1. To find the number of subsets of a given set and verify that if a set has n number of elements, then the total number of subsets is 2n.
2. To verify that for two sets A and B, n (A x B) = pq and the total number of relations from A to B is 2pq, where n (A) = p and n (B) = q.
3. To represent set-theoretic operations using Venn diagrams.
4. To identify a relation and a function.
5. To distinguish between a relation and a function.
6. To verify the relation between the degree measure and the radian measure of an angle.
7. To find the value of sine and cosine functions in the second, third, and fourth quadrants using their given values in the first quadrant.
8. To prepare a model to illustrate the values of the sine function and cosine function for different angles that are multiples of
9. To plot the graphs of sin x, sin 2x, 2 sin x, and sin x/2 using the same coordinate axes.
10. To interpret geometrically the meaning of i = -1 and its integral powers.
11. To obtain a quadratic function with the help of linear functions graphically.
12. To verify that the graph of a given inequality, say 2x + 3y - 6 < 0, of the form ax + by + c < 0, a, b > 0, c < 0, represents only one of the two halves.
13. To find the number of ways in which three cards can be selected from the given five cards.
14. To construct a Pascal’s Triangle and to write binomial expansion for a given positive integral exponent.
15. To obtain a formula for the sum of squares of the first n natural numbers.
16. An alternative approach to obtain a formula for the sum of squares of the first n natural numbers.
17. To demonstrate that the arithmetic mean of two different positive numbers is always greater than the geometric mean.
18. To verify that the equation of a line passing through the point of intersection of two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 is of the form a1x + b1y + c1 + (a2x + b2y + c2) = 0
19. To construct different types of conic sections.
20. To construct a parabola.
21. An alternative method of constructing a parabola.
22. To construct an ellipse using a rectangle.
23. To construct an ellipse with a given major axis and minor axis.
24. To construct an ellipse when two fixed points are given.
25. To explain the concept of octants by three mutually perpendicular planes in space.
26. To find analytically ………
27. Verification of the geometrical significance of the derivative.
28. To write the sample space when a die is rolled once, twice,....
29. To write the sample space when a coin is tossed once, two times, three times,...
