Page 7 - Mathematics Class - XII

4.4 To construct an open box of maximum volume from a given rectangular sheet by cutting equal 60
squares from each corner.
4.5 To find the time when the area of a rectangle of given dimensions become maximum, if the length 63
is decreasing and the breadth is increasing at given rates.

4.6 To verify that amongst all the rectangles of the same perimeter, the square has the maximum area. 66

TOPIC - 5: Integrals

b
5.1 To evaluate the definite integral 1 xdx as the limit of a sum and verify it by actual integration. 70
2
a
UNIT - IV : VECTORS AND THREE-DIMENSIONAL GEOMETRY

TOPIC - 6: Vector Algebra
      

a b
6.1 To verify geometrically that a b c 74
a c
6.2 To verify that angle in a semi-circle is a right angle, using vector method. 77
TOPIC - 7: Three-Dimensional Geometry

7.1 To locate the points to given coordinates in space, measure the distance between two points in space 81
and then to verify the distance using distance formula.
7.2 To measure the shortest distance between two skew lines and verify it analytically. 84

UNIT - VI : PROBABILITY

TOPIC - 8: Probability

8.1 To explain the computation of conditional probability of a given event A, when event B has already 88
occurred, through an example of throwing a pair of dice.

PROJECTS
1. Formation of differential equation to explain the process of cooling of boiled water to a given room 93
temperature.
2. Estimation of the population of a particular region/country under the assumptions that there is no 94
migration in or out of the existing population in a particular year.

3. History and contributions of various Indian Mathematicians like Aryabhatta, Brahmagupta, Mahavira, 95
Bhaskaracharya, Srinivasa Ramanujan and many more in the field of Mathematics.