Unit 1: Sets, Relations and Functions | Sets and their representations, intersection and complement of sets along with their algebraic properties, power sets. |
Unit 2: Complex Numbers and Quadratic Equations | Representation of complex numbers in the form of a + ib, argand diagram, algebra of complex numbers, square roots of complex numbers, quadratic equations, triangle inequality, nature of roots. |
Unit 3: Matrices and Determinants | Matrices, algebra of matrices, determinants, type of matrics, properties of determinants, evaluation of determinants. |
Unit 4: Permutations and Combinations | Fundamental principles of counting, permutation as arrangements, combinations as sections, the meaning of P and C, simple applications. |
Unit 5: Mathematical Inductions | Principle of mathematical induction and their simple applications. |
Unit 6: Binomial Theorem and its simple applications | Binomial theorem for positive integral index, general term of binomial, middle term of binomial, properties of binomial, simple applications of binomial. |
Unit 7: Sequence and Series | Arithmetic and geometric progressions, relation between A.M and G.M, Arithmetico-Geometric progression |
Unit 8: Limit, Continuity and Differentiability | Graphs of simple functions, real valued fractions, algebra of functions, polynomials, rational, trigonometric, logarithmic, differentiation of sum, difference, product,Rolle’s and Lagrange’s mean value theorems, differentiation of trigonometric, inverse trigometric, applications of derivation like change of quantities, monotonic increasing, maxima, tangents and normal. |
Unit 9: Integral Calculus | Fundamental integrals such as algebraic, trigonometric, exponential and logarithmic functions, integration using trigonometric identities, fundamental theorem of calculus, properties of definite integrals |
Unit 10: Differential Equations | Ordinary differential equations, its order and degree, formation of differential equations |
Unit 11: Co-ordinate Geometry | Cartesian system of rectangular coordinates in the plane, sections formula, distance formula, locus, coordinate geometry equations, translation of axes, slope of a line, parallel and perpendicular lines. |
Unit 12: Three-Dimensional Geometry | Coordinates of a point in space, the distance between two, directions ratio, section formula, direction cosines, angle between two intersecting lines, skew lines, coplanar lines. |
Unit 13: Vector Algebra | Vector and scalars, components of a vector in two dimensions and three dimensions, scalar and vector products. |
Unit 14: Statistics and Probability | Calculation of mean, median and mode of grouped and ungrouped data, variance, and mean deviation. Probability of an event, addition & multiplication theorems of probability, Baye’s theorem, probability distribution of random variate, binomial distribution |
Unit 15: Trigonometry | Trigonometrical identities and equations, inverse trigonometrical functions, trigonometrical functions & properties, heights and distance. |
Unit 16: Mathematical Reasoning | Statement logical operations, understanding of tautology, contradiction, converse and contrapositive. |
