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## Sample question paper (Released on Scheme change)

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1 | 22103-Sample-question-paper.pdf |

## Previous years question papers

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1 | 22103-2018-Winter-question-paper[Msbte-study-resources].pdf | |

2 | 22103-2018-Summer-question-paper.pdf |

## Model answer paper pdf of previous years

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1 | 22103-2018-Winter-model-answer-paper.pdf | |

2 | 22103-2018-Summer-model-answer-paper.pdf |

## Recommended Books and Notes

## Syllabus Details

Basic Mathematics (common) Course Code: ................. Maharashtra State Board of Technical Education (MSBTE) I – Scheme II – Semester Course Curriculum Course Title: Basic Mathematics (Common) (Course Code: ................... ) Diploma Programme in which this course is offered Semester in which offered Common to all programmes First 1. RATIONALE Mathematics is the core course to develop the competencies of most of the technological courses. This basic course of Mathematics is being introduced as a foundation which will help in developing the competency and the requisite course outcomes in most of the engineering diploma programmes to cater to the needs of the industry and thereby enhance the employability. This course is an attempt to initiate the multi-dimensional logical thinking and reasoning capabilities. It will help to apply the principles of basic mathematics to solve related technology problems. Hence, the course provides the insight to analyze engineering problems scientifically using logarithms, determinants, matrices, trigonometry, coordinate geometry, mensuration and statistics. 2. COMPETENCY The aim of this course is to help the student to attain the following industry identified competency through various teaching learning experiences: • Solve broad-based technology problems using the principles of basic mathematics. 3. COURSE OUTCOMES (COs) The theory, practical experiences and relevant soft skills associated with this course are to be taught and implemented, so that the student demonstrates the following industry oriented COs associated with the above mentioned competency: a. Apply the concepts of algebra to solve engineering related problems. b. Utilize basic concepts of trigonometry to solve elementary engineering problems. c. Solve basic engineering problems under given conditions of straight lines. d. Solve the problems based on measurement of regular closed figures and regular solids. e. Use basic concepts of statistics to solve engineering related problems. 4. TEACHING AND EXAMINATION SCHEME Teaching Scheme Total Credits Examination Scheme (In Hours) (L+T+P) Theory Marks Practical Marks Total Marks L T P C ESE PA ESE PA 100 4 2 - 6 70 30* - - (*): Under the theory PA, Out of 30 marks, 10 marks are for micro-project assessment to facilitate integration of COs and the remaining 20 marks is the average of 2 tests to be taken during the semester for the assessment of the cognitive domain LOs required for the attainment of the COs. NITTTR Bhopal-MSBTE/I- Scheme/17 Page 1 of 7 Basic Mathematics (common) Course Code: ................. Legends: L-Lecture; T – Tutorial/Teacher Guided Theory Practice; P - Practical; C – Credit, ESE - End Semester Examination; PA - Progressive Assessment. 5. COURSE MAP (with sample COs, Learning Outcomes i.e.LOs and topics) This course map illustrates an overview of the flow and linkages of the topics at various levels of outcomes (details in subsequent sections) to be attained by the student by the end of the course, in all domains of learning in terms of the industry/employer identified competency depicted at the centre of this map. Topic 5.2 Mean deviation and standard deviation from mean of grouped and ungrouped data LO 5b – Calculate mean and standard deviation of discrete and grouped data. CO (d) - Solve the problems based on measurement of regular closed figures and regular solids Topic 5.3 Variance and coefficient of variance LO 5c - Determine the variance and coefficient of variance of grouped and ungrouped data CO (e) - Use basic concepts of statistics to solve engineering related problems Competency Solve related technology problems using the principles of basic mathematics. CO (b) - Utilize basic concepts of trigonometry to solve elementary engineering problems Topic 3.1 Straight line and slope of straight line LO 3a – Calculate angle between given straight line. Topic 1.2. Determinant and CO (c) - Solve basic matrices engineering problems under given conditions of straight lines LO 1c- Calculate the area of triangle by determinant method CO (a) – Apply the concepts of algebra to solve engineering related problems. LO 4c - Compute LO 1b- Solve given surface area and volume problems based on of regular solids laws of logarithm LO 2c - Employ concept of factorization and de- factorization formulae to solve engineering problems Topic 4.2 Volume Topic 1.1. Laws of cuboids, cone, of logarithm cylinders and sphere Topic 2.2 Problem based on factorization and defactorization formulae Legends CO - Course Outcome LO in Cognitive ADO - Affective Domain Domain Outcome Topic Figure 1 - Course Map 6. SUGGESTED PRACTICALS/ EXERCISES The tutorials in this section are LOs (i.e.sub- components of the COs) to be developed and assessed in the student to lead to the attainment of the competency. S. Unit Appro. Tutorials Hrs. No. No. required 1 Solve simple problems of Logarithms based on definition and laws. I 2 2 Solve problems on determinant to find area of triangle, and solution I 2 NITTTR Bhopal-MSBTE/I- Scheme/17 Page 2 of 7 Basic Mathematics (common) Course Code: ................. S. Unit Appro. Tutorials Hrs. No. No. required of simultaneous equation by Cramer’s Rules. 