September 14, 2013

Junior Inter Maths Paper I A - Chapter wise Analysis

Here is Chapter wise Analysis of Paper - IA of Junior Intermediate Mathematics for the benefit of AP students. The Chapters 'Functions' and 'Matrices' of the Algebra unit are very important either knowledge point of view or marks scoring point of view. The definitions, theorems and their statements are very much useful in studying 'Calculus'. The chapters 'Limits and Continuity' and 'Differentiation' are mainly based on the conceptual properties of functions. Finding out the domain and range of real valued functions will be helpful in observing the nature of increasing and decreasing functions in calculus. Also, these concepts are again reviewed while dealing with lessons in Algebra of Second Year course. In Public Examinations, questions are set from functions frequently. Some of the problems belong to the standard at school level.

''Matrices" is the chapter that every mathematics student relies on for a good aggregate of marks. Though this is a pure theoretical chapter, students will feel it to be easier while studying. The problems involved in the exercises are easily solvable. Especially problems related to solving linear equations are very important and frequently set for examinations. "Matrix - Inversion Method" and "Gauss - Jordan Method" are used in solving the linear equations and verifying the consistency and inconsistency of them.

Students are required to have a good practice of all the sums in the text book exercises along with the solved problems. This practice makes every student perfect with the subject and helps in scoring maximum marks in this chapter.

In the same chapter 'Matrices', there exists a sub - topic called 'Determinants'. The definition and properties of a determinant are well dealt with in this sub - topic. Students need to thoroughly solve all the problems given in the exercise on determinants. One problem (essay type) is compulsorily expected from this exercise. Therefore, the chapter 'Matrices' along with 'Determinants' plays a vital role as far as Paper - IA is concerned.

Now, coming to 'Vector Algebra', this is a new chapter to the Junior Intermediate students. MEC students in comparison with MPC students may feel some difficulty in understanding this chapter as this deals with some of the
Physics concepts. This to some extent, resembles Three Dimensional Coordinate Geometry. Theorems, results and concepts are mainly important to be always studied. The addition and multiplication operations on vectors are to
be understood for which relentless effort is necessary. Hard work is needed even for scoring good marks in this theoretical chapter.

"Trigonometry Unit" is most important when compared to other units of Paper - IA. Many mathematics seeking students of MPC and MEC groups of Junior Intermediate are frightened over the chapters included in this unit. The reason
for this is, not having proper idea about trigonometry in their school level. Many of the students at school level must have either ignored or left this in choice. This unit comprises chapters which are totally formulae oriented and students are annoyed at learning the formulae. This is how, trigonometry is felt difficult by students of all levels. Formulae are to be applied at appropriate places and this requires a good understanding and practice. It is necessary that the formulae are to be derived and the results memorised. There exist problems in text book exercises concerned to compound, multiple and sub - multiple angles. These problems can be solved with proper understanding and application of the formulae that each problem is composed of. While 'Algebra' and 'Vector Algebra' units are theory oriented, 'Trigonometry unit' is totally formulae oriented. Hence, students are advised to be thorough with theoretical as well as formula based chapters.

The Chapter 'Hyperbolic Functions' contains formulae, similar to the formulae in trigonometrical ratios. These are to be learnt separately with no overlapping of them. However, the trigonometrical results can be converted into hyperbolic results with the inclusion of the complex quantity called i = √ -1 or i2 = -1.
Few illustrations about these conversions follow at the end.

Idea of a triangle is required to deal with the chapter 'Properties of Triangles'.
This, being a theoretical chapter, invites the attention of students towards knowing fully about this chapter. Theorems, results, solved problems and exercise problems are necessarily to be studied thoroughly. The concepts about In - circle and the Ex - circles are very much needed for solving the exercise problems. Students must strive hard for learning Trigonometry and scoring good marks in examinations.

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