Mathematics

Sets, Relations and Functions

Sets and their represention

Union

Intersection and complement of sets and their algebraic properties

Power set

Relation

Types of relations

Equivalence relations

Functions

One-one, into and onto functions

Composition of functions

Complex number and Quadratic Equations

Complex numbers as ordered pairs or reals

Representation of complex numbers in the form a+ib and their representation in a plane

Argand diagram

Algebra of complex numbers

Modulus and argument of a complex number

Square root of a complex number

Triangle inequality

Quadratic equation in real and complex number system and their solutions

Relation between roots and co-efficients

Nature of roots

Formation of quadratic equations with given roots

Matrices and Determinants

Matrices

Algebra of matrices

Types of matrices

Determinants and matrices of order two and three

Properties of determinants

Evaluation of determinants

Area of triangles using determinants

Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations

Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices

Permutations and Combinations

Fundamental principle of counting

Permutation as an arrangement and combination as selection

Meaning of P (n,r) and C (n,r). simple applications

Mathematical Induction

Principle of Mathematical Induction and its simple applications.

Binomial theorem and its simple applications

Binomial theorem for a positive integral index

General term and middle term

Properties of Binomial coefficients and simple applications

Sequences and Series

Arithmetic and Geometric progressions

Insertion of arithmetic, geometric means berween two given numbers

Relation between A.M. and G.M. Sum upto n terms of special series Sn, Sn2, Sn3

Arithmetico-Geometric progression

Limit, Continuity and Differentiability

Real

Valued functions

Algebra of functions

Polynomial functions

Rational Functions

Trigonometric Functions

Logarithmic and expotentials functions

Inverse functions

Graphs of simple functions

Limits, continuity and differentiability

Differentiation or the sum and difference

Product and quotient of two functions

Difftrentiation of trigonometric

Inverse trigonometric

Logarithmic exponential

Composite and implicit functions

Derivatives of order upto two

Rolle's and Lagrange's Mean value Theorems

Applications of derivatives

Rate of change of quantities

Monotonic - increasing and decreasing functions

Maxima and minima of functions of one variable

Tangents and normals

Integrals Calculus

Integral as an anti -derivative

Fundamental integrals involving algebraic, trigonometric , Exponential and logarithmic functions

Integration by substitution, by parts and by partial fractions

Integration using trigonometric identities

Integral as limit or a sum

Fundamental Theorem of Calculus

Properties of definite integrals

Evaluation of definite integrals

determining areas of the regions bounded by simple curves in standard form

Differential Equations

Ordinary differential equations and their order and degree

Formation of differential equations

Solution of differential equations by the method of seperations of variables

Solution of homogeneous and linear differential equations

Co-ordinate Geometry

Cartesian system of rectangular co-ordinates 10 in a plane

Distance formula

Section formula

Locus and its equation

Translation of axes

Slope of a line

Parallel and perpendicular lines

Intercepts of a line on the coordinate axes

Various forms of equations of a straight line

Intersection of lines

Angles between two lines

Conditions for concurmence of three lines

Distance of a point from a line

Equations of internal and external bisectors of angles between two lines

Coordinates of centroid

Orthocentre and circumcentre or a triangle

Equation of family of lines passing through the point of intersection of two lines

Standard form of equation of a circle

General form of the equation or a circle, its radius and centre

Equation of a circle when the end points of a diameter are given

Points of intersection of a line and a circle with the centre a the origin and condirion for a line to be tangent to a circle

Equation of the tangent

Sections of cones

Equation of Conic Sections in standard forms

Condition for y = mx + c to be a tangent and point (s) of tangency

Three-Dimensional Geometry

Coordinates of a point in space

Distance between two points

Section formula

Direction ratios and direction cosines

Angle between two intersecting lines

Skew lines and the shortest distance bctween them and its equation

Equations of a line and a plane in different forms

Intersection of a line and a plane

Coplanar lines

Vector Algebra

Vectors and scalars

Addition of vectors

Components of a vector in two dimensions and three dimensional space

Scalar and vector products

Scalar and vector triple product

Statistics and Probability

Measures of Dispersion

Calculation of mean and median

Mode of grouped and ungrouped data calculation of standard deviation

Variance and mean deviation for grouped and ungrouped data

Probability of an event

Addition and multiplication theorems or probability

Baye's theorem

Probability distribution of a random variate

Bermoulli trials and Binomial distribution

Trigonometry

Trigonometrical identities and equations

Trigonometrical functions

Inverse trigonometrical functions and their properties

Heights and Distances

Mathematical Reasoning

Statements

Logical operations and, or, implies, implied by, if and only if

Understanding ot tautology

Contradiction

Converse and contrapositive