Maths is a topic with chances of scoring that are enormous but it’s catchy in precisely the exact same time and may leave scope. Being at the top of class 12 Maths syllabus can allow you to take a step in the ideal way to get ready for the subject. Scoring marks requires commitment and hard work, however smart analyzing is demanded, to be on top of this table. Most pupils dive with no look in the syllabus into researching the topic. Knowing that the syllabus is vital since it is going to familiarise you enable you to gage depth, the policy and problem. Students concentrate effort and time to these subjects and may identify the regions where they are not robust.

**Chapters:**

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 | 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.

Read More – CBSE Class 12 Physics Syllabus 2018-19

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__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.

__Final Verdict:__

Students having difficulty with demanding math problems who would like to score better in their own math exams can consult with Course 12 Maths Syllabus and NCERT solutions that give pupils all that is essential to get ready for their exams and resolve various math related issues. All that pupils have to do is undergo those CBSE Class 12 Maths Syllabus and NCERT publications and resolve the exercises and questions offered in each chapter. Students can be sure of favorable outcomes if they do the needful. NCERT text books can be quite beneficial for pupils in attaining maximum marks within their own examinations.

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