## CBSE class 12 Maths Syllabus 2018-2019 Board Exam

A syllabus is an instructive document that tells us about what is expected during the complete course session. It is one of the first few items in a course that a student reviews. Syllabus of a course is a great place for a student to begin appreciating the nature of a given course. Let us look at a few tips to navigate the course syllabus effectively which acts as a roadmap with directions for succeeding in a class:

- At the beginning of the academic year, carefully read through the entire syllabus.
- Check the syllabus before each class and have an idea of what will be taught in the day’s topic.
- When something is unclear in the syllabus, make sure to talk to your teacher and clear your doubts beforehand.

Most students start studying with no targets and plans. But remember it always better to study looking at the syllabus first. This way students can identify the areas in which they are weak and can spend more time on those areas.

Math is a subject that can make your nervous. Although it seems impossible to score high marks in the math exam, if studied effectively there is a tremendous scoring opportunity in store for students in maths. Being on top of CBSE class 12 Maths will help you take a step in the right direction.

Students can make use of the syllabus provided here and refer to it at any point of time.

## Unit 1: Relations and Functions

### Relations and Functions

- Types of relations: reflexive, symmetric, transitive and equivalence relations.
- One to one and onto functions, composite functions, inverse of a function and Binary operations

### Inverse Trigonometric Functions

- Definition, range, domain, principal value branch
- Graphs of inverse trigonometric functions
- Elementary properties of inverse trigonometric functions

## Unit 2: Algebra

### 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)

### Determinants

- Division of a line segment in a given ratio (internally).
- Tangent to a circle from a point outside it.
- Construction of a triangle similar to a given triangle.

## Unit- 3: Calculus

### Continuity and Differentiability

- Simple and believable problems on heights and distances.
- Problems should not involve more than two right triangles.
- Angles of elevation / depression should be only 30Â°, 45Â°, 60Â°.

### Applications of Derivatives

- Simple and believable problems on heights and distances.
- Problems should not involve more than two right triangles.
- Angles of elevation / depression should be only 30Â°, 45Â°, 60Â°.

### 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 properties of definite integrals and evaluation of definite integrals

### 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)

### 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

## Unit 4: Vectors and Three-Dimensional Geometry

### 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

### 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 5: Linear Programming

### 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 6: Probability

### 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

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