Chapters  Topics 

Matrices and their Applications   Adjoint, inverse – properties, computation of inverses, solution of a system of linear equations by matrix inversion method
 The 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
 The solution of linear programming problems (LPP) in two variables

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

Analytical Geometry of two dimensions   Definition of a conic – general equation of a conic, classification concerning the general equation of a conic, classification of conics concerning 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 equation of chord of contact of tangents from a point (x1, y1) to all the abovesaid curves
 Asymptotes, Rectangular hyperbola – Standard equation of a rectangular hyperbola

Vector Algebra   Scalar Product – the angle between two vectors, properties of scalar product, and applications of the dot product
 Vector product, righthanded and lefthanded systems, properties of vector
product, applications of the cross product  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

Analytical Geometry of Three Dimensions   Direction cosines – direction ratios  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, point of intersection, collinearity of three points
 Sphere – equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given

Differential Calculus   Limits, continuity and differentiability of functions  Derivative as a rate of change, velocity, acceleration, related rates, derivative as a measure of 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

Integral Calculus and its Applications   Simple definite integrals – fundamental theorems of calculus, properties of definite integrals.
 Reduction formulae – reduction formulae for ∫sin ^{n }_{x dx and ∫cos }^{n}_{x dx}, Bernoulli’s formula
 Area of bounded regions, length of the curve

Differential Equations   Differential equations  formation of differential equations, order and degree, solving differential equations (1st order), variables separable, homogeneous, linear equations and applications
 Secondorder linear differential equations  second order linear differential equations with constant coefficients, finding the particular integral of f(x)=e MX_{, sin MX, cos MX,x,x }^{2}

Probability Distributions   Probability – Axioms – Addition law  Conditional probability – Multiplicative law  Baye’s Theorem  Random variable  probability density function, distribution function, mathematical expectation, variance
 Theoretical distributionsdiscrete distributions (Binomial, Poisson distributions) Continuous distributions (Normal distribution)

Discrete Mathematics   Functions–Relations –Sequence and series (AP, GP, HP) Binomial theoremBasics of counting
 Mathematical logic – logical statements, connectives, truth tables, logical equivalence,
tautology, contradiction  Groupsbinary operations, semigroups, monoids, groups, an order of a group, order of an element, properties of groups

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