Introduction to Three-dimensional GeometryĬoordinate axes and coordinate planes in three dimensions. Standard equations and simple properties of parabola, ellipse and hyperbola. Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Various forms of equations of a line: parallel to axis, point -slope form, slope-intercept form, two-point form, intercept form, Distance of a point from a line. Slope of a line and angle between two lines. and G.M.īrief recall of two dimensional geometry from earlier classes. and its sum, geometric mean (G.M.), relation between A.M. Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. Historical perspective, statement and proof of the binomial theorem for positive integral indices. (n!) Permutations and combinations, derivation of Formulae for n P r and n C r and their connections, simple applications. Permutations and Combinationsįundamental principle of counting. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Need for complex numbers, especially √−1, to be motivated by inability to solve some of the quadratic equations. Deducing identities like the following:\ġ. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx
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