Second year, which is also the final year, of two-year intermediate course, is crucial to students since it is career - deciding. MPC and MEC students, more prominently have to focus their attention on getting a decent aggregate of marks. With a good aggregate in hand, they can plan for anything high in their future education or life. Second year Intermediate Mathematics public Examination will be conducted in the form of paper-A and paper-B. Paper-A contains in it Algebra, Statistics and Probability units. Paper-B has only two units by name Coordinate Geometry and Calculus. In the examination, each paper carries a maximum of 75 marks.
Paper - A
Complex Numbers: This chapter involves definitions, geometrical representations, properties, polar forms and Argand diagram. This chapter is very much important with regard to preparation for IIT-JEE Examination. Application oriented problems may be given in such competitive examinations. Students are expected to be thorough with the above mentioned basic items.
De Moivre's Theorem: This theorem is proved by using the principle of mathematical induction, studied in first year paper-A. A complex number in polar form is used in the statement and proof of the theorem. The theorem is helpful in finding the nth roots of a complex number and thereby, nth roots of unity. This chapter carries a good weightage of marks along with the previous chapter. Students need to pay attention in their preparation with regard to every application of the theorem.
Quadratic Expressions: In this chapter, both quadratic expressions and equations in one variable are dealt with. Students will learn about signs of quadratic expressions, change in signs and extremum values in this chapter. The theorems based on these items are important in the examination point of view. The chapter also deals with quadratic inequations theoretically and also graphically. Students may feel this chapter easily understandable.
Theory of Equations: This chapter deals with the relation between the roots and the coefficients in an equation and also the methods of solving an equation when two or more of its roots are connected by certain relations. As a matter of reference, students can look into the solved problems and exercise 4(b) of the Akademi text book.
Another important topic in this chapter is, solving reciprocal equations. The methods of solving these equations must be understood carefully. For achieving perfection, students may practice the solved problems and exercise 4(d). Knowing thoroughly about this chapter leads to knowing algebra at any level in the study of future courses.
Permutations and Combinations: This chapter mainly deals with problems relating to puzzles that we come across in our daily life. This is based on the principle of counting. The knowledge of permutations and combinations helps to know about probability. This is treated as a self contained topic in Mathematics under the name of 'Vikalpa' by renowned mathematician 'Mahavira' in 9th century A.D. Several important theorems and results are stated in this chapter. This chapter is significant in view of a number of applications in day to day life.
Various instances can be cited with regard to the applications of permutations and combinations. Choosing five questions out of seven questions in a question paper, selecting a cricket team of eleven players from out of twenty members, etc... are based on the principle of this chapter only. . Permutations arranged circularly come under circular permutations. Making a garland with same or different coloured flowers is the best example in our day to day life. Students must solve all exercise problems so as to enable themselves to gain perfection.
Understanding the concept of combinations is much easier when compared to that of permutations. There exist good number of theorems and results which are useful at the time of solving problems. In competitive examinations, this chapter has a prominent role and students must be aware of all types of problems.
Binomial Theorem: This theorem is proved by using the principle of mathematical induction. This has a wide range of applications. 'Binomial Coefficients' is a special feature of 'Binomial Theorem'. They have many properties with which students must be thorough. The problems given in the text book on this topic are all important and examination worthy. Binomial theorem for rational index is very much significant and the last exercise in this chapter is an example to it. Students are advised to solve the last exercise completely.
Partial Fractions and Statistics: These two are easy chapters in terms of the subject content and marks. 'Less effort - More marks' best suits these two chapters.
Probability: This is based on the concept of permutations and combinations. In fact, probability is an extension of them. It deals with the phenomenon of chance or randomness. Postulates, results, theorems and illustrations are involved in this chapter. The theory of probability is the science of logic quantitatively treated. Students are required to thoroughly understand the concept of the theory of probability. They are also advised to solve all the exercise problems for a good score in the annual examination. Problems related to addition, multiplication and Bayee theorems are likely to appear in the examinations. This chapter needs a repeated practice before the examinations.
Distributions: Most of the problems of science as well as daily life are concerned with a numerical value associated with the outcome of an experiment. For instance, we may be able to know the probability of 12 coins showing up 10 heads, when tossed at a time. The concept of random variable solves the problems of this type. There exist derivations for finding mean and variance of a random variable and their formulae are very much to be remembered.
