বীজগণিত (Algebra)
Surds and Indices : Fundamental laws of Surds and Indices, simple applications.
Arithmetic Progression : (A.P.): Definition of A.P., Common difference, General term, Summation of first n terms. Sum of first n-natural numbers, A.M.
Geometric Progression : (G. P.): Definition of G.P., Common ratio, General term, Summation of first n-terms, G.M.
Logarithms : Definition, General properties of logarithms.
Complex numbers : Complex numbers in the form a + ib, Real and imaginary parts of a complex number, Geometrical representation of complex numbers, Complex Conjugate, Modulus and Argument of a complex number, Algebra of complex numbers, (fundamental operations). Triangle inequality | [tex]\left| {{Z_1} + {Z_2}} \right| \le \left| {{Z_1} + {Z_2}} \right|[/tex] and also [tex]\left| {{Z_1}{Z_2}} \right| = \left| {{Z_1}} \right|\left| {{Z_2}} \right|[/tex] . Cube roots of unity and their properties.
Theory of Quadratic Equations : Quadratic equations with real coefficients. Fundamental theorem of Algebra (Statement only). Roots, relations between roots and coefficients of a quadratic equation, Nature of roots, formation of quadratic equation, common root ax2 + bx + c. (a, b, c are rational numbers).
Permutation and Combination : Defination of Permutation. Permutation of n different things taken [tex] r( \le n) [/tex] at a time; Permutation of n things, not all different; Permutation with repetitions (circular permutation excluded).
Definition of Combination; Combination of n different things taken r at a time; Combination of n things when things are not all different; Basic properties.
