# Class 10 - Formative Assessment 3 - Mathematics (2016-2017)

Posted in QP Class X

Section A [1 x 4 = 4M]

1.) Check whether the following equation is quadratic or not:

$$(x + 1)^2 = 2 ( x + 3)$$

2.) What will be the nature of roots of the following quadratic equation:

$$x^2 + x + 1$$

3.) Find an, where a = 10, d = 4 and n = 7.

4.) Find whether the following are in A.P. or not?

$$\sqrt{2}$$, $$\sqrt{8}$$, $$\sqrt{18}$$, $$\sqrt{32}$$, ............ etc

Section B [ 2 x 5 = 10M]

5.) Find the two numbers whose sum is 25 and the product is 156?

6.) Find the value of k for the following quadratic equaltion, so that the  roots are equal:

$$2x^2 + kx + 3 = 0$$

7.) Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.

8.) A tower stands verticaaly on the ground. From a point on the ground which is 15m away from the foot of the tower is found to be 60°. Find the height of the tower. (The angle of elevation of top of the tower is 60°)

9.) Find the missing terms: 18, ____, ____, 3

SECTION - C [3 x 6 = 18M)

10.) A train travels 360km at uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for same journey. Find the speed of the train.

11.) Find the sum of the first 24 terms of the list of numbers (which are in A.P.) whose nth term is given by an = 3 + 2n

12.) How many three digit numbers are divisible by 3?

13.) Find the sum of first ten multiples of 7.

14.) Find the roots of the quadratic equation by using completing square method: $$3x^2 - 5x + 2 = 0$$

15.) An observer 1.5m tall is 28.5m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney.?

SECTION - D [4 x 2 = 8M]

16.) From the top of 100m tall building above sea level, the angles of depressions of two ships are 45° and 60°. If one ship is behind the other on the same side of the tower, find the distance between them.

17.) In the centre of a rectangular lawn of dimensions 50m x 40m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m2. Find the length and breadth of the pond.