UNIT 1 : SETS, RELATIONS AND FUNCTIONS:
Sets and their representation; Union, intersection and complement of sets and theiralgebraic 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 theform a+ib and their representation in a plane, Argand diagram, algebra of complexnumbers, modulus and argument (or amplitude) of a complex number, square root of acomplex number, triangle inequality, Quadratic equations in real and complex numbersystem 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. Propertiesof determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation ofinverse of a square matrix using determinants and elementary transformations, Test of consistency andsolution 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 asselection, 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 ITS SIMPLE APPLICATIONS:
Binomial theorem for a positive integral index, general term and middle term, propertiesof Binomial coefficients and simple applications.

UNIT 7 : SEQUENCES AND SERIES:
Arithmetic and Geometric progressions, insertion of arithmetic, geometric meansbetween two given numbers. Relation between A.M. and G.M. Sum upto n terms ofspecial 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 anddifferentiability. 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 typeIntegral as limit of a sum. Fundamental Theorem of Calculus. Properties of definiteintegrals. Evaluation of definite integrals, determining areas of the regions bounded bysimple curves in standard form.

UNIT 10: DIFFERENTIAL EQUATIONS:
Ordinary differential equations, their order and degree. Formation of differentialequations. 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

UNIT 11: CO-ORDINATE GEOMETRY:
Cartesian system of rectangular co-ordinates 10 in a plane, distance formula, sectionformula, locus and its equation, translation of axes, slope of a line, parallel andperpendicular lines, intercepts of a line on the coordinate axes.

Straight lines
Various forms of equations of a line, intersection of lines, angles between twolines, 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 ofcentroid, orthocentre and circumcentre of a triangle, equation of family of lines passingthrough the point of intersection of two lines.

Circles, conic sections
Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equationof a circle when the end points of a diameter are given, points of intersection of a line and a circle with thecentre at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections ofcones, 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: THREE DIMENSIONAL GEOMETRY:
Coordinates of a point in space, distance between two points, section formula, directionratios and direction cosines, angle between two intersecting lines. Skew lines, theshortest distance between them and its equation. Equations of a line and a plane indifferent forms, intersection of a line and a plane, coplanar lines.

UNIT 13: VECTOR ALGEBRA:
Vectors and scalars, addition of vectors, components of a vector in two dimensions andthree dimensional space, scalar and vector products, scalar and vector triple product.

UNIT 14: STATISTICS AND PROBABILITY:
Measures of Dispersion: Calculation of mean, median, mode of grouped and ungroupeddata calculation of standard deviation, variance and mean deviation for grouped andungrouped data.Probability: Probability of an event, addition and multiplication theorems of probability,Baye’s theorem, probability distribution of a random variate, Bernoulli trials andBinomial distribution.

UNIT 15: TRIGONOMETRY:
Trigonometrical identities and equations. Trigonometrical functions. Inversetrigonometrical functions and their properties. Heights and Distances.

UNIT 16: MATHEMATICAL REASONING:
Statements, logical operations and, or, implies, implied by, if and only if. Understandingof tautology, contradiction, converse and contrapositive.


Physics Syllabus for AIEEE 2012
Chemistry Syllabus for AIEEE 2012
Syllabus for Aptitude Test for B.Arch/B.Planning AIEEE 2012 

AIEEE 2012: Dates, Eligibility Criteria, Exam Pattern
How To Apply for AIEEE 2012

Tagged in MAT MAT test pattern MAT exam AIMA MAT exam structure

Like us on :