#### 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