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 2”.
2. To verify that for two sets A and B, n(AxB) = 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 verify the distributive law for three given non-empty sets, A, B, and C, that is, A (B C) = (A B) (A C).
5. To identify a relation and a function.
6. To distinguish between a relation and a function.
7. To verify the relation between the degree measure and the radian measure of an angle.
8. To find the values of sine and cosine functions in the second, third, and fourth quadrants using their given values in the first quadrant.
9. To prepare a model to illustrate the values of the sine function and cosine function for different angles that are multiples of r/2 and r.
10. To plot the graphs of sin x, sin 2x, 2sin x and sin x/2, using same coordinate axes.
11. To interpret geometrically the meaning of i = -1 and its integral powers.
12. To obtain a quadratic function with the help of linear functions graphically.
13. To verify that the graph of a given inequality, say 5x + 4y – 40 < 0, of the form ax + by + c < 0, a, b > 0, c < 0, represents only one of the two half planes.
14. To find the number of ways in which three cards can be selected from given five cards.
15. To construct a Pascal’s Triangle and to write binomial expansion for a given positive integral exponent.
16. 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 establish the formula for the sum of the cubes of the first n natural numbers.
19. To verify that the equation of a line passing through the point of intersection of two lines a1x + b1y + c1 = 0 is of the form (a1x + b1y + c1) + y (a2x + b2y + c2) = 0.
20. To construct different types of conic sections.
21. To construct a parabola.
22. To trace a parabola by an alternative method of construction.
23. To construct an ellipse using a rectangle.
24. To construct an ellipse with given major and minor axes.
25. To construct an ellipse when two fixed points are given.
26. To explain the concept of 3-dimensional geometry and octant by three mutually perpendicular planes in space.
27. To find analytically the limit of a function Lt x² – c² / x – c
28. To verify the geometrical significance of the derivative.
29. To obtain truth values of compound statements of the type p < q by using switch connections in series.
30. To obtain truth values of compound statements of the type p > q by using switch connections in series.
31. To write the sample space, when a die is rolled many times.
32. To write the sample space, when a coin is tossed once, twice, thrice etc.
