Mathematics 

1)  Algebra 

  • Definitions of A. P. and G.P.;  
  • General term  
  • Summation of first n-terms of series ∑n, ∑n², ∑n3  
  • Arithmetic/Geometric series, A.M., G.M. and their relation  
  • Infinite G.P. series and its sum 

    2) Logarithms 
     
  • Definition 
  • General properties  
  • Change of base 

       3)   Matrices 

  • Concepts of m x n (m ≤ 3, n ≤ 3) real matrices 
  • Operations of addition, scalar multiplication & multiplication of matrices  
  • Transpose of a matrix  
  • Determinant of a square matrix 
  • Properties of determinants (statement only)  
  • Minor, cofactor & adjoint of a matrix 
  • Non-singular matrix  
  • Inverse of a matrix 
  • Finding area of a triangle 
  • Solutions of system of linear equations. (Not more than 3 variables) 

       3)   Trigonometry 

  • Trigonometric functions, addition and subtraction formulae 
  • Formulae involving multiple and sub-multiple angles  
  • General solution of trigonometric equations.  
  • Properties of triangles, inverse trigonometric functions and their properties 

      4)    Coordinate geometry 

  • Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane  
  • Polar coordinates, transformation from Cartesian to polar coordinates and vice versa  
  • Parallel transformation of axes, concept of locus, elementary locus problems  
  • Slope of a line  
  • Equation of lines in different forms, angle between two lines 
  • Condition of perpendicularity and parallelism of two lines 
  • Distance of a point from a line 
  • Distance between two parallel lines  
  • Lines through the point of intersection of two lines  
  • Equation of a circle with a given center and radius  
  • Condition that a general equation of second degree in x, y may represent a circle  
  • Equation of a circle in terms of endpoints of a diameter 
  • Equation of tangent, normal and chord  
  • Parametric equation of a circle 
  • Intersection of a line with a circle  
  • Equation of common chord of two intersecting circles 

        5)   3-D Co-ordinate geometry 

  • Direction cosines and direction ratios 
  • Distance between two points and section formula, equation of a straight line, equation of a plane, distance of a point from a plane. 

       6)   Theory of Calculus 

  • Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivative of implicit functions and functions defined parametrically.  
  • Integration as a reverse process of differentiation, indefinite integral of standard functions. – Integration by parts.  
  • Integration by substitution and partial fraction  
  • Definite integral as a limit of a sum with equal sub-divisions 
  • Fundamental theorem of integral calculus and its applications 
  • Properties of definite integrals 
  • Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations 

        7)   Application of Calculus 

  • Tangents and normals, conditions of tangency.  
  • Determination of monotonicity, maxima and minima.  
  • Differential coefficient as a measure of rate 
  • Motion in a straight line with constant acceleration  
  • Geometric interpretation of definite integral as area, calculation of area bounded by elementary curves and Straight lines.  
  • Area of the region included between two elementary curves 

        8)   Permutation and combination 

  • Permutation of n different things taken r at a time (r ≤ n) 
  • Permutation of n things not all different 
  • Permutation with repetitions (circular permutation excluded) 
  • Combinations of n different things taken r at a time (r ≤ n) 
  • Combination of n things not all different  
  • Basic properties  
  • Problems involving both permutations and combinations 

       9)    Statistics and Probability 

  • Measure of dispersion, mean, variance and standard deviation, frequency distribution  
  • Addition and multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, repeated independent trails and Binomial distribution 

     B)  Drawing Test 

  • Ability to sketch a given object proportionately and rendering the same in visually appealing manner 
  • Visualizing and drawing the effects of light on the object and shadows cast on surroundings 
  • The sense of perspective drawing 
  • Geometric composition, shape, building forms and elements, aesthetics, color texture, harmony and contrast 
  • Combining and composing given three-dimensional elements to form a building or structural form 
  • Creating interesting two-dimensional compositions using given shapes and forms 
  • Creating visual harmony using colours in given composition 
  • Understanding of scale and proportions of objects 
  • Drawing from memory through pencil sketch on themes from day to day experiences