Class 11th and 12th is a very crucial phase in a student’s life. At this stage, students make career-related choices, which define the course of their lives. Students taking maths in Class 11th or 12th have huge scope in career options. Career roles vary greatly and the opportunities are endless for students. Students with a great interest in studying maths open up many options in their career as they may go for Engineering, computer programmers, software developers, and many more. You might be looking for a platform where you can get the Syllabus For CBSE Class 12 Maths.
The Central Board of Secondary Education (CBSE) has announced a subject-by-subject new CBSE Syllabus of classes 11th and 12th.
You will get all the information on the maths syllabus given below.
| CBSE Maths syllabus class 11th Unit-I: Sets and Functions Chapter 1: Sets • Sets and their representations • Empty set • Finite and Infinite sets • Equal sets. Subsets • Subsets of a set of real numbers especially intervals (with notations) • Power set • Universal set • Venn diagrams • Union and Intersection of sets • Difference of sets • Complement of a set • Properties of Complement Sets • Practical Problems based on sets Chapter 2: Relations & Functions • Ordered pairs o Cartesian product of sets • Number of elements in the cartesian product of two finite sets • Cartesian product of the sets of real (up to R × R) • Definition of − o Relation o Pictorial diagrams o Domain o Co-domain o Range of a relation • Function as a special kind of relation from one set to another • Pictorial representation of a function, domain, co-domain and range of a function • Real valued functions, domain and range of these functions − o Constant o Identity o Polynomial o Rational o Modulus o Signum o Exponential o Logarithmic o Greatest integer functions (with their graphs) • Sum, difference, product and quotients of functions. Chapter 3: Trigonometric Functions • Positive and negative angles • Measuring angles in radians and in degrees and conversion of one into other • Definition of trigonometric functions with the help of unit circle • Truth of the sin2x + cos2x = 1, for all x • Signs of trigonometric functions • Domain and range of trigonometric functions and their graphs • Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application • Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x • General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a. Unit-II: Algebra Chapter 1: Principle of Mathematical Induction • Process of the proof by induction − o Motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers • The principle of mathematical induction and simple applications Chapter 2: Complex Numbers and Quadratic Equations • Need for complex numbers, especially √1, to be motivated by inability to solve some of the quadratic equations • Algebraic properties of complex numbers • Argand plane and polar representation of complex numbers • Statement of Fundamental Theorem of Algebra • Solution of quadratic equations in the complex number system • Square root of a complex number Chapter 3: Linear Inequalities • Linear inequalities • Algebraic solutions of linear inequalities in one variable and their representation on the number line • Graphical solution of linear inequalities in two variables • Graphical solution of system of linear inequalities in two variables Chapter 4: Permutations and Combinations • Fundamental principle of counting • Factorial n • (n!) Permutations and combinations • Derivation of formulae and their connections • Simple applications. Chapter 5: Binomial Theorem • History • Statement and proof of the binomial theorem for positive integral indices • Pascal’s triangle • General and middle term in binomial expansion • Simple applications Chapter 6: Sequence and Series • Sequence and Series • Arithmetic Progression (A.P.) • Arithmetic Mean (A.M.) • Geometric Progression (G.P.) • General term of a G.P. • Sum of n terms of a G.P. • Arithmetic and Geometric series infinite G.P. and its sum • Geometric mean (G.M.) • Relation between A.M. and G.M. Unit-III: Coordinate Geometry Chapter 1: Straight Lines • Brief recall of two dimensional geometries from earlier classes • Shifting of origin • Slope of a line and angle between two lines • Various forms of equations of a line − o Parallel to axis o Point-slope form o Slope-intercept form o Two-point form o Intercept form o Normal form • General equation of a line • Equation of family of lines passing through the point of intersection of two lines • Distance of a point from a line Chapter 2: Conic Sections • Sections of a cone − o Circles o Ellipse o Parabola o Hyperbola − a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. • Standard equations and simple properties of − o Parabola o Ellipse o Hyperbola • Standard equation of a circle Chapter 3. Introduction to Three–dimensional Geometry • Coordinate axes and coordinate planes in three dimensions • Coordinates of a point • Distance between two points and section formula Unit-IV: Calculus Chapter 1: Limits and Derivatives • Derivative introduced as rate of change both as that of distance function and geometrically • Intuitive idea of limit • Limits of − o Polynomials and rational functions o Trigonometric, exponential and logarithmic functions • Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions • The derivative of polynomial and trigonometric functions Unit-V: Mathematical Reasoning Chapter 1: Mathematical Reasoning • Mathematically acceptable statements • Connecting words/ phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics • Validating the statements involving the connecting words difference between contradiction, converse and contrapositive Unit-VI: Statistics and Probability Chapter 1: Statistics • Measures of dispersion − o Range o Mean deviation o Variance o Standard deviation of ungrouped/grouped data • Analysis of frequency distributions with equal means but different variances. Chapter 2: Probability • Random experiments − o Outcomes o Sample spaces (set representation) • Events − o Occurrence of events, ‘not’, ‘and’ and ‘or’ events o Exhaustive events o Mutually exclusive events o Axiomatic (set theoretic) probability o Connections with the theories of earlier classes • Probability of − o An event o probability of ‘not’, ‘and’ and ‘or’ events | CBSE Maths syllabus class 12th Unit I: Relations and Functions Chapter 1: Relations and Functions • Types of relations − o Reflexive o Symmetric o transitive and equivalence relations o One to one and onto functions o composite functions o inverse of a function o Binary operations Chapter 2: Inverse Trigonometric Functions • Definition, range, domain, principal value branch • Graphs of inverse trigonometric functions • Elementary properties of inverse trigonometric functions Unit II: Algebra Chapter 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). Chapter 2: 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 • Ad joint 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 Chapter 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 Chapter 2: Applications of Derivatives • Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normal, 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) Chapter 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 $\int \frac{dx}{x^2\pm {a^2}’}$, $\int \frac{dx}{\sqrt{x^2\pm {a^2}’}}$, $\int \frac{dx}{\sqrt{a^2-x^2}}$, $\int \frac{dx}{ax^2+bx+c} \int \frac{dx}{\sqrt{ax^2+bx+c}}$ $\int \frac{px+q}{ax^2+bx+c}dx$, $\int \frac{px+q}{\sqrt{ax^2+bx+c}}dx$, $\int \sqrt{a^2\pm x^2}dx$, $\int \sqrt{x^2-a^2}dx$ $\int \sqrt{ax^2+bx+c}dx$, $\int \left ( px+q \right )\sqrt{ax^2+bx+c}dx$ • Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof) • Basic properties of definite integrals and evaluation of definite integrals Chapter 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) Chapter 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 − o dy/dx + py = q, where p and q are functions of x or constants o dx/dy + px = q, where p and q are functions of y or constants Unit IV: Vectors and Three-Dimensional Geometry Chapter 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 Chapter 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 − o Two lines o Two planes o A line and a plane • Distance of a point from a plane Unit V: Linear Programming Chapter 1: Linear Programming • Introduction • Related terminology such as − o Constraints o Objective function o Optimization o Different types of linear programming (L.P.) Problems o Mathematical formulation of L.P. Problems o Graphical method of solution for problems in two variables o Feasible and infeasible regions (bounded and unbounded) o Feasible and infeasible solutions o Optimal feasible solutions (up to three non-trivial constraints) Unit VI: Probability Chapter 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 |
