Mathematics, According to Reuben, is wisdom that studies figures, shapes, and logical interpretation of practical situations. CBSE provides a very vast and comprehensive syllabus that deals with colorful areas and conception to acclimatize logical interpretation of real situations and creates a strategic base for advanced studies in colourful fields like Mathematics and other courses i.e. Engineering, Physical and Biological wisdom, Commerce or Computer Applications.

**Class 12 maths syllabus:**

**Unit I: Relations and Functions**

**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

**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.
- Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices (restricted 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, cofactors 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 systems of linear equations by examples, solving systems 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 an 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 equations whose general solution is given.
- Solution of differential equations by the method of separation of variables solutions of homogeneous differential equations of the 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**

**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 −

- Two lines
- Two planes
- 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 −

- 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**

**Chapter 1: Probability**

- Conditional probability
- Multiplication theorem on probability
- Independent events, the total probability
- Bayes theorem
- Random variable and its probability distribution
- Mean and variance of a random variable
- Repeated independent (Bernoulli) trials and Binomial distribution

Out of the 100 marks, 80 marks are covered by these units, and the remaining 20 marks are covered by the internal assessment which is undertaken by the Periodic test, Mathematics assignments.

**FAQs (Frequently Asked Questions):**

**Q: What topics are covered under different units of Maths class 12th?**

A: The topics covered in Mathematics are Relation and Functions, Vectors and 3D geometry, Calculus, Algebra, Linear Programming, and Probability.

**Q: How many units are there in class 12 Mathematics?**

A: NCERT mathematics textbook for class 12 consists of a total of 6 units.

**Q: Is there any change in CBSE 12th Syllabus 2021-22?**

A: Yes, due to the spread of Coronavirus, the officials have reduced the CBSE Class 12 Maths Syllabus for session 2021-22 by up to 30% to manage the time lost.