AIEEE MATHEMATICS

ALGEBRA

UNIT 1: Sets, Relations and Functions
Sets and their Representations, Union, intersection and complements of sets, and their algebraic properties, Relations, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings.

UNIT 2: Complex Numbers
Complex number in the form a+ib and their representation in a plane. Argand diagram. Algebra of complex numbers, Modulous and Arguments (or amplitude) of a complex number, square root of a complex number. Cube roots of unity, triangle – inequality.

UNIT 3: Matrices and Determinants
Determinants and matrices of order two and three, properties of determinants, Evaluation of determinants. Area of triangles using determinants, Addition and multiplication of matrices, adjoint and inverse of matrix. Test of consistency and solution of simultaneous linear equations using determinants and matrices

UNIT 4: Quadratic Equations
Quadratic equation 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; Symmetric functions of roots.

UNIT 5: Permutation and Combination
Fundamental principle of counting; Permutation as an arrangement. Meaning of P(n,r) and C(n,r). Simple applications.

UNIT 6: Mathematical Induction and Its applications

UNIT 7: Binomial Theorem and its Applications
Binomial Theorem for a positive integral index; general term and middle term; Binomial Theorem for any index. Properties of Binomial Co-efficients. Simple applications for approximations.

UNIT 8: Sequences and Series
Arithmetic, Geometric and Harmonic progressions. Special cases of Sn, Sn2, Sn3 . Arithmetic-Geometric Series, Exponential and Logarithmic series.

CALCULUS

UNIT 9: Differential Calculus
Polynomials, rational, trigonometric, logarithmic and exponential functions, Inverse functions. Graphs of simple functions. Limits, Continuity; 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 three. Applications of derivative: monotonic functions, Maxima and minima of functions of one variable.

UNIT 10: 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. Integral as limit of a sum. Properties of definite integrals. Evaluation of indefinite integrals; Determining areas of the regions bounded by simple curves.

UNIT 11: Differential Equations
Ordinary differential equations, their order and degree. Solution of differential equations by the method of separation of variables. Solution of homogeneous and linear differential equations.

TWO AND THREE DIMENSIONAL GEOMETRY

UNIT 12: Two dimensional Geometry
Recall of Cartesian system of Rectangular co-ordinates in a plane, distance formula, area of a triangle, condition for the collinearity of three points and section formula, centroid and in-centre of a triangle, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.

The straight line and pair of straight lines
Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrency of three lines, distance of point from a line, coordinates of orthocentre and circumcentre of triangle, equation of family of lines passing through the point of intersection of two lines, homogeneous equation of second degree in x and y, angle between pair of lines through the origin, combined equation of the bisectors of the angles between a pair of lines, condition for the general second degree equation to represent a pair of lines, point of intersection and angle between two lines represented by S = O and the factors of S.

Circles and system of Circles
Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle in the parametric form, 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 the circle, length of the tangent, equation of the tangent, equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal.

Conic Section
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 13: Three dimensional Geometry
Coordinates of a point in space, distance between the points; Section formula, direction ratios and direction cosines, angle between two intersecting lines, equations of a line and a plane in different forms; intersection of a line and a plane, coplanar lines, equation of a sphere, its centre and radius. Diameter form of the equation of a sphere.

VECTORS

UNIT 14: Vector Algebra
Vectors and Scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, vector triple product. Application of vectors to plane geometry.

STATISTICS

UNIT 15: Measures of Central Tendency and Dispersion
Calculation of Mean, median and mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.

UNIT 16: Probability
Probability of an event, addition and multiplication theorems of probability and their applications; Conditional probability; Probability distribution of a random variable; Binomial distribution and its properties.

TRIGONOMETRY

UNIT 17
Trigonometrical ratios, identities and equations. Inverse trigonometric functions and their properties. Properties of triangles, solution of triangles. Heights and Distances.

STATICS AND DYNAMICS

UNIT 18: Statics
Resultant of Coplanar forces; moments and couples. Equilibrium of three concurrent forces.

UNIT 19: Dynamics
Speed and velocity, average speed, instantaneous speed, acceleration and retardation, resultant of two velocities, relative velocity and its simple applications. Motion of a particle along a line, moving with constant acceleration. Motion under gravity. Laws of motion, Projectile motion.