Vidya Niketan

Cinema Road, Mahnar (Vaishali)

Affiliated to CBSE New Delhi
An ISO 9001:2015 Certified English Medium School

Class XII
Mathematics
Project
Project work in mathematics may be performed individually by a
student or jointly by a group of students. These projects may be in the
form of construction such as curve sketching or drawing of graphs,
etc. It may offer a discussion of a topic from history of mathematics
involving the historical development of particular subject in mathematics/
topics on concepts. Students may be allowed to select the topics of
their own choice for projects in mathematics. The teacher may act as
a facilitator by creating interest in various topics. Once the topic has
been selected, the student should read as much about the topic as is
available and finally prepare the project.
Project 1
To minimise the cost of the food, meeting the dietary requirements of the staple
food of the adolescent students of your school.

Task to be done

(i) Make a survey of atleast 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 pulse 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.

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.
Task 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 t (say). Let
P(t): denote the population in a particular year t
B(t): denote the number of births in one year between t and t + 1.
D(t): denote 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

B(t)
b=
P(t ) represents the birth rate for the time interval t to t + 1.

D(t)
d=
P(t ) represents death rate for the time interval t to t + 1.

5. From (1), we have

P ( t + 1) = P (t) + B (t) – D (t)

B(t) D(t)
= P (t) [1 + – ]
P(t ) P(t)
= P (t) (1 + b – d) (2)
6. Taking t = 0 in equation (2), we get
P (1) = P (0) (1 + b – d).
For t = 1, we get
P (2) = 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 and death rate remains the same for consecutive
years. P(0) denote 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.
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.
Tasks to be done
1. Choose any corner of your classroom as the origin.
2. Take three perpendicular edges of walls as x–, y– and z-axes.
3. Find the coordinates of each corner of the room, corners of windows,
doors and blackboard etc.
4. Find the coordinate of the tips of ceiling fan, bulbs 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.
Project 4
Formation of differential equation to explain the process of cooling of boiled
water to a given room temperature.
Task 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 hour till the temperature
of the water reaches the room temperature. Prepare a corresponding table
as shown below:
Time (t) Temperature of Room Temperature Difference
at an interval water (T) (P) T–P
1
of hour
2

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.
dT
 T – P.
dt
 dT
or = – k (T – P), k is proportionality constant and minus sign signifier
dt
that temperature is decreasing.

dT
or = – kdt. Integrating, we have
T –P
log |T – P| = – kt + C (1)
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).