### Clinometer Mathematics Project & Model

CLINOMETER  Mathematics Project Work Working model on Clinometer, Mathematics Project Clinometer, Mathematics Model for measuring the angle of elevation, angle of depression and slope of the objects. Clinometer An inclinometer or clinometer is an instrument used for measuring angle of elevation,  angle of depression and slope of the object. It is also called an inclinometer. Special Protractor For Clinometer Apparatus Wooden Base 30 cm x 20 cm covered with Aluminium edge,  Aluminium Stand with holes at different heights up to 90 cm,  A sample tower made up of an Aluminium, fitted with a simple plyboard of about 120 cm.  Meter scale and permanent markers,  Thread, small weight, laser light, nuts and bolts, Pillar, Screw driver, drilling machine etc. Base of Clinometer Construction of Clinometer First of all we take a wooden base of size 30cm X 20cm and with the help of a drilling machine we arrange a stand and tower at 52 cm distance from each other. Now we make holes on the stand

# Project Work For Class XII

Every student chose any one of the following topics and prepare a project report. Four projects are given with brief description. Students need to write all aspects with full explanation.

Steps followed for Project work

• Certificate
• Bibliography or Acknowledgement
• Introduction of the Project
• Identification and statement of the project
• Planning the project
• Observations from the data collected
• Result
• References
• Interpretation and application of the project.

Scheme of Evaluation

The following weightage are assigned for evaluation at Higher Secondary Stage in mathematics.

 Theory Examination 80 marks Internal Assessment 20 marks Total 100 marks

1.)  Internal assessment of 20 marks, based on school based examinations will have following break-up:

 Performance of activities 5 marks Assessment of Project Work / activities 3 marks Viva-Voice 2 marks Total 20 marks

Assessment of activity work

(a) Every student will be asked to perform two given activities during the allotted time.

(b) The assessment may be carried out by a team of two mathematics teachers, including the teacher who is taking practical classes.

Evaluation of Project Work

a) Every student will be asked to do at least one project based on the concepts learnt in the classroom.

b) The project may be carried out individually (or in a group of two or three students.)

c) Weightage of 3 marks for the project may be as under.

 Identification and statement of the project 1/2 marks Planning the project 1/2 marks Procedure adopted 1 marks Observations from data collected 1/2   marks Interpretation and application of the result 1/2   marks Total 3 marks

Sample Project

Students can see the sample project work on the topic Vectors, Conic Sections and Three Dimensional Geometry.
For complete explanation

# SAMPLE  PROJECT - 1

To minimize the cost of the food, meeting the dietary requirements of the staple food of the adolescence students of your school.

(i) Make a survey of at least 100 students to find which staple food they consume on daily basis.

(ii) Select two food items constituting one cereal and one pulse.

(iii) Find from dietician the minimum requirement of protein and carbohydrate for an adolescent and also find the content of protein  and carbohydrate in 1 Kg. of selected cereal and pulses respectively.

(iv) Find the minimum cost of the selected cereal and pulse from market.

(v) Formulate the corresponding Linear Programming problem.

(vi) Solve the problem graphically.

(vii) Interpret the result.

# SAMPLE  PROJECT - 2

Estimation of the population of a particular region/country under the assumptions that there is no migration in or out of the existing population in a particular year.

1. find the population of a selected region in a particular year.

2. Find the number of births and number of deaths in the existing population in a particular year (say).

Let,  P(t): denote the population in a particular year t

B(t): denotes the number of births in one year between t and t + 1.

D(t): denotes the number of deaths in one year between t and t + 1.

3. Obtain the relation

P(t + 1) = P(t) + B(t) - D(T)  ………………..  (1)

4. Assume that

5.    From equation  (1) , we have

P(t + 1)     = P(t) + B(t) - D(t)

P(t + 1)   = P(t) (1 + b - d)  ………………..   (2)

6. Putting, t = 0 in equation (2), we get

P(1) = P(0) (1 + b - d).

For t = 1,we get

P(2) = P(1) (1 + b - d)

= P(0) (1 + b – d)(1 + b – d)

= P(0) (1 + b – d)2

Continuing above equation, we get

P(t) = P(0) (1 + b - d)t         ………………………….   (3)

Here it is assumed that birth rate remains the same for consecutive years .P(0) denotes the initial population. Equation (3) gives the mathematical model for calculation the population in t year.

