BITSAT 2015 Mathematics Syllabus:
Complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, roots of complex numbers, geometric interpretations; Fundamental theorem of algebra.
Theory of Quadratic equations; quadratic equation in real and complex number systems and their solutions; relations between roots and coefficients, nature of roots, equations reducible to quadratic equations.
Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means; arithmetic-geometric series, sum of finite arithmetic and geometric progressions; infinite geometric series; sums of squares and cubes of the first n natural numbers
Logarithms and their properties
Permutations and combinations; Permutations as an arrangement and combination as selection, simple application
Binomial theorem for a positive integral index, properties of binomial coefficients; Pascal’s triangle
Matrices and determinants of order two or three, properties and evaluation of determinants; addition and multiplication of matrices, adjoint and inverse of matrices, Solutions of simultaneous linear equations in two or three variables, elementary row and column operations of matrices.
Sets, Relations and Functions; Algebra of set applications, equivalence relations; mappings, one-one into and onto mappings, composition of mappings, binary operation, inverse of function, functions of real variable like polynomial, modulus, signum and greatest integer.
Linear Inequalities, solution of linear inequalities in one and two variables
Measurement of angles in radians and degrees, positive and negative angles, trigonometric ratios, functions and identities
Solution of trigonometric equations
Properties of triangles and solutions of triangles
Inverse trigonometric functions
Heights and distances
(c)Two-dimensional Coordinate Geometry:
Cartesian coordinates, distance between 2 points, section formulae, shift of origin
Straight lines and pair of straight lines: Equation of straight lines in various forms, angle between two lines, distance of a point from a line, lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrent lines.
Circles and family of circles: Equation of circle in various form, equation of tangent, normal & chords, parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of circle through point of intersection of two circles; conditions of two intersecting circle to be orthogonal
Conic sections: parabola; ellipse and hyperbola their eccentricity, directrices & foci, parametric forms, equations of tangent & normal conditions for y=mx+c to be a tangent and point of tangency.
(d)Three dimensional Coordinate Geometry:
Co-ordinate axes and co-ordinate planes, distance between two points, section formula, direction cosines and direction ratios, equation of a straight line in space and skew lines.
Angle between two lines whose direction ratio are given, shortest distance between two lines.
Equation of plane, distance of a point from a plane, condition for coplanarity of three lines, angles between two planes, angle between a line and a plane.
Domain and range of a real valued function, Limits and Continuity of the sum, difference, product and quotient of two functions, Differentiability.
Derivative of different types of functions (polynomial, rational, trigonometric, inverse trigonometric, exponential, logarithmic, implicit functions), derivative of the sum, difference product and quotient of two functions, chain rule
Geometric interpretation of the derivative, tangents and Normals
Increasing and decreasing functions; Maxima and minima of a function
Rolle’s theorem, mean value Theorem and Intermediate Value Theorem
Integration as the inverse process of differentiation , indefinite integrals of standard functions.
Methods of integration: Integration by substitution, Integration by parts, integration by partial fractions; and integration by trigonometric identities
Definite integrals and their properties; Fundamental Theorem of Integral Calculus, applications in finding areas under simple curves.
Applications of definite integrals to the determination of areas of regions bounded by simple curves.
(g)Ordinary Differential Equations:
Order and degree of a differential equation, formulation of a differential equation whole general solution is given, variable separable method.
Solution of homogeneous differential equation of the first order and first degree.
Linear first order differential equations.
Various terminology in probability, axiomatic and other approaches of probability, addition and multiplication rules of probability.
Conditional probability, total probability and Baye’s theorem
Discrete random variables and distributions with mean and variance
Measures of dispersion
Measures of skewness and Central Tendency, Analysis of frequency distributions with equal means but different variances,
Various terminology and formulation of linear programming
Solution of linear programming using graphical method, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (upto three nonitrivial constraints)