## September 14, 2013

### Junior Inter Mathematics Paper - IB - Chapter Wise Analysis

Following is the Chapter - wise Analysis Junior Intermediate Mathematics Paper - IB. Paper - IB comprises two units in the form of 'Coordinate Geometry' and 'Calculus'. Students may consider them difficult units in view of the topics that are involved in these two units. However, hard work towards them may make them easier.

The first chapter 'Locus' in Coordinate Geometry is an easier one, fetching marks to students even with minimum effort.

'Transformation of Axes' is the second chapter. This contains two or three theorems, the results of which are applicable in many contexts in higher classes. Understanding the theorems may not pose a problem to students.

Let us consider the next two chapters 'Straight line' and 'Pair of straight lines'. These are interlinked with each other. The properties of straight lines are useful in the study of pair of straight lines. Students are required to be perfect with the theorems of both the chapters. These are important in public examinations point of view. The exercise problems are based on the theorems and properties of straight lines and pair of straight lines. The problems related to finding 'Orthocentre' and 'Circumcentre' are frequently asked in examinations and students must practise all the problems given in the exercises in order to score good marks. These two theoretical chapters need so much of analysis and students should improve their analysing capabilities in dealing with such chapters as these.

'Three Dimensional Coordinate Geometry' deals with Three Dimensional Coordinates, Direction Cosines and Direction Ratios and the concept of the Plane. Minimum effort is sufficient that students can secure good marks in these topics.

In 'Calculus', real valued functions are dealt with for their nature, properties and applications. The problems in the first chapter 'Limits and Continuity' are formulated on the concept of limit of a function. Students are required to understand the basic concepts of functions possessing limits. They are also required to observe the continuous and discontinuous nature of functions. The definition of limit of a function plays a key role in the entire 'Calculus' even in higher classes also.

'Defferentiation' chapter is full of methods of differentiation and formulae. When studied perfectly and properly, this chapter gives a strong foundation to learn 'Integration' in Senior Intermediate class.

Obtaining derivative from the definition is a basic concept. Various derivatives are derived by using this method called 'Derivative from first principles'. A compulsory question appears every year on this method in Annual Examinations. Apart from this, Addition, Product and Quotient rules play a prominent role. A thorough practice of problems of all exercises paves the way for acquiring knowledge on differentiation. Negligence and complacence are
better avoided for the sake of obtaining skills on the methods of differentiation.

After a thorough study of differentiation, the student is aimed at learning various applications. The applications include....
(i) Errors - approximations.
(ii) Equations of tangent and normal.
(iii) The geometrical interpretation of derivative.
(iv) Lengths of tangent, subtangent, normal, subnormal.
(v) Angle between two curves.
(vi) Differentiation - rate of change.
(vii) Rolle's and Lagrange's mean value theorems.
(viii) Increasing and decreasing functions.
(ix) Maximum and minimum values.

All the above topics are specially dealt with analytically and theoretically. A thorough understanding of all the topics helps every mathematics student gain grip over differentiation and its applications. These topics are specially mentioned even in competitive examinations. Each and every problem is important in examination point of view, be it subjective or objective.

The syllabus is designed in such a way that students are expected to excel in their academic pursuit without facing any obstacles now and in future. Hence, students are advised to strive hard in reaching their goals.

Students, at this juncture, should make it a point that in each of the Papers IA and IB, 27 out of 75 is a pass mark, 47 leads to first class and 67 to distinction. So, carry on your preparation accordingly and succeed.
Remember that "Hard work pays tomorrow, though not today".