**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