AIEEE Syllabus of Mathematics

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AIEEE Maths Syllabus

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 ITS 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: Sn, Sn2, 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.

UNIT 10: Differential Equations:

Ordinary differential equations, their order and degree. Formation of differential equations. 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 in a plane, distance formula, section formula, locus and its equation, 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.

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. 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.

UNIT 12: Three Dimensional Geometry:

Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, 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, 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 and three 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 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 Distances.

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

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Entrance Exams

ACDS 2013 | AFMC 2013 | AIBE 2013 | AICET 2013 | AIEEA 2013 | AIEEE 2013 | AIIMS 2013 | AIMS 2013 | AIPGMEE 2013 | AIPMT 2013 | AIJS 2013 | AIOAT 2013 | AMRITA 2013 | AMU 2013 | APTET 2013 | ARCHITECTURE 2013 | ARMPMC UP 2013 | ASSAM JAT 2013 | ASSO CET 2013 | ATMA 2013 | BANASTHALI 2013 | BCECE 2013 | BEEE 2013 | BHU 2013 | BINC 2013 | BITSAT 2013 | BVP EEE 2013 | BVPEEE 2013 | CA CPT 2013 | CAT 2013 | CATE 2013 | CBEE 2013 | CEED 2013 | CEEP 2013 | CENTAC JET 2013 | CET 2013 | CG PET 2013 | CIPET JEE 2013 | CLAT 2013 | CMAT 2013 | COMEDK 2013 | COMEDK PGET 2013 | CPT 2013 | CSAT 2013 | CTET 2013 | CUCET 2013 | CUSAT 2013 | DAIICT 2013 | DNB CET 2013 | DTU 2013 | DUPGMET 2013 | DUMET 2013 | EAMCET 2013 | EDCET 2013 | ENAT 2013 | ENGINEERING 2013 | ESE 2013 | G2CET 2013 | GAT 2013 | GATE 2013 | GBTU 2013 | GCET 2013 | GMAT 2013 | GPAT 2013 | GPT 2013 | GRE 2013 | GUJCET 2013 | HPMT 2013 | HP CPMT 2013 | HSEE 2013 | IAS 2013 | IBSAT 2013 | ICET 2013 | ICFAI 2013 | ICWA 2013 | IELTS 2013 | IFS 2013 | IIEST 2013 | IIFT 2013 | IISC 2013 | IISER 2013 | IIT JAM 2013 | IITJEE 2013 | ILI CAT 2013 | ILSAT 2013 | IPCC 2013 | IPS 2013 | IPUCET 2013 | ISAT 2013 | ISI 2013 | IUET 2013 | JK BPEE CET 2013 | JCECE 2013 | JEE 2013 | JEST 2013 | JET 2013 | JET ABM 2013 | JIIT 2013 | JIPMER 2013 | JKCET 2013 | JMET 2013 | JMI 2013 | JSSU UGET 2013 | KAIET 2013 | KCET 2013 | KEAM 2013 | KEE 2013 | KERALA CEE 2013 | KIITEE 2013 | KLE PGAIET 2013 | KLEE 2013 | KLEU AIET 2013 | KLSAT 2013 | KRLMPCA 2013 | LAW 2013 | LAWCET 2013 | LNMIIT 2013 | LSAT 2013 | MAH CET 2013 | MAHER 2013 | MANAGEMENT 2013 | MANIPAL UGET 2013 | MAT 2013 | MBA CET 2013 | MBA 2013 | MCA 2013 | MEDICAL 2013 | MGIMS 2013 | MGM CET 2013 | MHT CET 2013 | MMUCET 2013 | MP DMAT 2013 | MP PET 2013 | NAT 2013 | NATA 2013 | NCHMCT JEE 2013 | NDA 2013 | HTTP: WWW.ICBSE.COM NEET 2013 | NEIGRIHMS 2013 | NEE 2013 | NEST 2013 | NET 2013 | NIFT 2013 | NIMCET 2013 | NLU 2013 | NMAT 2013 | NUPGET 2013 | OCET 2013 | OPENDEN 2013 | OPENMAT 2013 | OJEE 2013 | PECET 2013 | PGCET 2013 | PGD CET 2013 | PGECET 2013 | PGM CET 2013 | PGMEE 2013 | PMEE 2013 | PMET 2013 | POLYTECHNIC 2013 | PSTET 2013 | PTET 2013 | PUCET 2013 | RPET 2013 | RPMT 2013 | RTET 2013 | RULET 2013 | SAAT 2013 | SAT 2013 | SCRA 2013 | SET 2013 | SLEEE 2013 | SLET 2013 | SNAP 2013 | SRMEEE 2013 | STET 2013 | TANCET 2013 | TET 2013 | THAPAR 2013 | TMISAT 2013 | TNEA 2013 | TNPCEE 2013 | TOEFL 2013 | TRIPURA JEE 2013 | UGC NET 2013 | UJET 2013 | UKSEE 2013 | UP CPMT 2013 | UPCAT DENTAL 2013 | UPCMET 2013 | UPCPMT 2013 | UPGMEE 2013 | UPSC 2013 | UPSEE 2013 | UTTARAKHAND CPMEE 2013 | VEE 2013 | VITEEE 2013 | VMU AICEE 2013 | WBJEE 2013 | XAT 2013 |