Mathematics

Ellipse and Hyperbola : Reduction to standard form of general equation of second degree when xy term is absent. Conjugate hyperbola. Simple properties. Parametric equations. Location of a point with respect to a conic.

Straight line : 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.

Co-ordinate Geometry

Trigonometry

Trigonometric ratios, compound angles, multiple and submultiple angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions. Co-ordinate geometry of two dimensions

Probability : Classical definition, addition rule, conditional probability and Bayes’ theorem, independence, multiplication rule.

Sets, Relations and Mappings : Idea of sets, subsets, power set, complement, union, intersection and difference of sets, Venn diagram, De Morgan’s Laws, Inclusion / Exclusion formula for two or three finite sets, Cartesian product of sets.

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.

Infinite series : Binomial theorem for negative and fractional index. Infinite G.P. series, Exponential and Logarithmic series with range of validity (statement only), simple applications.

Binomial theorem (positive integral index) :Statement of the theorem, general term, middle term, equidistant terms, properties of binomial co-efficients.

Principle of Mathematical Induction : Statement of the principle. Proof by induction for the sum of squares, sum of cubes of first n natural numbers, divisibility properties like 2²ⁿ–1 is divisible by 3 (n≥1), 7 divides 3²ⁿ⁺¹+2ⁿ⁺²(n≥1).