Algebra A.P., G.P., H.P.: Definitions of A. P. and G.P.; General term Arithmetic/Geometric series, A.M., G.M. and their relation; ; Summation of first n-terms of series ∑n, ∑n²,∑n3 ;Infinite G.P. series and its sum.
Permutation and combination: Permutation of n different things taken r at a time (r ≤ n), Permutation with repetitions (circular permutation excluded), Permutation of n things not all different, Combinations of n different things taken r at a time (r ≤ n), Basic properties, Combination of n things not all different, Problems involving both permutations and combinations.
Complex Numbers: Definition in terms of ordered pair of real numbers and properties of complex numbers, Triangle inequality; amplitude of complex numbers and its properties; Complex conjugate; Square root of complex numbers; De Moiré’s theorem (statement only) and its elementary applications, Cube roots of unity, Solution of quadratic equation in complex number system.
Binomial theorem (positive integral index): Statement of the theorem, middle term, equidistant terms, general term, properties of binomial coefficients.
Trigonometry: Trigonometric functions, formulae involving multiple and submultiple angles, addition and subtraction formulae, general solution of trigonometric equations, inverse trigonometric functions and their properties, Properties of triangles.
Co-ordinate geometry of three dimensions: Direction cosines and direction ratios, equation of a straight line, equation of a plane, distance between two points and section formula, distance of a point from a plane.
Sets, Relations and Mappings: Idea of sets, subsets, power set, complement, union, intersection and difference of sets, De Morgan’s Laws, Venn diagram, Inclusion/ Exclusion formula for two or three finite sets, Relation and its properties, Cartesian product of sets, Equivalence relation — definition and elementary examples, injective, subjective and bijective mappings, mappings, range and domain, composition of mappings, inverse of a mapping.
Integral calculus: Integration as a reverse process of differentiation, Integration by parts, indefinite integral of standard functions, Integration by substitution and partial fraction, Fundamental theorem of integral calculus and its applications, Definite integral as a limit of a sum with equal subdivisions, Properties of definite integrals.
Logarithms: Definition; General properties, Change of base.
Polynomial equation: nth degree equation has exactly n roots (statement only), Relations between roots and coefficients; Nature of roots; Formation of a quadratic equation, Quadratic Equations: Quadratic equations with real coefficients, sign and magnitude of the quadratic expression ax2 +bx+c (where a, b, c are rational numbers and a ≠ 0).
Application of Calculus: Tangents and normal, Determination of monotonicity, maxima and minima, conditions of tangency, Differential coefficient as a measure of rate, Geometric interpretation of definite integral as area, Motion in a straight line with constant acceleration, calculation of area bounded by elementary curves and Straight lines, Area of the region included between two elementary curves.
Principle of mathematical induction: Statement of the principle, sum of cubes of first n natural numbers, proof by induction for the sum of squares, divisibility properties like 22n — 1 is divisible by 3 (n ≥ 1), 7divides 3 2n+1+2n+2 (n ≥ 1).
Matrices: Concepts of m x n (m ≤ 3, n ≤ 3) real matrices, scalar multiplication and multiplication of matrices, operations of addition, Determinant of a square matrix, Transpose of a matrix, Properties of determinants (statement only), Nonsingular matrix, Inverse of a matrix, Minor, cofactor and adjoin of a matrix, Finding area of a triangle, Solutions of system of linear equations.
