NTRCA college written syllabus

E:\NTRCA\Exam\17th Exam'20\Written\Syllabus\Written_College level_17th Exam-2020 (1-52 code) (Main).doc    32 
 
পলদর িাম: প্রভাষক (গশণত্) 
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Examination Duration: Three (03) Hours 
 
Instructions: Candidates will have to answer 10 questions prepared from 10 units each carrying 10 
marks. . Each question will have 2 to 3 sub items (e. g. a, b, c). The distribution of marks for each 
question can be 5+5, 4+6, 3+7, 2+3+5, 2+4+4. Question will be prepared following bloom’s 
taxonomy of cognitive learning.       A minimum of 20% marks should be allotted to higher order 
questions which require  analyzing, evaluating, complex problem solving or creating/synthesizing. 
There will be alternatives for any three questions.   An alternative question must be prepared from the 
same unit with same structure covering same sub-domain and marks distribution.   
 
 Assessment Targets 
Candidates will be able to- 
Contents Marks 
1a 
• explain order properties of real numbers 
1b 
•solve inequality related problems using order  
properties and theorems 
 
1c 
•carry out the operations of complex numbers 
• solve equations of complex numbers 
• sum up algebraic and trigonometric  
series 
Unit 1 
    Real Number System: Field and order 
properties, Natural numbers, Integers 
and rational numbers, Absolute value 
and their properties, Basic inequalities. 
(Including inequalities of me ans, powers; 
inequalities of Cauchy, Chebyshev, 
Weierstrass) 
 Complex number system: Complex 
numbers and De Moiver's theorem with 
applications.  
 Summation of series: Summation of 
algebraic and trigonometric series.  
10 
2a 
• define different types of sets and functions. 
2b 
•solve real life problems using functions  
and sets 
 
2c 
•make  a relationship between roots and    
co-efficients of an equation. 
• construct equation with given roots 
• find  nature of the roots of an equation  
Unit 2 
 Set theory:  Set and s ubsets, Set 
operations, Cartesian product of two 
sets, Operations on family of sets.  
 Function:  One-one function, Onto 
function, Inverse function, Domain and 
Range.  
 Theory of Equations: Relations between 
roots and coefficients, Symmetric 
functions of roots, Sum of the powers of 
roots, Synthetic division, Des Cartes rule 
of signs, multiplicity of roots,  
10 
3a 
convert a matrix representation of a system of 
linear equation 
3b 
Solve system of linear equation  
3c 
•find the eigenvalues and eigenvectors of  
2x2 and 3x3 matrices algebraically. 
3d 
Unit 3 
 System of Linear Equations: System of 
linear equations (homogeneous and 
non-homogeneous ) and their solutions, 
application of matrices and 
determinants for solving system of linear 
equations, applications of system of 
equations in real life problems.  
 Linear Transformation: Linear 
10