macroeconomics by Sandeep Garg