Similarly, knowledge of binomial theorem and binomial coefficients is helpful in tackling the problems of probability distributions. The exercises under this chapter need a good practice for a good score.
Paper - A
Complex Numbers: This chapter involves definitions, geometrical representations, properties, polar forms and Argand diagram. This chapter is very much important with regard to preparation for IIT-JEE Examination. Application oriented problems may be given in such competitive examinations. Students are expected to be thorough with the above mentioned basic items.
De Moivre's Theorem: This theorem is proved by using the principle of mathematical induction, studied in first year paper-A. A complex number in polar form is used in the statement and proof of the theorem. The theorem is helpful in finding the nth roots of a complex number and thereby, nth roots of unity. This chapter carries a good weightage of marks along with the previous chapter. Students need to pay attention in their preparation with regard to every application of the theorem.
Quadratic Expressions: In this chapter, both quadratic expressions and equations in one variable are dealt with. Students will learn about signs of quadratic expressions, change in signs and extremum values in this chapter. The theorems based on these items are important in the examination point of view. The chapter also deals with quadratic inequations theoretically and also graphically. Students may feel this chapter easily understandable.
Theory of Equations: This chapter deals with the relation between the roots and the coefficients in an equation and also the methods of solving an equation when two or more of its roots are connected by certain relations. As a matter of reference, students can look into the solved problems and exercise 4(b) of the Akademi text book.
Another important topic in this chapter is, solving reciprocal equations. The methods of solving these equations must be understood carefully. For achieving perfection, students may practice the solved problems and exercise 4(d). Knowing thoroughly about this chapter leads to knowing algebra at any level in the study of future courses.
Permutations and Combinations: This chapter mainly deals with problems relating to puzzles that we come across in our daily life. This is based on the principle of counting. The knowledge of permutations and combinations helps to know about probability. This is treated as a self contained topic in Mathematics under the name of 'Vikalpa' by renowned mathematician 'Mahavira' in 9th century A.D. Several important theorems and results are stated in this chapter. This chapter is significant in view of a number of applications in day to day life.
Various instances can be cited with regard to the applications of permutations and combinations. Choosing five questions out of seven questions in a question paper, selecting a cricket team of eleven players from out of twenty members, etc... are based on the principle of this chapter only. . Permutations arranged circularly come under circular permutations. Making a garland with same or different coloured flowers is the best example in our day to day life. Students must solve all exercise problems so as to enable themselves to gain perfection.
Understanding the concept of combinations is much easier when compared to that of permutations. There exist good number of theorems and results which are useful at the time of solving problems. In competitive examinations, this chapter has a prominent role and students must be aware of all types of problems.
Binomial Theorem: This theorem is proved by using the principle of mathematical induction. This has a wide range of applications. 'Binomial Coefficients' is a special feature of 'Binomial Theorem'. They have many properties with which students must be thorough. The problems given in the text book on this topic are all important and examination worthy. Binomial theorem for rational index is very much significant and the last exercise in this chapter is an example to it. Students are advised to solve the last exercise completely.
Partial Fractions and Statistics: These two are easy chapters in terms of the subject content and marks. 'Less effort - More marks' best suits these two chapters.
Probability: This is based on the concept of permutations and combinations. In fact, probability is an extension of them. It deals with the phenomenon of chance or randomness. Postulates, results, theorems and illustrations are involved in this chapter. The theory of probability is the science of logic quantitatively treated. Students are required to thoroughly understand the concept of the theory of probability. They are also advised to solve all the exercise problems for a good score in the annual examination. Problems related to addition, multiplication and Bayee theorems are likely to appear in the examinations. This chapter needs a repeated practice before the examinations.
Distributions: Most of the problems of science as well as daily life are concerned with a numerical value associated with the outcome of an experiment. For instance, we may be able to know the probability of 12 coins showing up 10 heads, when tossed at a time. The concept of random variable solves the problems of this type. There exist derivations for finding mean and variance of a random variable and their formulae are very much to be remembered.
Similarly, knowledge of binomial theorem and binomial coefficients is helpful in tackling the problems of probability distributions. The exercises under this chapter need a good practice for a good score.
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