The Central Board of Secondary Education (CBSE) is the apex board of education in India which is not only having a pan Indian jurisdiction but also has global presence with nearly 141 affiliated schools across 21 countries. CBSE grants affiliation to Schools up to higher secondary level and develops common curriculum keeping nationwide requirements in focus. The CBSE affiliation is considered as a prestigious recognition as it requires the schools to follow rigid quality standards.
CBSE conducts the Board examinations for Class 10 and Class 12 every year in the month of March. This year also CBSE is going to conduct the Board examination and the Datesheet has also been released officially for the students. There are lakhs of students across the country who are going to participate in the CBSE Board Examination. I know all the students are preparing hard for their exams specially for their Mathematics paper as it is the only exam in which the students can gain full marks.
In this article we are providing the pdf files of Mathematics sample papers. These questions will help the students in their exam preparation. They will have an idea about the questions that might come in the exam.
CBSE Board 2017 Maths Sample Papers
The Central Board of Secondary Education is going to conduct the Board Examination for class 12th. The exam is commencing from March 2017 and will finish on 22nd April 2017.
Exam preparation tips for Mathematics
Mathematics, one of the most scoring subjects is to be held on March 14. For all those nervous about the of Mathematics paper, here’s a list of tips and tricks that can help you for the examination.
- Plan well. Study different topics according to their difficulty levels;
- Make a list of all Maths formulae and keep it on your study table for repetitive revision;
- Self study (Do lots of practice to achieve proficiency in Maths);
- Try to solve CBSE practice papers and sample papers within three hours (time management is must);
- If finding difficulty in solving problems of a particular topic, give thorough revision to that specific topic and take help from your teacher;
- Sleep well on the night before the exam to keep the mind and body relaxed.
On the day of exam:
- Review all the formulae and important topics early in the morning;
- Be confident and keep a positive attitude
- In the first 15 minutes allotted as reading time, wisely select the appropriate question to be solved in which internal choices have been provided to avoid wastage of time later;
- Write neatly with proper margins (presentation matters too);
- Do not get stuck to a question for a long time, if unable to solve, leave space for it and move on to the next question;
- Even if the complete solution to a particular question is not known, try to write till the known steps;
- Leave at least 10 minutes for revision of answer sheets.
Syllabus for CBSE 12th Mathematics Exam
Chapter 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.
Chapter 2. Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
Chapter 3. 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).
Chapter 4. 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.
Chapter 5. 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.
Chapter 6. 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).
Chapter 7. 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 types given in the syllabus 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.
Chapter 8. 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).
Chapter 9. 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 given in the syllabus.
Chapter 10. 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.
Chapter 11. 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.
Chapter 12: 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).
Chapter 13. Probability
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.
Sample Papers for CBSE Clas 12th Mathematics
Sample papers help students a lot as they are essentially board certified question papers. Students can learn a lot about the type of questions asked and that helps beat stress. The other thing that sample papers help students with, according to experts, is time management. By attempting sample papers like actual board exam papers and giving themselves three hours, students can manage their time much better. Sample papers are a very important tool to understand the division of marks, type of questions asked and develop a familiarity with the examination patterns.
Below we are providing sample paper for mathematics. Students can download them and start their exam preparation.
Click the below link for downloading Mathematics Sample Papers
We wish all the students best of luck for Board exams. For any queries you can write us in the below provided box and keep visiting our site for more updates.