7. Using calculator find the population in different number of years.

8. compare the population data obtained theoretically and draw the inferences.

# SAMPLE PROJECT - 3

Finding the coordinates of different points identified in your classroom using the concepts of three  dimensional geometry and also find the distances between the identified points

1. Choose any corner of your class room as the origin

2. Take three perpendicular edges of walls as x-axis, y-axis and z-axis.

3. Find the coordinates of each corner of the room, corners of the windows, doors and blackboard etc.

4. Find the coordinate tips of ceiling fan and all other possible points in the space of the classroom.

5. Find the distances between different points by measurement as well as by using distance formula.

6. Find the coordinates of the diagonals of the room and length of the diagonals by distance formula.

# SAMPLE PROJECT - 4

Formation of differential equation to explain the process of cooling of boiled water to give room temperature

1. Boil 1 litre of water in a pan/beaker

2.Note the room temperature and the temperature of the boiled water.

3. Note the temperature at an interval of every half till the temperature of the water reaches the room temperature. Prepare a corresponding table as shown below:

 Time (t) at an interval of ½ hour Temperature of water(T) Room Temperature(P) Difference(T – P)

4) Let T denote the temperature of the boiled water at time t. P denote the room temperature under the assumption it remains constant throughout the experiment.

5. Find the value of C and k, by using two initial values of T and t from the observation table to get the particular solution of the differential equation(1).

# List of other projects that student may chose

1. Project on history of Mathematicians. It may include history of Indian mathematicians such as Aryabhata, Brahmgupta, Varahamihir, Sridhara, Bhaskaracharya, Ramanujan etc. and history of foreign mathematicians such as Cantor, Pythagoras, Thales, Euclid, Appollonius, Descartes, Fermat, Leibnitz, Euler, Fibonac, Gauss, Newton, etc.

2. On linear programming problems related to day-to-day life like collecting data from families of their expenditures and requirements from the factories to maximum out put.

3. Collect data from dieticians, transporters, agents and formulate linear programming problems.

4. Make a chart of the formulae of applications of calculus.

5. Applications of conic sections, vectors, three dimensional geometry, calculus etc., in Mathematics and Physics.

6. Mathematics and Chemistry : Study structure of organic compounds.

7. Mathematics and Biology : Study of science of heredity etc.

8. Mathematics and Music.

9. Mathematics and Environment.

10. Mathematics and Arts : Construction of shapes using curves.

11. Mathematics and Information and Communication Technology : Writing of Mathematical Programme, flow charts, algorithm, circuit diagrams etc.

12. Collection of statistical data and analyzing it for standard deviation and mean deviation.

13. Observes the various patterns and properties in Pascal’s triangle and make a project.

14. Prepare a project based on the Fibonacci sequence, their properties and similar pattern found in nature.

15. Form a differential equation for the growth of bacteria in different environments.

16. Study the nature of mathematics and make a project showing where three aspects of nature of mathematics – formalism, logic, intuition is applied in the development of mathematics.

## Mathematics Project Work for Class XI

Project work based on Chapter 7 : PERMUTATIONS AND COMBINATIONS

This project work based on the Method of finding the Rank or Dictionary order of any English word with the help of Permutations and combinations.

Work Assigned to the Students
Every student is asked write any 10 different English words from their surroundings and find the Rank or dictionary order of that words with one method and then verified with second method. Also conclude both the methods by comparing.
For any help for the project work on RANK OF ENGLISH ALPHABET, Click Here

Project Work based on Chapter 11 : CONIC SECTIONS

This project work is based on the collecting different types of conic sections and interpret the data.

Work Assigned to the Students
Every student or students in small groups are asked collect all the information of different types of conic sections like Circle, Parabola, Ellipse and Hyperbola and write in their project file.
Students may do the following
1) Introduction, definitions and sources of conic sections.
2) Topic-wise pictures of different conic sections.
3) Explanation of all the terms related to the different conic sections like, axis, foci, directrix, major axis, minor axis, length of latex rectum, eccentricity, transverse axis and conjugate axis etc.
4) Combinations of all conic sections with the help of Geo-Gerba app (Picture of smiley)
For any help on the Project Work on Conic Section Click Here

1. 2. Collect data from dieticians, transporters, agents and formulate linear