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
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:
|
Unit test / Pen Test |
10 Marks |
|
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 Download pdf file
To minimize
the cost of the food, meeting the dietary requirements of the staple food of
the adolescence students of your school.
Task to be
done
(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.
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.
Tasks to be
done
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.
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
Tasks to be
done
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.
Formation
of differential equation to explain the process of cooling of boiled water to
give room temperature
Tasks to be
done
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).
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.
Please upload the answers of these projects
ReplyDeleteCollect data from dieticians, transporters, agents and formulate linear
ReplyDeleteprogramming problems. Please help