Unit 1: Sets, Relations, and Functions 
 Sets and their representation.
 Union, intersection, and complement of sets and their algebraic properties.
 Powerset.
 Relation, types of relations, equivalence relations.
 Functions; oneone, into and onto functions, the composition of functions.

Unit 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.
 The relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots.

Unit 3: Matrices and Determinants 
 Matrices: Algebra of matrices, types of matrices, and matrices of order two and three.
 Determinants: Properties of determinants, evaluation of determinants, the 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.

Unit 4: Permutations and Combinations 
 The fundamental principle of counting.
 Permutation as an arrangement and combination as a selection.
 The meaning of P (n,r) and C (n,r), simple applications.

Unit 5: Mathematical Induction 
The principle of mathematical induction and its simple applications. 
Unit 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.

Unit 7: Sequence and Series 
 Arithmetic and geometric progressions, insertion of arithmetic, geometric means between two given numbers.
 The relation between A.M. and G.M sum up to n terms of special series: Sn, Sn2, Sn3.
 ArithmeticoGeometric progression.

Unit 8: Limit, Continuity and Differentiability 
 Realvalued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions.
 Graphs of simple functions.
 Limits, continuity, and differentiability.
 Differentiation of the sum, difference, product, and quotient of two functions.
 Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order up to two.
 Rolle’s and Lagrange’s mean value theorems.
 Applications of derivatives: Rate of change of quantities, monotonic increasing and decreasing functions, Maxima, and minima of functions of one variable, tangents, and normal.

Unit 9: Integral Calculus 
 Integral as an antiderivative.
 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.
 Evaluation of simple integrals:
 Fundamental theorem of calculus.
 Properties of definite integrals, evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

Unit 10: Differential Equations 
 Ordinary differential equations, their order, and degree.
 Formation of differential equations.
 The solution of differential equations by the method of separation of variables.
 The solution of a homogeneous and linear differential equation of the type:
dy/dx + P(x)y = Q(x)

Unit 11: Coordinate Geometry 
 Cartesian system of rectangular coordinates in a plane, distance formula, section formula, locus, and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
 Straight lines: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines.
 Distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of the centroid, orthocentre, and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.
 Circles, conic sections: Standard form of the equation of a circle, the general form of the equation of a circle, its radius and centre, 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 a circle, equation of the tangent.
 Sections of conics, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.

Unit 12: 3D Geometry 
 Coordinates of a point in space, the distance between two points.
 Section formula, direction ratios and direction cosines, the 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, the intersection of a line and a plane, coplanar lines.

Unit 13: Vector Algebra 
 Vectors and scalars, the addition of vectors, components of a vector in two dimensions and threedimensional space.
 Scalar products and vector products, and vector triple product.

Unit 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 theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials, and binomial distribution.

Unit 15: Trigonometry 
 Trigonometrical identities and equations.
 Trigonometrical functions, inverse trigonometrical functions, and their properties.
 Heights, and distance.

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