CHAPTER I: RELATIONS AND FUNCTIONS
-
Inverse of a function, Binary operations
CHAPTER II: INVERSE TRIGONOMETRICAL FUNCTIONS
-
Definition, range, domain, principal value branches
-
Graphs of inverse trigonometric functions
CHAPTER VI: APPLICATIONS OF DERIVATIVE
-
Geometrical application-tangent and normal at a point
-
Mean value theorem and their geometrical interpretation (without proof)
-
Derivative as a rate measure-introduction
-
Approximation (without proof)
-
Maxima and minimaintroduction of extrema and extreme values
-
First derivative test, second derivative test
CHAPTER VIII: APPLICATIONS OF DEFINITE INTEGRAL
-
Area under the curve : area bounded by curve and axis (simple problems), area bounded by two curves
-
Volume of solid of revolution-volume of solid obtained by revolving the area under the curve about the axis (simple problems)
CHAPTER IX: DIFFERENTIAL EQUATION
-
Definition-differential equation, order, degree, general solution, particular solution of differential equation, formation of differential equation-formation of differential equation by eliminating arbitary constants (at most two constants)
-
Solution of first order and first degree differential equation-variable separable method, homogeneous differential equation (equation reducible to homogeneous form are not expected)
-
Linear differential equation
-
Applications : population growth, bacterial colony growth, surface area, Newton’s laws of cooling, radioactive decay
CHAPTER X: VECTORS ALGEBRA
-
Vectors and scalars, magnitude and direction of a vector
-
Direction cosines/ratios of vectors
-
Types of vectors (equal, unit, zero, parallel and collinear vectors)
-
Position vector of a point
-
multiplication of a vector by a Scalar
-
position vector of a point dividing a line segment in a given ratio
-
Scalar (dot) product of vectors, projection of a vector on a line
-
Vector (cross) product of vectors
CHAPTER XI: THREE-DIMENSIONAL GEOMETRY
-
Direction cosines/ratios of a line joining two points
-
Cartesian 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 XII: LINEAR PROGRAMMING
-
Definition of related terminology such as constraints
-
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
-
Feasible and infeasible solutions
-
Optimal feasible solutions (up to three non-trivial constraints)
CHAPTER XIII: PROBABILITY
-
Multiplication theorem on probability Conditional probability
-
Repeated independent (Bernoulli) trials and Binomial distribution
BETA
