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# AIEEE 2012 Mathematics Syllabus

• ## Sets, Relations And Functions

Topics: Types of relations, equivalence relations, function, one-one, into and onto function, composition of functions, Sets and their representation, Union, intersection and complement of sets and their algebraic properties, Power set, Relation

• ## Complex Numbers And Quadratic Equations

 Topics: Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots, Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, 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 Laws & Theorems: Argand diagram
• ## Matrices And Determinants

 Topics: 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, 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.
• ## Permutations And Combinations

 Topics: Permutation as an arrangement and combination as selection, Meaning of P (n, r) and C (n, r), simple applications.  Laws & theorems: Fundamental principle of counting
• ## Mathematical Induction

 Laws & theorems: Principle of Mathematical Induction and its simple applications.
• ## Binomial Theorem And Its Simple Applications

 Topics: Properties of Binomial coefficients and simple applications.  Laws & Theorems: Binomial theorem for a positive integral index, general term and middle term
• ## Sequences And Series

 Topics: Relation between A.M. and G.M. Sum up to n terms of special series: Sn, Sn2, Sn3. Arithmetico - Geometric progression, Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers.
• ## Limit, Continuity And Differentiability

 Topics: 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. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals. Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Laws & Theorems: Rolle’s and Lagrange’s Mean Value Theorems.
• ## Integral Calculus

 Topics: Integral as limit of a sum. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Evaluation of simple integrals of the type:   Integral as an anti - derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions Laws & Theorems: Fundamental Theorem of Calculus
• ## Differential Equations

 Topics: Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type: dy -- + p (x) y = q (x) dx Ordinary differential equations, their order and degree. Formation of differential equations.
• ## Co-Ordinate Geometry

 Topics: Sections of cones, 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. Circles, conic sections Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points 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. translation of axes, 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 centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines. Laws & Theorems: Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation
• ## Three Dimensional Geometry

 Topics: Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines, Skew lines, the shortest distance between them and its equation, Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines
• ## Vector Algebra

 Topics: scalar and vector products, scalar and vector triple product, Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space
• ## Statistics And Probability

 Topics: Probability of an event, addition and multiplication theorems of probability, probability distribution of a random variate, 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. Laws & Theorems: Baye’s theorem, Bernoulli trials and Binomial distribution
• ## Trigonometry

 Topics: Trigonometrical functions. Inverse Trigonometrical functions and their properties. Trigonometrical identities and equations. Heights and Distances.
• ## Mathematical Reasoning

 Topics: Understanding of tautology, contradiction, converse and contra positive, Statements, logical operations and, or, implies, implied by, if and only if.