UNIT –I : RELATIONS AND FUNCTIONS
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.
2. Inverse Trigonometric Functions.
Definition range, domain, principal value branches, Graphs of Triangle & inverse trigonometric functions. Elementary properties of inverse trigonometric functions. Periodicity of function and fundamental period.
UNIT – II : ALGEBRA
1. Matrices :
Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix. Symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication Non-commutatively 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 :
Determinant of a square matrix (up to 3 x 3 matrices) properties of determinations, minors, of actors 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. Limits , Continuity and Differentiability :
Revision of algebraic limits, exponential limits, logarithmic limits, limits of trigonometric and inverse trigonometric functions. Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concept of
exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivatives of ax, ex, log x , apx+q, eax+b, log ( ax + b ) using first principle. Derivative of functions expressed in parametric forms. Second order derivatives Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.
2. Applications of Derivatives :
Applications of derivatives rate of change, increasing/decreasing functions, tangents & normals, 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 :
Integration as inverse process of differentiation. Integration of a variety of functions by substitution by partial fractions and by parts, only simple integrals of the type to be evaluated. 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 :
Applications in finding the area under simple curves, especially lines, area of circles/parabolas/ellipses (in standard form only), are between the two above said curves (the region should be clearly identifiable).
5. 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 methods of separation of variables, homogeneous differential
equations of first order and first degree. Solutions of linear differential equation of the
type.
UNIT – IV : VECTORS AND THREE–DIMENSIONAL
GEOMETRY
1. Vectors :
Vectors and scalars, magnitude and direction of a vector. Direction cosines /rations of vectors. 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 ration. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors, scalar triple product , volume of a parallelepiped, vector triple product and its properties.
2. 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.
UNITS – V : PROBABILTY
1. Probability :
Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trial and Binominal distribution
Recommended Books for GOA CET 2013 Mathematics Preparation :
Prescribed textbooks (Published by Goa Board of Secondary and Higher Secondary
Education, Porvorim)
1. Mathematics Part-I Textbook for Class XIIth
2. Mathematics Part-II Textbook for Class XIIth
For More Updates on : Goa Common Entrance Test GCET 2013 Admission
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