1. Matrices and their Applications 
Adjoint, inverse  properties, computation of inverses, a solution of a system of linear equations by matrix inversion method. Rank of a matrix  elementary transformation on a matrix, consistency of a system of linear equations, Cramer’s rule, nonhomogeneous equations, homogeneous linear system and rank method. A solution of linear programming problems (LPP) in two variables.

2. Trigonometry and Complex Numbers 
Definition, range, domain, principal value branch, graphs of inverse trigonometric functions and their elementary properties. Complex number system  conjugate, properties, ordered pair representation. Modulus  properties, geometrical representation, polar form, principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De Moivre’s theorem and its applications. Roots of a complex number  nth roots, cube roots, fourth roots.

3. Analytical Geometry of two dimensions 
Definition of a conic  general equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity. Equations of conic sections (parabola, ellipse and hyperbola) in standard forms and general forms Directrix, Focus and Latusrectum  a parametric form of conics and chords.  Tangents and normals  Cartesian form and parametric form  the equation of chord of contact of tangents from a point (x1, y1) to all the abovesaid curves. Asymptotes, Rectangular hyperbola  the Standard equation of a rectangular hyperbola.

4. Vector Algebra 
Scalar Product  angle between two vectors, properties of the scalar product, and applications of the dot product. Vector product, right handed and left handed systems, properties of vector product, applications of the cross product. The product of three vectors  Scalar triple product, properties of the scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors

5. Analytical Geometry of Three Dimensions 
Direction cosines  direction ratios  the equation of a straight line passing through a given point and parallel to a given line, passing through two given points, the angle between two lines. Planes  equation of a plane, passing through a given point and perpendicular to a line, given the distance from the origin and unit normal, passing through a given point and parallel to two given lines, passing through two given points and parallel to a given line, passing through three given noncollinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines (coplanar lines), angle between a line and a plane.Skew lines  the shortest distance between two lines, condition for two lines to intersect, the point of intersection, collinearity of three points. Page 18 VITEEE 2018 Sphere  the equation of the sphere whose centre and radius are given, the equation of a sphere when the extremities of the diameter are given.

6. Differential Calculus 
Limits, continuity and differentiability of functions  Derivative as a rate of change, velocity, acceleration, related rates, derivative as a measure of the slope, tangent, normal and the angle between curves. Mean value theorem  Rolle’s Theorem, Lagrange Mean Value Theorem, Taylor ’s and Maclaurin’s series, L’ Hospital’s Rule, stationary points, increasing, decreasing, maxima, minima, concavity, convexity and points of inflexion. Errors and approximations  absolute, relative, percentage errors  curve tracing, partial derivatives, Euler’s theorem

7. Integral Calculus and its Applications 
Simple definite integrals  fundamental theorems of calculus, properties of definite integrals.Reduction formulae  reduction formulae for and, Bernoulli’s formula. Area of bounded regions, length of the curve.

8. Differential Equations 
Differential equations  formation of differential equations, order and degree, solving differential equations (1st order), variables separable, homogeneous and linear equations. Second order linear differential equations  second order linear differential equations with constant coefficients, finding the particular integral if f(x) = emx, sin mx, cos mx, x, x2.

9. Probability Distributions 
Probability  Axioms  Addition law  Conditional probability  Multiplicative law  Baye’s Theorem  Random variable  probability density function, distribution function, mathematical expectation, variance. Theoretical distributions  discrete distributions, Binomial, Poisson distributions Continuous distributions, Normal distribution.

10.Discrete Mathematics 
Functions  Relations Basics of counting. Mathematical logic  logical statements, connectives, truth tables, logical equivalence, tautology, a contradiction. Groupsbinary operations, semigroups, monoids, groups, the order of a group, order of an element, properties of groups.
