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In this chapter we will study to find the surface area and volume of solid figure , like parallelepiped , cube, cuboid, cylinder , cone , frustum of cone , sphere and hemisphere and we will study to find the surface area and volume of combination of solid figures combination of two or more different or similar solid figures. SOLID FIGURES The objects which occupy space (i.e. they have three dimensions ) are called solids. The solid figures can be derived from the plane figures. e.g. In figure (i) , we have a paper cut in the form as shown. It is a plane figure. But when we fold the paper along the dotted lines, a box can be made as shown in figure (ii) , which occupies some part of the space. It has more than two dimensions and therefore it fulfils the criteria of being a solid figure.

Today we are going to study about   rational expressions, RATIONAL EXPRESSIONS An expression of the form p(x) / q (x) , where p(x) and q(x) are polynomials and q(x) ≠ 0 is called a rational expression. * In the rational expression p(x) / q(x) , p(x) is called the numerator and q(x) is called the denominator of the rational expression. * Every polynomial can be said to be rational expression. Since p(x) can always be written as p(x) / 1 . * Every rational expression need not be a polynomial .

COMBINED EXERCISES FOR NUMBER SYSTEM , SURDS AND RADICALS & PROGRESSION

Today we are going to learn about how the sequence of various numbers work and how we can trace out what number would follow after a certain number , or at a particular index, PROGRESSION Sequence following certain patterns are called progression. e.g. 2,3,4,5,..... is a progression, here each term is interesting, here each term is increasing by 1. ARITHMETICAL PROGRESSION An arithmetic progression is a sequence in which the difference between any term and its just preceding term is constant through. The constant 'd' is called the common difference. The first term of AP is represented by 'a' and the formula for the xth term is  aₓ = a + (x - 1) d

Today we are going to learn about surds and radicals  in this blog post . Before beginning with 'surds and radicals' you should visit and revise the concepts of number system , NUMBER SYSTEM So, lets begin with surds and radicals Let x be a rational number and n be a positive number such that ⁿ√x is  irrational , then ⁿ√x is called a radical of order n or surd and here x is called the radicand. * A surd of order 2 is called quadratic surd, i.e. √2 * A surd of order 3 is called a cubic surd i.e. ³√5 * A surd of order 4 is called a biquadratic surd * A surd has no fraction under the radical sign . * The radicand has no factor with exponent n. * A surd is not equal to any surd of order lower than n. * ⁿ√x is a surd only if x is a rational and ⁿ√x is irrational. * When x is irrational or ⁿ√x is rational then ⁿ√x is not a surd.