Class XII
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The Updated Syllabus Taken From CBSE Website
Unit One: Relations and Functions
Unit Two: Algebra
Unit Three: Calculus
Unit Four: Vectors & Three-Dimensional geometry
Unit Five: Linear Programming
Unit Six: Probability
- Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. - Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.
- Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operations 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 matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries). - Determinant
Determinant of a square matrix (up to 3 x 3 matrices), 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.
- Continuity and Differentiability
Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, like arcsin x, arccos x and arctan x, 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. - Application of Derivatives
Applications of derivatives: rate of change of quantities, increasing/decreasing functions, 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). - 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.
- Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only) - Differential Equations
Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of basic linear differential equation.
- 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. - Three Dimensional Geometry
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.
- Linear Programming
Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
- Probability
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable.
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Chapters
1. Relation and Function
Unit 1
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Types of Relations, Equivalence Class | |
Concept Exploration Exercise (CEE)-02 | Based on concepts of One-one and Onto functions | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
2. Inverse Trigonometric Function
Unit 1
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on domain and principal values of ITF | |
Concept Exploration Exercise (CEE)-02 | Based on basic properties of ITF | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
3. Matrices
Unit 2
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on definition, type, formation of matrices etc. | |
Concept Exploration Exercise (CEE)-02 | Based on operations, of Matrices | |
Concept Exploration Exercise (CEE)-03 | Based on Transpose, symmetric and skew- symmetric matrices etc. | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
4. Determinants
Unit 2
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Evaluation of determinant, minor and cofactors | |
Concept Exploration Exercise (CEE)-02 | Based on adjoint and inverse of the matrix | |
Concept Exploration Exercise (CEE)-03 | Based on application of Det. (Area of triangle, system of equations) | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
5. Continuity And Derivatives
Unit 3
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Continuity and Differentiability | |
Concept Exploration Exercise (CEE)-02 | Based on Chain rule, implicit derivatives | |
Concept Exploration Exercise (CEE)-03 | Based on logarithmic derivatives | |
Concept Exploration Exercise (CEE)-04 | Based on parametric differentiation | |
Concept Exploration Exercise (CEE)-05 | Based on second order derivatives | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 60 plus questions with answers |
6. Application of Derivatives
Unit 3
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Relate Rates (derivative as rate measurer) | |
Concept Exploration Exercise (CEE)-02 | Increasing and Decreasing Functions | |
Concept Exploration Exercise (CEE)-03 | Maxima and Minima | |
Concept Exploration Exercise (CEE)-04 | Optimization Problems | |
Learning Progress Assignment (LPA) | Based on all the topics, contains 50 plus questions with answers |
7A. Indefinite Integrals
Unit 3
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Applying Basic Integrals | |
Concept Exploration Exercise (CEE)-02 | Based on Integration by Transformation | |
Concept Exploration Exercise (CEE)-03 | Based on Integration by Substitution | |
Concept Exploration Exercise (CEE)-04 | Based on Application of Special Nine Integrals | |
Concept Exploration Exercise (CEE)-05 | Based on Integration of Partial Fractions | |
Concept Exploration Exercise (CEE)-04 | Based on Integration By Parts |
7B. Definite Integrals
Unit 3
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Evaluation of Definite Integration Directly, and by Substitution | |
Concept Exploration Exercise (CEE)-02 | Evaluation of Definite Integration by Using Properties | |
Learning Progress Assignment (LPA) | Based on both Indefinite and Definite Integrals contains 80 plus questions with answers |
8. Application of Integrals (Area)
Unit 3
9. Differential Equations
Unit 3
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Identifying Degrees and Order etc. | |
Concept Exploration Exercise (CEE)-02 | Solving DE by Separable Variable Method | |
Concept Exploration Exercise (CEE)-03 | Solving Homogeneous DE | |
Concept Exploration Exercise (CEE)-04 | Solving Linear DE | |
Learning Progress Assignment (LPA) | Based on all types of DE, contains 50 plus questions with answers |
10. Vector Algebra
Unit 4
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Magnitude, Co-linearity, Basic Operations of Vectors. | |
Concept Exploration Exercise (CEE)-02 | Dot Product and Properties | |
Concept Exploration Exercise (CEE)-03 | Cross Product and Properties | |
Learning Progress Assignment (LPA) | Based on all topics contains 50 plus questions with answers |
11. Three-D Geometry
Unit 4
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Based on Based on direction ratios and direction cosines | |
Concept Exploration Exercise (CEE)-02 | Based on Lines: Equation, Angle, Shortest distance | |
Learning Progress Assignment (LPA) | Based on all topics contains 30 plus questions with answers |
13. Probability
Unit 6
Types of material | Short Description | Download |
Revision Note | Chapter synopsis for quick revision | |
Concept Exploration Exercise (CEE)-01 | Basic concepts of probability | |
Concept Exploration Exercise (CEE)-02 | Based on Conditional Probability | |
Concept Exploration Exercise (CEE)-03 | Based on Independent Events | |
Concept Exploration Exercise (CEE)-04 | Total Probability and Bayes Theorem | |
Learning Progress Assignment (LPA) | Based on all topics contains 30 plus questions with answers |
Continue practicing the art of mathematics, for in its persistent pursuit lies the gateway to intellectual empowerment and a deeper understanding of the intricate patterns woven into the fabric of our world.