NERIST NEE II 2015 Vocational Mathematics Syllabus:
Trigonometry ratios of compound; multiple and sub-multiple angles; general solution of trigonometric equations; properties and solutions of triangles; inverse circular functions.
(i)Complex Numbers: Complex number and its properties; Different forms of complex numbers; roots of complex numbers; cube roots of unity and their properties; De-Moivre’s theorem (ii) progressions: Arithmetic and Geometric means; Harmonic progression; sum of n- terms and nth terms of AP & GP (iii) Permutation and combinations; binomial theorem for positive integral index; middle term; greatest term; binomial coefficients; (iv) partial fractions of different forms; (v) determinants of order two, three and their properties
Coordinate Geometry (2D):
Coordinates of a point in a plane; distance between two points; division of a line segment in a given ratio (internal and external division) different forms of equation of a straight line; distance of a point from a line; Equation of a circle; tangent and normal to a circle; equation of second degree representing a conic section; basic ideas about parabola, ellipse and hyperbola.
Coordinate Geometry (3D):
Coordinates of a point in three dimensions; distance between two points; division of join of two points; angle between two lines; direction cosines and direction ratios of a line; projection of a point on a line; equation of a plane; different forms of equation to a plane; angle between two planes; plane through three given points; angle between plane and line; equation of a straight line in space; coplanar lines; shortest distance; centre and radius of sphere.
Vector and its components; Different kinds of vectors; addition and subtraction of vectors; scalar and vector products of two and three vectors.
Functions and their representation limit; continuity and differentiability of a function; derivatives of elementary functions derivatives of sum; product and quotient of functions; derivatives of exponential, logarithmic and hyperbolic functions. Successive differentiation and Leibnitz theorem; Rolle’s theorem and Lagrange’s mean value theorem; L Hospital’s Rule; Curvature; Asymptotes and concepts of curve tracing; Maxima & minima of functions of one variable
Integration; Integral of elementary functions; integration by parts and by substitution; integral of rational functions and trigonometric functions; integration of irrational functions; definite integrals; area under simple curves
Mean, median, mode and standard deviation of discrete and grouped data