Unit 1: Sets, Relations & Functions | Sets, Relations, Functions | Sets and their representations, Cartesian product of sets, union, intersection and their algebraic properties, relations, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings. |
Unit 2: Complex Numbers & Quadratic Equations | Complex Numbers, Quadratic Equations | Equations Complex numbers in the form a+ib and their representation in a plane. Quadratic equation in real and complex number systems and their solutions. Algebraic properties of complex numbers, Relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots; symmetric functions of roots, equations reducible to quadratic equations. |
Unit 3: Matrices, Determinants & Applications | Matrices, Determinants | Determinants and matrices of order two and three, minors, cofactors and applications of determinants in finding the area of a triangle, equality, types zero and identity matrix, transpose, symmetric and skew Symmetric. Evaluation of determinants. Addition and multiplication of matrices, simple properties, adjoint and inverse of matrix, solution of simultaneous linear equations using determinants and matrices using inverses, Consistency of system of linear equations by rank method. |
Unit 4: Combinatorics | Permutations, Combinations | Fundamental principle of counting, permutation as an arrangement without repetitions and constraint repetitions, no circular permutations. Combination as selection, problems in P(n,r) and C(n,r), factorial, simple applications |
Unit 5: Algebra | Theory of Equations | The relation between the roots and coefficients in an equation. Solving the equations when two or more roots of it are connected by a certain relation. Equation with real coefficients, occurrence of complex roots in conjugate pairs and its consequences. Transformation equations- Reciprocal Equations. |
Unit 6: Differential Calculus & Applications | Polynomials and Differentiation | Polynomials, rational, trigonometric, logarithmic and exponential functions. Inverse functions. Graphs of simple functions. Limits, continuity, differentiation of the sum, difference, product and quotient of two functions, differentiation of trigonometric, inverse Trigonometric, logarithmic, exponential, composite and implicit functions, up to second order derivatives. |
| Applications of Differential Calculus | Rate of change of quantities, monotonic increasing and decreasing functions, maxima and minima of functions of one variable, tangents and normal, Rolle’s and Lagrange’s mean value theorems. Ordinary differential equations, order and degree. Formation of differential equations, solution of differential equations by the method of separation of variables. Solution of homogeneous and linear differential equations and those of the type dy/dx +p(x)y=q(x). |
Unit 7: Integral Calculus & Its Applications | Integration, Definite Integrals | Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, integration using trigonometric identities, properties of definite integrals. Evaluation of definite integrals excluding application of definite integrals |
Unit 8: Analytical Geometry | Straight Lines in Two Dimensions | Straight line- Normal form– Illustrations. Straight line– Symmetric form. Straight line- Reduction into various forms. Intersection of two Straight Lines. Slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes. Family of straight lines- Concurrent lines. Condition for Concurrent lines. Cartesian system of rectangular coordinates in plane, distance formula, area of a triangle and condition for the collinearity of three points and section formula, Concurrent lines– properties Related to a triangle. Centroid and incentre of a triangle, locus and its equation. |
| Circles in Two Dimensions | Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle in the parametric form, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to the circle. |
| Conic Sections in Two Dimensions: | Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard form. Problems using their geometrical properties |
Unit 9: Vector Algebra | Vectors, Scalars, Geometry | Vectors and scalars, addition of vectors, Direction cosines and direction ratios of a vector. Components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar and vector triple product. Application of vectors to plane geometry |
Unit 10: Statistics & Probability | Central Tendency, Probability Distribution | Measures of Central Tendency and Dispersion: Calculation of mean, median and mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data. Probability: Probability of an event, addition and multiplication theorems of probability and thei |
Unit 11: Trigonometry | Trigonometric Ratios, Angles | Trigonometry ratios, compound angles, solution of triangles, Trigonometric identities and equations-Inverse trigonometric functions definition range and domain Properties of triangles, including, incentre, circumcenter and solution orthocenter, Problems distances. of related to triangles, Heights and distances |