3 Solve elementary problems on Algebra of matrices. I 2 4 Solve solution of Simultaneous Equation using inversion method. I 2 5 Resolve into partial fraction using linear non repeated, repeated, and I 2 irreducible factors. 6 Solve problems on Compound, Allied, multiple and sub multiple II 2 angles. 7 Practice problems on factorization and de factorization. II 2 8 Solve problems on inverse circular trigonometric ratios. II 2 9 Practice problems on equation of straight lines using different forms. III 2 10 Solve problems on perpendicular distance, distance between two III 2 parallel lines, and angle between two lines. 11 Solve problems on Area, such as rectangle, triangle, and circle. IV 2 12 Solve problems on surface and volume, sphere, cylinder and cone. IV 2 13 Solve practice problems on the surface area, volumes and its IV 2 applications. 14 Solve problems on finding range, coefficient of range and mean V 2 deviation. 15 Solve problems on standard deviation. V 2 16 Solve problems on coefficient of variation and comparison of two V 2 sets. Total 32 Note: The above tutorial sessions are for guideline only. The remaining tutorial hours are for revision and practice. 7. MAJOR EQUIPMENT/ INSTRUMENTS REQUIRED - Not applicable - 8. UNDERPINNING THEORY COMPONENTS The following topics/subtopics should be taught and assessed in order to develop LOs in cognitive domain for achieving the COs to attain the identified competency. Unit Major Learning Outcomes Topics and Sub-topics (in cognitive domain) Unit – I 1a. Solve the given simple problem Algebra based on laws of logarithm. 1b. Calculate the area of the given triangle by determinant method. 1c. Solve given system of linear equations using matrix inversion method and by Cramer’s rule. 1d. Obtain the proper and improper partial fraction for the given simple rational function. 1.1 Logarithm: Concept and laws of logarithm 1.2 Determinant and matrices a. Value of determinant of order 3x3 b. Solutions of simultaneous equations in three unknowns by Cramer’s rule. c. Matrices, algebra of matrices, transpose adjoint and inverse of matrices. Solution of simultaneous equations by matrix inversion method. NITTTR Bhopal-MSBTE/I- Scheme/17 Page 3 of 7 Basic Mathematics (common) Course Code: ................. Unit Major Learning Outcomes Topics and Sub-topics (in cognitive domain) d. Types of partial fraction based on nature of factors and related problems. Unit– II 2a. Apply the concept of Compound 2.1 Trigonometric ratios of Trigonome angle, allied angle, and multiple Compound, allied, multiple and try angles to solve the given simple sub-multiple angles (without engineering problem(s). proofs) 2b. Apply the concept of Sub- multiple 2.2 Factorization and de-factorization angle to solve the given simple formulae(without proofs) engineering related problem(s). 2.3 Inverse trigonometric ratios and 2c. Employ concept of factorization related problem. and de-factorization formulae to 2.4 Principle values and relation solve the given simple engineering between trigonometric and problem(s). inverse trigonometric ratio. 2d. Investigate given simple problems utilizing inverse trigonometric ratios. Unit– III 3a. Calculate angle between given two 3.1 Straight line and slope of straight Coordinate straight lines. line Geometry 3b. Formulate equation of straight lines a. Angle between two lines. related to given engineering b. Condition of parallel and problems. perpendicular lines. 3c. Identify perpendicular distance 3.2 Various forms of straight lines. from the given point to the line. a. Slope point form, two point form. 3d. Calculate perpendicular distance b. Two points intercept form. between the given two parallel c. General form. lines. d. Perpendicular distance from a point on the line. e. Perpendicular distance between two parallel lines. Unit-IV 4a. Calculate the area of given triangle 4.1 Area of regular closed figures, Mensurati and circle. Area of triangle, square, on 4b. Determine the area of the given parallelogram, rhombus, trapezium square, parallelogram, rhombus and circle. and trapezium. 4.2 Volume of cuboids, cone, 4c. Compute surface area of given cylinders and sphere. cuboids, sphere, cone and cylinder. 4d. Determine volume of given cuboids, sphere, cone and cylinder. NITTTR Bhopal-MSBTE/I- Scheme/17 Page 4 of 7 Basic Mathematics (common) Course Code: ................. Unit Major Learning Outcomes Topics and Sub-topics (in cognitive domain) Unit –V 5a. Obtain the range and coefficient of 5.1 Range, coefficient of range of Statistics range of the given grouped and discrete and grouped data. ungrouped data. 5.2 Mean deviation and standard 5b. Calculate mean and standard deviation from mean of grouped deviation of discrete and grouped and ungrouped data, weighted data related to the given simple means engineering problem. 