'The Circle', 'System of Circles', 'Parabola', 'Ellipse', and

'Hyperbola' all theoretical in nature. 'Locus' and 'Transformation of

Axes' of first year course

are involved in these chapters.

While 'locus' is used to define these geometrical figures,

'translation of axes' is used to derive certain results like obtaining

parametric equations of a circle. 'Learn to be silent and let your

quiet mind listen and absorb' is the famous quotation best suitable in

classrooms in learning about the circle

and its various features.

It also can be noted that the foot of the perpendicular relation

studied in first year Straight Line chapter is used to find the

midpoint of the chord intercepted by a given circle and a line. Also,

section formulae are applied in studying about the relative positions

of two circles. Thus, students are

reminded to remember the fundamentals wherever and whenever studied.

The chapter 'System of Circles' introduces the concepts of (i) angle

between two intersecting circles and (ii) radical axis of two

circles.

'Law of Cosines' formula of first year properties of Triangles is used

in deriving the expression for the angle between two intersecting

circles. 'Locus' concept is used to define the radical axis of two

circles. Also,

concept of S + .L = 0, studied in straight line chapter of first year

course, is applied in solving certain problems related to radical

axis. Thus, the first year fundamentals come into use in some of the

second year chapters.

The knowledge of definitions and various derivations studied in the

chapter 'Circle' is helpful to understand about the three conics such

as Parabola, Ellipse and Hyperbola. . In the second unit calculus of

Paper - B,

'Integration', 'Definite Integrals' and 'Differential Equations' are

the chapters

involved. The concept of differentiation is recollected in learning

the concept of integration, which is regarded as the inverse process

of differentiation.

Standard forms and properties of integrals are discussed in the

chapter integration. Method of integration by parts, partial fractions

method and reduction formulae are very important features of

integration.

"Definite Integrals" chapter deals with applications of integration in

terms of deriving reduction formulae and computation of areas of

closed regions. Both are important topics as far as examinations are

concerned. Solved problems and all exercise problems must be attempted

and practised time to time. Then only students can have a grip over

the subject matter, which helps them to perform well in higher levels

of examinations.

In the chapter 'differential equations', formation and solution of

equations are learnt. Various methods exist in solving differential

equations and students must be thorough with each and every method.

Differential equations have applications in many branches of Physics,

Physical Chemistry etc. As usual, students are expected to look into

the solved examples and exercise problems for gaining perfection.

To conclude in Paper-B, Circle, Parabola, Integration, Definite Integrals and

Differential Equations are very very important chapters, carrying a

reasonable weightage of marks in the Intermediate examination. Regular

practice of the methods, remembering formulae and solving all types of

problems repeatedly in every chapter is the key to success in the

examinations.

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