*CBSE Class 12 Commerce Maths Question Papers*

*CBSE Class 12 Commerce Maths Question Papers*

*CBSE Class 12 Commerce Maths Question Papers : The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. Senior Secondary stage is a launching stage from*

* where the students go either for higher academic education in Mathematics or for professional courses like Engineering, Physical and Bioscience, Commerce or Computer Applications. *

*The present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of students. Motivating the topics from real life situations and other subject areas, greater emphasis has been laid on **application of various concepts.*

*CBSE Class 12 Commerce Maths Question Papers*

*Objectives*

* The broad objectives of teaching Mathematics at senior school stage intend to help the students:*

*to acquire knowledge and critical understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles, symbols and mastery of underlying processes and skills.**to feel the flow of reasons while proving a result or solving a problem.**to apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method.**to develop positive attitude to think, analyze and articulate logically.**to develop interest in the subject by participating in related competitions.**to acquaint students with different aspects of Mathematics used in daily life.**to develop an interest in students to study Mathematics as a discipline.**to develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers, elimination of gender biases.**to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics.*

*CBSE Class 12 Commerce Maths Question Papers*

*CLASS-XII*

Sl No. | Contents | No. of Periods | Marks |

1. | Relations and Functions | 30 | 40 |

2. | Algebra | 50 | 13 |

3. | Calculus | 80 | 44 |

4. | Vectors and Three – Dimensional Geometry | 30 | 17 |

5. | Linear Programming | 20 | 06 |

6. | Probability | 30 | 10 |

| Total | 240 | 100 |

CBSE Class 12 Commerce Maths Question Papers

CBSE Class 12 Commerce Maths Question Papers

*Unit-I: Relations and Functions*

*1. Relations and Functions (15 Periods)**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 (15 Periods)*

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

*Unit-II: Algebra*

*1. Matrices (25 Periods)*

*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 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 (25 Periods)*

*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 (20 Periods)*

*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 (10 Periods)*

*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 (20 Periods)**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.*

*4. Applications of the Integrals (15 Periods)*

*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 (15 Periods)*

*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.*

*Unit-IV:Vectors and Three-Dimensional Geometry*

*1. Vectors (15 Periods)*

*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 (15 Periods)*

*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 (20 Periods)*

*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 (30 Periods)*

*Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.*

*CBSE Class 12 Commerce Maths Question Papers*

*Prescribed Books:**1) Mathematics Textbook for Class XI, NCERT Publications*

*2) Mathematics Part I – Textbook for Class XII, NCERT Publication*

*3) Mathematics Part II – Textbook for Class XII, NCERT Publication*

*4) Mathematics Exemplar Problem for Class XI, Published by NCERT*

*5) Mathematics Exemplar Problem for Class XII, Published by NCERT*

*CBSE Class 12 Commerce Maths Question Papers*

*The top five benefits of practicing CBSE Class 12 Commerce Maths Question Papers to know why more and more practice is required if you want to ace CBSE with a good score.*

*Benefit 1: Improves Time Management Skills*

*Practicing CBSE Class 12 Commerce Maths Question Papers helps in familiarizing the students with pattern of the exam. Also, it gives a fair idea about the time taken to solve the complete question paper. Students can know whether the question paper can be solved by them in the given time. By calculating their actual speed, students can improve their time management skills and perform well on the D-day as they will be able to devote time to each question calculatedly.*

*Referring sample test series helps in building a winning exam temperament. Various coaching experts suggest that solving the CBSE Class 12 Commerce Maths Question Papers is must if one wants to improve time management skills.*

*Benefit 2: Checks Level of Preparation*

*Once you have completed the syllabi of Class XII, you can start your practice from last years’ papers. By practicing CBSE Class 12 Commerce Maths Question Papers, you can check your level of preparation for CBSE exam. Besides, it helps you in commanding over the subject, speed in writing the exam and knowing strong and weak areas. This regular practice will lead to the periodic monitoring of performance of students.*

*Benefit 3: Builds Speed & Accuracy*

*Speed and accuracy are important aspects, which come from extensive practice of similar questions. Regular practice of solving previous years’ question papers increases your speed and you take comparatively lesser time in solving the complete paper. Good speed puts you to a good rank in CBSE. Coaching experts also advise that students must practice a good number of MCQs to build up speed and accuracy.*

*The daily practice of solving puzzles enables you to spot difficulty level of a question and also guides you about the time to be devoted for solving the questions. *

*Benefit 4: Enhances Question Solving Skills*

*Making a game plan as per your time and pace, and following it thoroughly is an essential for gaining success in CBSE. Your study plan shall include solving CBSE Class 12 Commerce Maths Question Papers on a daily basis, as more and more practice will lead to strengthening of question solving skills. By doing this, your performance will be better after each test. *

*Benefit 5: Boosts Confidence*

*According to the coaching experts, solving CBSE Class 12 Commerce Maths Question Papers gives you confidence and enhances your examination temperament. Solving more and more questions in a stipulated time frame is a must to do in order to get the real examination temperament. This will create a sense of self-assurance. By solving CBSE Class 12 Commerce Maths Question Papers on a regular basis, students get familiar with the exam pattern and get an overview about how the actual CBSE exam would be.*

*for more details On CBSE Class 12 Commerce Maths Question Papers** ***check here Maths Syllabus**

*CBSE Class 12 Commerce Maths Question Papers*

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Sl No. | CBSE Class 12 Commerce Maths Question Papers | Download Link |

1. | CBSE Class 12 Commerce Maths Question Paper 01 | check here |

.2 | CBSE Class 12 Commerce Maths Question Paper 02 | check here |

3. | CBSE Class 12 Commerce Maths Question Paper 03
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4. | CBSE Class 12 Commerce Maths Question Paper 04
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5. | CBSE Class 12 Commerce Maths Question Paper 05
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6. | CBSE Class 12 Commerce Maths Question Paper 06
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7. | CBSE Class 12 Commerce Maths Question Paper 07
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8. | CBSE Class 12 Commerce Maths Question Paper 08
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9. | CBSE Class 12 Commerce Maths Question Paper 09
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10. | CBSE Class 12 Commerce Maths Question Paper 10
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11. | CBSE Class 12 Commerce Maths Question Paper 11
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12. | CBSE Class 12 Commerce Maths Question Paper 12
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