May 28th, 2015
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AlgebraAlgebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.Logarithms and their properties.Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.Addition and multiplication rules of probability, conditional probability, independence of events, computation of probability of events using permutations and combinations.TrigonometryTrigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multipl

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