Unit |
Unit Topic |
Topic wise Syllabus |

1 | Sets, Relations And Functions | Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations,functions;. One-one, into and onto functions, composition of functions |

2 | Complex Numbers and Quadratic Equations |
Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots. |

3 | Matrices And Determinants | Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices. |

4 | Permutations And Combinations |
Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications |

5 | Mathematical Induction | Principle of Mathematical Induction and its simple applications |

6 | Binomial Theorem And Its Simple Applications |
Binomial theorem for a positive integral index, general term and middle term,properties of Binomial coefficients and simple applications |

7 | Sequences And Series | Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series: S n, S n2, Sn3. Arithmetico – Geometric progression |

8 | Limit, Continuity And Differentiability |
Real valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of change of |

9 | Integral Calculus | Integral as an anti derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Integral as limit of a sum. Fundamental Theorem of Calculus. |

10 | Differential Equations | Ordinary differential equations, their 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 of the type |

11 | Coordinate Geometry | Cartesian system of rectangular coordinates 10 in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three orthocentre and circumcentre of a triangle, equation of family
Standard form of equation of a circle, general form of the |

12 | Three Dimensional Geometry | Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines |

13 | Vector Algebra | Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product. |

14 | Statistics And Probability | Measures of Dispersion: Calculation of mean, median, 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 |

15 | Trigonometry | Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances |

16 | Mathematical Reasoning | Statements, logical operations and, or, implies, implied by, if and only if. Understanding of tautology, contradiction, converse and contrapositive |