**Matrices.. A tool for marks**

**Matrices**

Students start learning about matrices from school level itself. Hence, they feel this chapter to be comparatively easier. The study in inter level will be more theoretical and analytical. The definitions, theorems on various types of matrices create interest while reading, whereas the problems involved will fetch marks easily.

- The study of determinants is a part of the study of matrices. The properties of determinants are useful in other branches of mathematics also. The coplanarity of vectors, the concurrency of straight lines etc. are well verified by using the determinants. The problems given in the Telugu Academy text book are useful for a good score in the examinations.
- Problems related to finding the inverse of a matrix, solving equations by matrix-inversion method are important and students can easily get good marks on these items. However, students will feel Gauss-Jordan method, to solve the equations, to be a hard nut. With proper understanding of the steps involved in this method, the equations can be solved with much more interest. The concept of the rank of a given matrix is useful in verifying the consistency or non-consistency of the equations. Overall, the chapter is very much helpful in scoring maximum marks.
- 'Vector Algebra" is the newly introduced unit for Junior Inter students in Paper-A. The knowledge of fundamentals with regard to addition and product of vectors is mainly applicable in the study of physics for MPC group students. For MEC students, this is only a tool to get marks in the examinations.

**Trigonometry**

It makes paper-A much more significant. Trigonometry involves a number of formulae and for this reason, this used to be ignored by a section of students at school level. The same difficulty is felt by them at Intermediate level also. But this is to be compulsorily studied as it has wide range of applications in the study of calculus in Paper-B. This cannot be ignored at all in marks point of view also.

- Not only formulae but also graphical structures of various trigonometric and inverse trigonometric functions need a good practice. Finding the periodicity, domain and range of certain functions also needs attention for a good score in Intermediate examinations. The students in this regard are advised to solve completely the exercise 6(b) of Telugu Academy text book. Also, they are directed to go through the articles 6.1.14, 6.1.15, 8.1.4 and 8.2 of the text book repeatedly for gaining command over the subject.
- The chapter 'Hyperbolic Functions' is fairly easier. A very short answer type question will appear in the public examination.

**Properties of triangles**

'Properties of triangles' is a very special and important chapter in 'Trigonometry' unit in Paper-A. Quite a number of formulae and their derivations are involved in it, thus making the chapter more analytical and significant. Each and every problem in the text book exercises has its own importance and any problem is

expected in intermediate examinations. The solved problems also need a repeated practice.

- Reasonable weightage of marks is allotted to all the chapters of Trigonometry and therefore, students are advised not to give scope to lethargy in their preparation.

**The tentative chapter wise weightage of marks**

**Paper - A**

**Algebra:**

1. Functions - 11

2. Mathematical induction - 7

3. Matrices - 22

**Vector Algebra:**

4. Additions of Vectors - 8

5. Product of vectors - 13

**Trigonometry:**

6. Trigonometric Ratios up to Transformations - 15

7. Trigonometric equations - 4

8. Inverse Trigonometric Functions - 4

9. Hyperbolic Functions - 2

10. Properties of Triangles - 11

**Paper - B**

**Coordinate Geometry:**

1. Locus - 4

2. Transformation of Axes - 4

3. The straight line - 15

4. Pair of straight lines - 14

**3-Dimensional Coordinate Geometry:**

5. Three Dimensional Coordinates - 2

6. Direction Cosines and Direction Ratios - 7

7. Plane - 2

**Calculus:**

8. Limits and Continuity - 8

9. Differentiation - 15

10. Applications of Derivatives - 26

Board of Intermediate education prescribed the syllabus in Mathematics in the form of paper-A and Paper-B for each year. The textbooks are also available separately for both the papers and for both the years. The

contents of the syllabus are as given above.

Students now can plan their study programme and score marks. It is reminded in this context, that 27 out of 75 is a pass mark and 47 is a first class mark. 67 out of 75 stands for distinction marks in any paper.

- Now, let us try to analyse the subject chapter wise and paper wise so as to have a thorough understanding and planning.

**Paper - A**

The first chapter in Algebra unit of Paper-A is 'Functions'. Learning functions lays a foundation stone for learning calculus in Paper-B. The knowledge of different types of functions, their definitions and the theorems involved, paves way to know about the conceptual facts of functions in calculus. Modulus of a function, signum function and step function are three important types, the properties of which are well analysed

in paper-B in calculus in terms of "limits and continuity". The definitions and theorems of functions will help students in scoring good marks in this chapter. In competitive examinations, concept oriented problems will generally appear. Students are advised to concentrate on problems related to finding the domain and

range.

- The second chapter 'Mathematical Induction' is purely theoretical. Various mathematical statements and their proofs are verified by using the principle of mathematical induction. One question appears in examinations as a long answer type question. The induction principle is applied in proving certain theorems in the second year course also.

**Paper - B**

In Paper-B at Intermediate level, two important units in the name of 'Coordinate Geometry' and 'Calculus' are dealt with. 'Coordinate Geometry' comprises theoretical chapters whereas 'Calculus' consists of theory

based problem oriented chapters.

- The first chapter 'Locus' in coordinate Geometry is quite simple and easy. Every geometric figure is constructed based on the concept of locus only. Marks can be scored with minimum effort in this chapter.
- 'Transformation of Axes' is another easy chapter in Paper-B. A short answer type question is set in the pubic examination, from this chapter.

**The Straight line**

'The Straight line' is the next important and significant chapter. It involves various definitions, formulae and derivations. Students require concentration and dedication to read all these items.

- Students must thoroughly study the definitions and derivations of centroid, orthocentre, circumcentre and in-centre of a triangle. Translation of axes is used in this chapter to find the length of the perpendicular from a given point to a given straight line. Students are expected to concentrate on application oriented problems like this.

**Pair of Straight lines**

This is an extension of the previous chapter. This chapter deals with two straight lines at a time, the properties of a straight line remaining unchanged. The students are directed to solve the text book problems of all exercises of this chapter. Two long answer type questions are being set every year in the public examinations.

- The next unit is 'Three dimensional coordinate geometry'. Three dimensional coordinates, direction cosines, direction ratios and plane are the chapters included. Students can get more marks with minimum effort.
- 'Limits and continuity' is the important chapter in Calculus. It deals with concept based and knowledge oriented problems. Calculus deals with real valued functions which are algebraic and non-algebraic. Students need to go through the solved and exercise problems in the text book for a reasonably good score.
- The next chapter 'Differentiation' deals with limit values of a given function. Different methods of differentiation are in common use for different types of functions. Students must have to learn each and every method.

**Applications of Derivatives**

This chapter mainly depends upon the concept of differentiation. This chapter deals with various characteristics of functions. Finding the equations of tangent and normal at given points in the geometrical representation of curves defined by functions, the maximum and minimum values processed by functions etc. are included in the applications.

- This is a lengthy chapter and hence carries more weightage of marks. Students are advised to be perfect with every item of the chapter for a good aggregate of marks in Public Examinations.