5.3 Variance and coefficient of 5c. Determine the variance and variance. coefficient of variance of given 5.4 Comparison of two sets of grouped and ungrouped data. observation. 5d. Justify the consistency of given simple sets of data. Note: To attain the COs and competency, above listed Learning Outcomes (LOs) need to be undertaken to achieve the ‘Application Level’ of Bloom’s ‘Cognitive Domain Taxonomy’ 9. SUGGESTED SPECIFICATION TABLE FOR QUESTION PAPER DESIGN Unit Unit Title Teaching Distribution of Theory Marks No. Hours R U A Total Level Level Level Marks I Algebra 20 02 08 10 20 II Trigonometry 18 02 08 10 20 III Coordinate Geometry 08 02 02 04 08 IV Mensuration 08 02 02 04 08 V Statistics 10 02 05 07 14 Total 64 10 25 35 70 Legends: R=Remember, U=Understand, A=Apply and above (Bloom’s Revised taxonomy) Note: This specification table provides general guidelines to assist student for their learning and to teachers to teach and assess students with respect to attainment of LOs. The actual distribution of marks at different taxonomy levels (of R, U and A) in the question paper may vary from above table. 10. SUGGESTED STUDENT ACTIVITIES Other than the classroom learning, following are the suggested student-related co-curricular activities which can be undertaken to accelerate the attainment of the various outcomes in this course. a. Identify engineering problems based on real world problems and solve with the use of free tutorials available on the internet. b. Use graphical softwares: EXCEL, DPLOT and GRAPH for related topics. c. Use MathCAD as Mathematical Tools and solve the problems of Calculus. d. Identify problems based on applications of matrix and use MATLAB to solve these problems. e. Prepare models to explain different concepts. f. Prepare a seminar on any relevant topic. NITTTR Bhopal-MSBTE/I- Scheme/17 Page 5 of 7 Basic Mathematics (common) Course Code: ................. 11. SUGGESTED SPECIAL INSTRUCTIONAL STRATEGIES (if any) These are sample strategies, which the teacher can use to accelerate the attainment of the various outcomes in this course: a. Massive open online courses (MOOCs) may be used to teach various topics/sub topics. b. ‘L’ in item No. 4 does not mean only the traditional lecture method, but different types of teaching methods and media that are to be employed to develop the outcomes. c. About 15-20% of the topics/sub-topics which is relatively simpler or descriptive in nature is to be given to the students for self-directed learning and assess the development of the LOs/COs through classroom presentations (see implementation guideline for details). d. With respect to item No.10, teachers need to ensure to create opportunities and provisions for co-curricular activities. e. Guide student(s) in undertaking micro-projects. f. Apply the mathematical concepts learnt in this course to branch specific problems. 12. SUGGESTED MICRO-PROJECTS Only one micro-project is planned to be undertaken by a student assigned to him/her in the beginning of the semester. S/he ought to submit it by the end of the semester to develop the industry oriented COs. Each micro-project should encompass two or more COs which are in fact, an integration of practicals, cognitive domain and affective domain LOs. The microproject could be industry application based, internet-based, workshop-based, laboratory-based or field-based. Each student will have to maintain dated work diary consisting of individual contribution in the project work and give a seminar presentation of it before submission. The total duration of the micro-project should not be less than 16 (sixteen) student engagement hours during the course. In the first four semesters, the micro-project could be group-based. However, in higher semesters, it should be individually undertaken to build up the skill and confidence in every student to become problem solver so that s/he contributes to the projects of the industry. A suggestive list is given here. Similar micro-projects could be added by the concerned faculty. a. Prepare charts using determinants to find area of regular shapes. b. Prepare models using matrices to solve simple problems based on cryptography. c. Prepare models using matrices to solve simple mixture problems. d. Prepare charts displaying regular solids. e. Prepare charts displaying regular closed figures. f. Prepare charts for grouped and ungrouped data. 13. SUGGESTED LEARNING RESOURCES S. Title of Book Author Publication No. 1 Higher Engineering Grewal, B.S. Khanna publications, New Delhi, 2015 Mathematics ISBN: 8174091955 2 Advanced Engineering Krezig, Ervin Wiley Publications, New Delhi, 2014 Mathematics ISBN :978-0-470-45836-5 3 Engineering Mathematics Croft, Anthony Pearson Education, New Delhi, 2014 (third edition). ISBN 978-81-317-2605-1 4 Getting Started with Pratap, Rudra Oxford University Press, New Delhi, MATLAB-7 2014, ISBN: 0199731241 NITTTR Bhopal-MSBTE/I- Scheme/17 Page 6 of 7 Basic Mathematics (common) Course Code: ................. S. Title of Book Author Publication No. 5 Advanced Engineering Das, H.K. S. Chand & Co.; New Delhi; 2008, Mathematics ISBN-9788121903455 14. SOFTWARE/LEARNING WEBSITES a. www.scilab.org/ - SCI Lab b. www.mathworks.com/products/matlab/ - MATLAB c. www.dplot.com/ - DPlot d. www.allmathcad.com/ - MathCAD e. www.wolfram.com/mathematica/ - Mathematica f. https://www.khanacademy.org/math?gclid=CNqHuabCys4CFdOJaAoddHoPig g. www.easycalculation.com h. www.math-magic.com