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