#### First Term Half Test

9th Standard

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Maths

Time : 02:00:00 Hrs
Total Marks : 100

Section-A

10 x 1 = 10
1. If A∪B = A∩B, then

(a)

A ≠ B

(b)

A = B

(c)

A ⊂ B

(d)

B ⊂ A

2. If X = {x : x = 4(n – 1), n ∈ N} and Y = {y : y = 3n – 2n – 1, n ∈ N}, then X∪Y is

(a)

W

(b)

X

(c)

Y

(d)

N

3. Sets having the same number of elements are called ___________

(a)

overlapping sets

(b)

disjoints sets

(c)

equivalent sets

(d)

equal sets

4. Which one of the following has terminating decimal expansion?

(a)

$\frac { 7 }{ 9 }$

(b)

$\frac { 8 }{ 15 }$

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 5 }{ 32 }$

5. Let the polynomials be (A)–13q5 + 4q2 + 12q (B)(x2 +4 )(x2 + 9) (C)4q8 – q6 + 2 (D)-$\frac {5}{7}$y12+y3+y5
Then ascending order of their degree is

(a)

A,B,D,C

(b)

A,B,C,D

(c)

B,C,D,A

(d)

B,A,C,D

6. The area of a rectangle with length $2l^{ 2 }m$ and breadth $3l^{ 2 }m$ is_______________________

(a)

$6l^{ 3 }m^{ 3 }$

(b)

$l^{ 3 }m^{ 3 }$

(c)

$2l^{ 3 }m$

(d)

$4l^{ 3 }m^{ 3 }$

7. The correct statement out of the following is

(a)

ΔABC ≅ ΔDEF

(b)

ΔABC ≅ ΔDEF

(c)

ΔABC ≅ ΔFDE

(d)

ΔABC ≅ ΔFED

8. One angle of a parallelogram is a right angle. The name of the quadrilateral is ______

(a)

square

(b)

rectangle

(c)

rhombus

(d)

kite

9. The point M lies in the IV quadrant. The coordinates of M is _______

(a)

(a,b)

(b)

(–a, b)

(c)

(a, –b)

(d)

(–a, –b)

10. On which quadrant does the point (- 4, 3) lie?

(a)

I

(b)

II

(c)

III

(d)

IV

11. Section-B

5 x 1 = 5
12. Consider the set A = {Ashwin, Muralivijay , Vijay Shankar, Badrinath }.
Fill in the blanks with the appropriate symbol $\in$ or $\notin$.
Muralivijay ____ A.

()

Muralivijay $\in$ A.

13. Consider the following sets A = {0, 3, 5, 8}, B = {2, 4, 6, 10} and C = {12, 14,18, 20}.
18 _______ B.

()

$\notin$

14. Sets having atleast one element in common are called ___________

()

overlapping sets

15. The value of $3\sqrt { 3 } +\sqrt { 3 }$ is ______________.

()

$4\sqrt { 3 }$

16. The sum of 7x2 - 4x + 5 and 9x - 10 is __________

()

7x2 + 5x - 5

17. Section-C

15 x 2 = 30
18. Write all the subsets of A = {a, b}.

19. If A={1, 2, 6} and B={2, 3, 4} , find A∪B.

20. Draw a Venn diagram similar to one at the side and shade the region representing the following sets

(A – B)′

21. In a class, all students take part in either music or drama or both. 25 students take part in music, 30 students take part in drama and 8 students take part in both music and drama. Find
(i) The number of students who take part in only music.
(ii) The number of students who take part in only drama.
(iii) The total number of students in the class.

22. Which of the following are sets?
The Collection of good Hockey players.

23. Represent the following sets in descriptive form.
R = {x : x $\in$ N, x < 5}

24. Identify the following sets as null set or singleton set.
D = The set of all triangles having four sides.

25. Using the given Venn diagram, write the elements of
B

26. Using the given Venn diagram, write the elements of
A'

27. If U={a, b, c, d, e, f, g, h}, A={b, d, f, h} and B={a, d, e, h}, find the following sets. (A′)′

28. Find the value of the polynomial f (y) =  6y - 3y2 + 3 at y = 0

29. Find the number of zeros of the following polynomials represented by their graphs.

30. Section-D

11 x 5 = 55
31. Discuss with your friends and give examples of subsets of sets from your daily life situation.

32. The length of a rectangle is (3x+2) units and it’s breadth is (3x–2) units. Find its area in terms of x. What will be the area if x = 20 units.

33. The base of a parallelogram is (5x+4). Find its height, if the area is 25x2–16.

34. If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 –2x+ a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.

35. Construct an isosceles triangle PQR where PQ= PR and ㄥQ = 500, QR = 7cm. Also draw its circumcircle.

36. Which type of quadrilateral satisfies the following properties?
(i) Both pairs of opposite angles are equal in size.
(ii) Both pairs of opposite sides are equal in length.
(iii) Each diagonal is an angle bisector.
(iv) The diagonals bisect each other.
(v) Each pair of consecutive angles is supplementary.
(vi) The diagonals are equal.
(vii) Can be divided into two congruent triangles.

37. The side of a rhombus is 13 cm and the length of one of the diagonal is 24 cm. Find the length of the other diagonal?

38. If a triangle and a parallelogram lie on the same base and between the same parallels, then prove that the area of the triangle is equal to half of the area of parallelogram.

39. Show that the points A(7,10), B(-2,5), C(3,-4) are the vertices of a right angled triangle.

40. Find the type of triangle formed by (-1, -1), (1, 1) and ($-\sqrt{13},\sqrt{13}$)