SETS,  RELATIONS AND FUNCTIONS

Sets  and  their  representation:  Union, intersection  and  complement  of  sets  and their  algebraic  properties;  Power  set; Relation,  Type  of  relations,  equivalence relations,  functions;  one-one,  into  and  onto functions,  the  composition  of  functions. 

UNIT  2:  COMPLEX NUMBERS AND QUADRATIC EQUATIONS

Complex  numbers  as  ordered  pairs  of reals,  Representation  of  complex  numbers in  the  form  a  +  ib  and  their  representation in  a  plane,  Argand  diagram,  algebra  of complex  number,  modulus  and  argument (or  amplitude)  of  a  complex  number, square  root  of  a  complex  number,  triangle inequality,  Quadratic  equations  in real  and complex  number  system  and  their solutions  Relations  between  roots  and  coefficient,  nature  of  roots,  the  formation  of quadratic equations with given roots. 

MATRICES AND DETERMINANTS

Matrices,  algebra  of  matrices,  type  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. 

MATHEMATICAL INDUCTIONS

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.

SEQUENCE AND SERIES

Arithmetic  and  Geometric  progressions, insertion  of  arithmetic,  geometric  means between  two  given  numbers,  Relation between  A.M  and  G.M  sum  up  to  n  terms of  special  series;  Sn,  Sn2,  Sn3. Arithmetico-Geometric progression.

PERMUTATIONS AND   COMBINATIONS

The  fundamental  principle  of  counting, permutation  as  an  arrangement  and combination  as  section,  Meaning  of  P  (n,r) and C (n,r),  simple applications.

LIMIT,  CONTINUITY  AND DIFFERENTIABILITY

Real  –  valued  functions,  algebra  of functions, polynomials, rational, trigonometric,  logarithmic  and  exponential functions,  inverse  function.  Graphs  of simple  functions.  Limits,  continuity  and differentiability.  Differentiation  of  the sum,  difference,  product  and  quotient  of two functions. trigonometric, Differentiation inverse of trigonometric,logarithmic,  exponential,  composite  and implicit  functions;  derivatives  of  order  up to  two,  Rolle’s  and  Lagrange's  Mean  value Theorems,  Applications  of  derivatives: Rate  of  change  of  quantities,  monotonicIncreasing  and  decreasing  functions, Maxima  and  minima  of  functions  of  one variable, tangents  and normal.

INTEGRAL  CALCULUS

Integral  as  an  anti-derivative,  Fundamental Integrals involving algebraic, trigonometric,  exponential  and  logarithmic functions.  Integrations  by  substitution,  by parts  and  by  partial  functions.  Integration using  trigonometric  identities. Evaluation of  simple integrals of  the  type

Integral  as  limit  of  a  sum.  The  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,  their  order and  degree,  the  formation  of  differential equations, solution  of  differential  equation by  the  method  of  separation  of  variables, solution  of  a  homogeneous  and  linear differential  equation of  the  type

CO-ORDINATE  GEOMETRY

Cartesian  system  of  rectangular  coordinates  in  a  plane,  distance  formula, sections  formula,  locus  and  its  equation, translation  of  axes,  the  slope  of  a  line, parallel  and  perpendicular  lines, intercepts of  a  line on  the  co-ordinate  axis.   Straight  line Various  forms  of  equations  of  a  line, intersection  of  lines,  angles  between  two lines,  conditions  for  concurrence  of  three lines,  the  distance  of  a  point  form  a  line, equations  of  internal  and  external  by sectors  of  angles  between  two  lines  coordinate  of  the  centroid,  orthocentre  and circumcentre  of  a  triangle,  equation  of  the family  of  lines  passing  through  the  point  of intersection  of  two lines. Circle, conic  sections A  standard  form  of  equations  of  a  circle, the  general  form  of  the  equation  of  a  circle, its  radius  and  central,  equation  of  a  circle when  the  endpoints  of  a  diameter  are given,  points  of  intersection  of  a  line  and  a circle  with  the  centre  at  the  origin  and condition  for  a  line  to  be  tangent  to  a  circle, equation  of  the  tangent,  sections of  conics, equations  of  conic  sections    (parabola, ellipse  and  hyperbola)  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,  the distance  between  two  points,  section formula,  directions  ratios  and  direction cosines,  the  angle  between  two  intersecting lines.  Skew  lines,  the  shortest  distance between  them  and  its  equation.  Equations of  a  line  and  a  plane  in  different  forms,  the intersection  of  a line  and a  plane,  coplanar lines.

VECTOR ALGEBRA

Vectors  and  scalars,  the  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  discretion;  calculation  of mean,  median,  mode  of  grouped  and ungrouped  data  calculation  of  standard deviation,  variance  and  mean  deviation  for grouped and  ungrouped  data. Probability:  Probability  of  an  event, addition  and  multiplication  theorems  of probability,  Baye's  theorem,  probability distribution  of  a  random  variate,  Bernoulli trials and  binomial  distribution.

TRIGONOMETRY

Trigonometrical  identities  and  equations, trigonometrical functions, trigonometrical functions properties, heights and distance. inverse and their properties, heights and distance.

MATHEMATICAL REASONING 

Statement  logical  operations  and,  or, implies,  implied  by,  if  and  only  if, understanding  of  tautology,  contradiction, converse  and  contrapositive.