# Amrita Engineering Entrance Exam 2019 Mathematics Syllabus

AEEE stands for Amrita Engineering Entrance Exam. It is conducted by Amrita Vishwa Vidyapeetham every year. These exams are for the candidates those who live in India and wish to pursue their career in engineering. This exam provides admission to undergraduate engineering courses offered in the three campuses at Amritapuri (Kollam), Bengaluru and Ettimadai (Coimbatore). So candidates those who are planning for these exams should be ready and start preparing hard. All those candidates who have applied for this exam search for the syllabus so in this article we will discuss about the syllabus of mathematics

## AEEE Syllabus 2019 Mathematics

• Complex Numbers

Cube roots of unity, triangle inequality; form a+ib, representation in a plane. Arg and diagram. Algebra, Modulus and argument (or amplitude), square root.

• Relations and Functions

Definition, Domain, codomain and range of a relation their fuinctions. Real valued function. Constant, identity, polynomial, rational. Modulus, signum and greatest integer functions. Sum. Product, Difference, quotient of functions.

• Linear Inequalities

Linear inequalities. Algebraic solutions in one variable, representation on the number line.

• Permutation and Combinations

Fundamental principle of counting; Simple applications; Permutation as an arrangement and combination as selection, Meaning of P(n,r)and C(n,r).

• Matrices and Determinants

Determinants and matrices of order two and three, properties, Evaluation. Addition and multiplication, adjoint and inverse of matrix; Solution of simultaneous linear equations using determinants.

• Binomial Theorem

Pascal’s triangle; Binomial theorem for positive integral indices. General and middle terms, simple applications.

• Sequences and Series

Arithmetic, Geometric and Harmonic progressions and Insertion between two given numbers. Relation between A.M., G.M. and H.M. Special series ∑n, ∑n 2, ∑n 3. Arithmetic-Geometric Series, Exponential and Logarithmic Series.

Real and complex number system with solutions. Nature and relation between roots and co-efficient, formation of quadratic equations with given roots; One to one and onto functions. Composite functions, inverse of a function, Types of relations: reflexive, symmetric, transitive and equivalence relations.

• Probability

Probability of an event, addition and multiplication theorems and applications; Conditional probability; Bayes’ theorem, Probability distribution of a random variate; Binomial and Poisson distributions and their properties.

• Trigonometry

Inverse trigonometric- functions, properties, Trigonometrical identities and equations. Properties of triangles- centroid, incentre, circumcentre and orthocentre, Heights and distances, solution of triangles.

• Measures of Central Tendency and Dispersion

Calculation of Mean, Median and Mode standard deviation, variance.

• Integral Calculus

Integral as an anti-derivative. Fundamental integrals- algebraic, trigonometric, exponential and logarithmic functions. Integration- substitution, parts, partial fractions. Integration using trigonometric identities, Integral as a limit of sum. Properties and Evaluation of definite integral, simple curves determination.

• Differential Calculus

Applications of derivatives: Maxima and Minima of functions one variable, tangents and normals,. Polynomials, rational, trigonometric, logarithmic and exponential functions. Graphs of simple functions. Limits, Continuity; Rolle’s and Langrage’s Mean Value Theorems, differentiation of the sum, difference, product and quotient of two functions, logarithmic, exponential, composite and implicit functions; derivatives of order upto two.

• Differential Equations

Order and degree. Formation and Solutions of differential equations by the method of separation of variables. Solution of Homogeneous and linear differential equations, typed 2 y/dx2 = f(x).

• Straight Line and Pair of Straight Lines

Various forms of equations, intersection, distance of a point from a line, angles between two lines, conditions for concurrence of three lines. Equations of internal and external bisectors of angles between two lines, equation of family 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

• Vector Algebra

Vector and scalars products and triple products, addition of two vectors, components of a vector in two and three dimensional space, Application of vectors to plane geometry

• Circles and Family of Circles

Standard and general form of equation of a circle- radius and centre, equation of a circle-parametric form, when end points of a diameter are given, equation of a family of circles through the intersection of two circles,  points of intersection of a line and circle with the centre at the origin and condition for a line to be tangent, condition for two intersecting circles to be orthogonal

• Two Dimensional Geometry

Review of Cartesian system of rectangular co-ordinates in a plane, distance formula, area of triangle, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes, condition for the collinearity of three points.

• Conics Sections

conditions for y = mx+c to be a tangent and point(s) of tangency ;Sections and equations of conic sections (parabola, ellipse and hyperbola) in standard forms,.

• Three Dimensional Geometry

Angle between (i) two lines (ii) two planes (iii) a line and a plane Distance of a point from a plane; Distance between two points. Direction cosines of a line joining two points. Cartesian and vector equation of a line. Coplanar and skew lines. Shortest distance between two lines. Cartesian and vector equation of a plane.