Krishna’s Solved Papers Mathematics 10 Years for XII Board CBSE Exam | Code 2101 | 1st Edition | 390 + Pages

Unit I: Relations and Functions

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

Unit II: Algebra

Chapter 1: Matrices

• Operation on matrices: Addition and multiplication and multiplication with a scalar

• Simple properties of addition, multiplication and scalar multiplication

• Concept of elementary row and column operations

• Invertible matrices and proof of the uniqueness of inverse, if it exists;

Chapter 2: Determinants

• Ad joint and inverse of a square matrix

Unit III: Calculus

Chapter 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

geometric interpretation

Chapter 2: Applications of Derivatives

• Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normal, use of derivatives in approximation, maxima and minima

• Simple problems Chapter 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

 Basic properties of definite integrals and evaluation of definite integrals

Chapter 4: Applications of the Integrals

 Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses

 Area between any of the two above said curves (the region should be clearly identifiable)

Chapter 5: Differential Equations

 Definition, order and degree, general and particular solutions of a differential equation

 Formation of differential equation whose general solution is given

 Solutions of linear differential equation of the type:

Unit IV: Vectors and Three-Dimensional Geometry

Chapter 1: Vectors

 Vectors and scalars, magnitude and direction of a vector

 Direction cosines and direction ratios of a vector

Chapter 2: Three – dimensional Geometry

 Direction cosines and direction ratios of a line joining two points

 Cartesian and vector equation of a plane

 Angle between:

 Two lines

 Two planes

 A line and a plane

 Distance of a point from a plane

Unit V: Linear Programming

Chapter 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

• Feasible and infeasible regions

• Feasible and infeasible solutions

• Optimal feasible solutions

Unit VI: Probability

Chapter 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