CBSE: All India Engineering
Entrance Examinations (AIEEE)
Syllabus: Mathematics - 2012
Unit 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.
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. Relation
between roots and co-efficients, nature of roots, formation of quadratic
equations with given roots.
Unit 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.
Unit 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.
Unit 5 : Mathematical Induction:
Principle of Mathematical Induction and its simple applications.
Unit 6 : Binomial Theorem and It's Simple Applications:
Binomial theorem for a positive integral index, general term and middle term,
properties of Binomial coefficients and simple applications.
Unit 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.
Unit 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 sum, difference, product and quotient of two functions.
Differentiation of trigonometric, inverse trigonometric, logarithmic,
exponential, composite and implicit functions; derivatives of order upto 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 normals.
Unit 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. Evaluation of simple integrals of the type
Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of
definite integrals. Evaluation of definite integrals, determining areas of the
regions bounded by simple curves in standard form.