For some students mathematics is the nightmare, and on the other hand , for some students mathematics is their favorite subject. So it is a very unpredictable subject for student but it is one of those subjects where you can surely score high if given the proper preparation pattern and time. To score high in mathematics , all you need to do is thorough study of syllabus and practice the problems as much as possible.
Over the past 3-4 years, CBSE has moved from giving the standard NCERT questions to questions that are application based . This has made the paper quit difficult to score if one expects only the NCERT type questions to come in the exam.
One Paper
Max Marks: 80
| No. | Units | Marks |
| I. | Relations and Functions | 08 |
| II. | Algebra | 10 |
| III. | Calculus | 35 |
| IV. | Vectors and Three – Dimensional Geometry | 14 |
| V. | Linear Programming | 05 |
| VI. | Probability | 08 |
| Total | 80 | |
| Internal Assessment | 20 |
Unit-I: Relations and Functions
- Relations and Functions
15 Periods
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one andonto functions, composite functions, inverse of a function. - 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
- 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). - Determinants
25 Periods
Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors 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
- Continuity and Differentiability
20 Periods
Continuity and differentiability, derivative of composite functions, chain rule, derivative 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. - 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). - 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. - 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). - 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. Solutions of linear differential equation of the type:
dydx+py=qdydx+py=q, where p and q are functions of x or constants.
dxdy+px=qdxdy+px=q, where p and q are functions of y or constants.
Unit-IV: Vectors and Three-Dimensional Geometry
- 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.
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- two lines,
- two planes,
- a line and a plane. Distance of a point from a plan
Unit-V: Linear Programming
- 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 or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
Unit-VI: Probability
- 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.Read More
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