**Algebra**

- Definitions of A. P. and G.P.
- General term
- Summation of first n-terms of series ∑n, ∑n²,∑n 3
- Arithmetic/Geometric series, A.M., G.M. and their relation
- Infinite G.P. series and its sum

**Logarithms**

- Definition
- General properties
- Change of base

**Matrices**

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

**Trignometry**

- Trigonometric functions, addition and subtraction formulae, formulae involving multiple and submultiple angles, general solution of trigonometric equations.
- Properties of triangles, inverse trigonometric functions and their properties

**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

**Dimensional 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
- 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 subdivisions. 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

**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

**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

**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

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