B.A. 1st Semester Mathematics Examination Scheme (2018-19)

Introduction

The Bachelor of Arts (B.A.) Mathematics program offers students a comprehensive study of mathematical concepts at the undergraduate level. The examination scheme for the 1st semester of the 2018-19 academic year is designed to assess students' understanding of fundamental mathematical principles and their problem-solving capabilities. This scheme provides a structured framework for evaluating students' performance in the initial phase of their mathematical journey.

Overall Examination Structure

The B.A. 1st Semester Mathematics program typically consists of one core paper focusing on foundational mathematical concepts. The examination scheme divides the assessment into two components: theory examination and internal assessment.

Component	Marks	Maximum Marks
Theory Paper	80	100
Internal Assessment	20

Core Paper: Differential Calculus

The core paper for the 1st Semester B.A. Mathematics program is Differential Calculus, which forms the foundation of mathematical analysis and serves as a prerequisite for higher-level mathematics courses.

	Details
Paper Code	MAT-101 or as per university convention
Paper Title	Differential Calculus
Theory Marks	80
Internal Assessment Marks	20
Duration of Examination	3 Hours

Internal Assessment Scheme

The internal assessment component of 20 marks is distributed as follows:

Assessment Component	Marks
Class Attendance	5
Class Assignments	5
Mid-Semester Examination	5
Tutorial/Practical Work	5

Question Paper Pattern

The question paper for Differential Calculus follows a structured format to test various aspects of students' understanding:

Section	Type of Questions	No. of Questions	Questions to Attempt	Marks per Question	Total Marks
A	Very Short Answer Type	10	All	2	20
B	Short Answer Type	6	5	5	25
C	Long Answer Type	4	3	12	36

Syllabus for Differential Calculus

The syllabus for Differential Calculus of B.A. 1st Semester covers fundamental concepts essential for understanding higher mathematics.

Unit I: Limit and Continuity

• - definition of limit
• Properties of limits
• Standard limits
• Continuity and types of discontinuities
• Properties of continuous functions on closed intervals

Unit II: Differentiation

• Definition of derivative and its geometrical interpretation
• Differentiation of algebraic, trigonometric, exponential and logarithmic functions
• Differentiation of implicit functions and parametric functions
• Differentiation of functions represented parametrically
• Logarithmic differentiation
• Successive differentiation
• Leibnitz's theorem and its applications

Unit III: Applications of Differentiation

• Tangents and normals
• Angle of intersection of curves
• Increasing and decreasing functions
• Maxima and minima of functions
• Rolle's Theorem, Mean Value Theorem, and their applications
• Lagrange's Mean Value Theorem
• Cauchy's Mean Value Theorem
• Taylor's Theorem and Maclaurin's Theorem
• Expansions of functions

Unit IV: Partial Differentiation

• Functions of two or more variables
• Partial derivatives
• Homogeneous functions and Euler's theorem
• Total derivatives
• Chain rule
• Change of variables
• Jacobian

Recommended Textbooks

• Differential Calculus by Shanti Narayan
• Differential Calculus for B.A. and B.Sc. Students by R.K. Pachauri
• Calculus by Howard Anton
• Calculus by Thomas and Finney

Examination Guidelines

• Students must bring their admit cards to the examination hall.
• Electronic devices, including calculators, are not permitted unless specifically allowed.
• Students should report at the examination center at least 30 minutes before the commencement of the examination.
• All answers must be written in the prescribed answer book.
• Rough work must be done in the answer book with clear demarcation.
• Any form of malpractice will lead to cancellation of the examination.

Grading System

The grading system for B.A. 1st Semester Mathematics Examination follows the university guidelines:

Marks Range	Grade
75% and above	A (Excellent)
65% - 74%	B (Very Good)
55% - 64%	C (Good)
45% - 54%	D (Satisfactory)
40% - 44%	E (Pass)
Below 40%	F (Fail)

Passing Criteria

To successfully clear the B.A. 1st Semester Mathematics Examination, students must obtain:

• Minimum 40% marks in the theory examination separately
• Minimum 40% marks in internal assessment separately
• Minimum 40% marks in aggregate

Evaluation and Result Declaration

The answer scripts are evaluated by appointed examiners following a standardized marking scheme. After evaluation, the results are declared according to the university's schedule. Students can access their results through the official university website or campus notice boards.

Re-evaluation and Re-checking

In case of dissatisfaction with the results, students may apply for:

• Re-checking of answer scripts (to verify totaling)
• Re-evaluation of answer scripts (detailed re-assessment)

Applications for re-evaluation or re-checking must be submitted within the specified timeframe after result declaration, along with the prescribed fee. The exact procedure and timeline should be ascertained from the university office.

Preparation Tips

• Understand the fundamental concepts thoroughly rather than rote memorization.
• Practice solving a variety of problems from each unit of the syllabus.
• Solve previous years' question papers to familiarize with the examination pattern.
• Prepare concise notes highlighting important formulas, theorems, and concepts.
• Focus on time management during practice sessions to complete the paper within the allocated time.
• Seek clarification from faculty members whenever required.
• Form study groups to discuss complex topics and solve problems collectively.

Conclusion

The B.A. 1st Semester Mathematics Examination Scheme for the 2018-19 academic year provides a comprehensive framework for evaluating students' understanding of Differential Calculus. Success in this examination requires consistent effort, conceptual clarity, and systematic preparation. By following the outlined syllabus, understanding the examination pattern, and adhering to the preparation guidelines, students can approach the examination with confidence and achieve favorable results.