SYLLABUS

Syllabus For The Entrance Examination

MATHEMATICS - 1 PAPER (3 HRS.)

Covering the following topics:

1. Binomial Theorem for positive integral indices.General Binomila Theorem and its application.

   
   

2. Permutation and Combination and its application.

   
   

3. Multinomial Theorem

   
   

4. Inequalities

   
   

5. Method of Mathematical Induction

   
   

6. Roots of the equation and relation between roots and coefficient of equations

   
   

7. Group : Defn. and axioms, Defn of a sub group, Lagrange`s Theorem, Cyclic Groups.

   
   

8. Determinants : Determinants of 3rd and 4th order, properties of determinants. Solution of not more than 3 simultaneous equatins.

   
   

9. Matrices : Matrices upto fourth order, addition and multiplication of matrices. Inverse of a matrix Transformation and properties of matrices. Programmes of calculation, including block diagram, modification and conditional jump instructions.

   
   

10. Infinite series and recurring series, simple test of covergence and divergence of series.

    
    

11. Exponential and logarithmic series : Uses and application of these series Approximate evaluation of function from an expansion either know, or to be obtained by Taylor method. Remainder Theorem.

    
    

12. Differentiation of standard form and applications of differentiation to tangents, stationary values, maxima and minima, linear approxiamation and small values.

    
    

13. Integration of standard form, simle reduction formula for integrals, partial fractions to be used as a tool for integrals of polynomial approximation only not involving more than one quadratic factor. Fundamentals theorem of integral calculus. The application of integral calculus to the calculation of lengths, plane areas and volumes.

    
    

14. Repeated differentiatin and Leibnitz`s theorem, partial differentiation & implicit equations.

    
    

15. Analytical solution of differential equations of first and second order.

OTHER DETAILS REGARDING ENTRANCE EXAMINATION

1. A candidate who has passed the Entrance Examination or who is exempted from the Entrance Examination, may apply to the Society for admission, as a Student-Member. On Admission a Student-Member can appear for Examination leading to Professional qualification as an Actuary.

   
   

2. The Examinations cover those Subjects, the knowledge of which is required by an Actuary in practice of his profession. The Subjects to be studied fall into two broad groups. The first group covers Mathematical, Statistical and other Actuarial techniques and second group is, in effect, the application of the above techniques to professional problems.

   
   

3. The Examinations conducted by the Society can correspondingly be divided into two groups viz. Subjects 1 to 6 and 7 to 9. For Subject 1 to 6, Examinations are held twice a year - in May and November. For Subject 7 to 9, Examinations are held only once a year in November. The Examinations are normally held at Mumbai, Calcutta, Delhi, Hyderabad, Kanpur, Madras and Bhopal.
   
   

4. Completion of Subjects 1 to 6 will lead to admission to ASSOCIATE MEMBERSHIP and Subjects 7 to 9 to FELLOW MEMBERSHIP of the Society.

   
   

For a basic understanding of the subjects one or more of the following books may be helpful.

1. Mathematics for Arts & Science for Std.XII by Prof - Anil Nayak-Reliable Series, Mumbai.
   

2. Comprehensive Mathematicsw by Permanand Gupta - Laxmi Publications, New Delhi
   

3. Systematic Mathematics for Arts & Science by Khandare, Thakare, Sarode, Gadkari, Shirolkar, Alexander, Oza & Panjawani.
   

4. A New approach to Mathematics and Statistics by chitale, Joshi, Dumasia, Kitekar,Mishra, Patel, Karandikar and Pandit Sheth Publishers, Nagpur.
   

5. Fundamental Mathematics by P.N.Arora, S.Chand & Sons.