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# CBSE Class 12 Commerce Mathematics Syllabus

## CBSE Class 12 Commerce Mathematics Syllabus

CBSE Class 12 Commerce Mathematics Syllabus Mathematics is an important subject of study for students who want to pursue a career in the field of engineering, business administration, chartered accountancy, statistics or even economics.

### CBSE Class 12 Commerce Mathematics Syllabus

CBSE Class 12 Commerce Mathematics Syllabus

### CBSE Class 12 Commerce Mathematics Syllabus

Unit

Topic

Marks

I.

Relations and Functions

10

II.

Algebra

13

III.

Calculus

44

IV.

Vectors and 3-D Geometry

17

V.

Linear Programming

6

VI.

Probability

10

## 100

### CBSE Class 12 Commerce Mathematics Syllabus

CBSE Class 12 Commerce Mathematics Syllabus

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.

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.

### CBSE Class 12 Commerce Mathematics Syllabus

Mathematics : Mathematics is an important subject of study for students who want to pursue a career in the field of engineering, business administration, chartered accountancy, statistics or even economics.

Important topics

• Calculus 44 marks
• Vectors and 3-D Geometry – 17 marks
• Algebra – 13 marks
• Relations and functions and Probability – 10 marks
• CBSE Class 12 Commerce Preparation tips

Tips for preparation

• To score well in mathematics in a CBSE exam, it is very important to complete your NCERT book. Almost the entire paper revolves around the concepts given in your NCERT book.
• Move to a reference book only if and when you are through with each and every question and you know each and every question (both, solved and unsolved) by-heart, given in your NCERT book. To ace the CBSE mathematics exam, you need to know the NCERT book really well.
• Some formulas are very general and require you to identify the parts in the problem that correspond to parts in the formula.  If you don’t understand how the formula works and the principle behind it, it can often be very difficult to use the formula.For example, while performing integration, it is not difficult to memorize the formula for integration by parts, however, if you don’t understand how to use this formula, you will find the memorized formula of no use.
• Some formulas have certain rules that you need to follow, in order to correctly use them.  For instance, in order to use the quadratic formula, you must change the equation to standard quadratic form first.
• Make a sheet of important concepts/formulas. Make sure you know these formulas and more importantly, their usage.
• For a problem based question, Read the problem to get an idea of what you’re being asked to do. Write down what you are given and what you need to find. Work with the things given in a systematic way and try to find what is asked.
• Solve all the miscellaneous solved and unsolved questions too. Solve the Sample Papers available on CBSE website.

### CBSE Class 12 Commerce Mathematics Syllabus

How to score well

• Follow a pattern. For example, in case you start with long answer questions, complete that section and only then move to short or very short answer section.
• Highlight the important points and write your answer in points to enhance visibility.
• Among the questions with internal choices, select the ones that you plan to attempt, and frame skeletons of the answers you are going to write for these questions.
• Before you start the exam, utilize the first 15 minutes to scan the paper. Read the question paper thoroughly before jumping to write the answers.

### CBSE Class 12 Commerce Mathematics Syllabus

Recommended for such an enthusiastic audience:

### CBSE Class 12 Commerce Mathematics Syllabus

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