Swami Shri Ram Sharan internal Board of Education

Gandhi Vidya Mandir,Sardar Shahar

WORKSHEET
Class 09 - Mathematics

Section A
1. The simplest form of 0.123 is ¯
¯¯
[1]

a) none of these b) 37

330

c) 41

330
d) 41

333

p
2. The value of 0. 2 in the form
¯
¯¯

q
where p and q are integers and q ≠ 0 is [1]

a) 2

9
b) 1

c) 2

5
d) 1

3. The decimal expansion that a rational number cannot have is [1]

a) 0.2528 ¯
¯¯¯
¯
b) ¯
¯¯¯¯¯¯¯¯
0. 2528
¯

c) 0.5030030003... d) 0.25
S
4. The sum of 0. 3 and 0. 4 is [1]
¯
¯¯ ¯
¯¯
BP

a) b)
7 7

11 99

c) 7

10
d) 7

5. The product of a nonzero rational number with an irrational number is always a/an [1]

a) irrational number b) whole number

c) natural number d) rational number

6. If x + 1 is a factor of the polynomial 2x 2
+ kx + 1 , then the value of ‘k’ is [1]

a) 2 b) -3

c) -2 d) 3
7. The degree of a constant polynomial is [1]

a) 3 b) 1

c) 2 d) 0

8. The zeros of the polynomial p(x) = 3x2 - 1 are [1]

a) 1

3
and 3 b) 1
and −1

√3 √3

– –
c) and √3 d) and √3
−1 1

√3 √3

9. (x + 1) is a factor of the polynomial [1]

a) x3 + x2 - x + 1 b) x3 + x2 + x + 1

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 c) x4 + 3x3 + 3x2 + x + 1 d) x4 + x3 + x2 + 1

10. The zeroes of the polynomial 3x 2

− 5x − 2 , are: [1]

a) −1

3
, −2 b) −1

3
,2

c) 1

3
,2 d) 1

3
, −2

11. If the x co-ordinate of a point is zero, then this point always lies: [1]

a) in quadrant IV b) in quadrant III

c) on y-axis d) on x-axis
12. The abscissa of any point on the y-axis is [1]

a) 0 b) 1

c) y d) -1
13. The point (7, 0) lies [1]

a) on the positive direction of y-axis b) on the positive direction of x-axis

c) in quadrant IV d) in quadrant II
14. If the coordinates of a point are (-5, 11), then its abscissa is [1]

a) -5 b) 11

c) 5 d) -11
S
15. The perpendicular distance of the point P (3, 4) from the y-axis is [1]
BP

a) 7 b) 4

c) 3 d) 5
16. x = 2, y = -1 is a solution of the linear equation [1]

a) 2x + y = 0 b) x + 2y = 0

c) x + 2y = 4 d) 2x + y = 5
17. The value of k if x = 3 and y = -2 is a solution of the equation 2x - 13y = k is [1]

a) 31 b) 23

c) 32 d) 30
18. x = 5 and y = -2 is the solution of the linear equation. [1]

a) x + 3y = 1 b) 2x + y = 9

c) 3x + y = 0 d) 2x – y = 12
19. Which of the following pair is a solution of the equation 3x – 2y = 7? [1]

a) (-2, 1) b) (1, -2)

c) (5, 1) d) (1, 5)
20. If (4, 19) is a solution of the equation y = ax + 3, then a = [1]

a) 4 b) 6

c) 3 d) 5

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21. It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is: [1]

a) Second Axiom b) Fourth Axiom

c) First Axiom d) Third Axiom

22. Two distinct intersecting lines cannot be parallel to the ________ line. [1]

a) Same b) Each

c) Both Same and Different d) Different

23. Euclid belongs to [1]

a) Rome b) Babylonia

c) Egypt d) Greece
24. The basic facts which are taken for granted, without proof, are called [1]

a) theorems b) axioms

c) propositions d) lemmas
25. How many dimensions does a point have? [1]

a) 3 b) 2

c) 0 d) 1
26. The measure of an angle is five times its complement. The angle measures [1]
S
a) 75° b) 65°

c) 25° d) 35°
BP

27. In the given figure (not drawn to scale), lines XY and MN intersect at O. lf ∠ POY=90°and a : b = 2 : 3, then [1]
∠ XON is equal to ________.

a) 180° b) 126°

c) 130° d) 90°
28. In the given figure (not drawn to scale), if OCD is an isosceles triangle in which OD and OC are equal, then [1]
what will be the value of ∠ OCD?

a) 50° b) 65°

c) 45° d) 70°
29. The number of line segments determined by three given non-collinear points is: [1]

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 a) infinitely many b) two

c) three d) four
30. If two angles are complements of each other then each angle is [1]

a) a reflex angle b) an acute angle

c) a straight angle d) an obtuse angle

31. In △ABC, it is given that base = 12 cm and height = 5 cm. Its area is [1]

a) 60 cm2 b) 30 cm2
–
c) 15√3cm 2
d) 45 cm2

32. The perimeter of an equilateral triangle is 60 m. The area is [1]

– –
a) 10√3 m 2
b) 20√3 m
2

– –
c) 15√3 m 2
d) 100 √3 m 2

33. If the volume of a sphere is 4851 cm3, then its surface area is [1]

a) 1386 cm2 b) 693 cm2

c) 2079 cm2 d) 1039.5 cm2

34. The volume of a sphere of radius 10.5 cm is [1]

a) 4851 cm3 b) 19404 cm3

S
c) 14553 cm3 d) 9702 cm3
BP

35. The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, the ratio of their curved surface [1]
areas, is

a) 5 : 4 b) 4 : 5

c) 16 : 25 d) 25 : 16
36. If the circumference of the base of a 9 m high conical tent is 44 m, then the volume of air contained in it is [1]

a) 693 m3 b) 924 m3

c) 462 m3 d) 1386 m3

37. The diameter of a sphere is 14 cm. Its volume is [1]

a) 1437 1
cm3 b) 1428 cm3
3

c) 1440 cm3 d) 1439 cm3

38. A histogram is a pictorial representation of the grouped data in which class intervals and frequency are [1]
respectively taken along

a) horizontal axis only b) horizontal axis and vertical axis

c) vertical axis and horizontal axis d) vertical axis only

39. In a bar graph, 0.25 cm length of a bar represents 100 people. Then, the length of bar which represents 2000 [1]
people is

a) 4.5 cm b) 4 cm

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 c) 5 cm d) 3.5 cm
40. In a histogram the area of each rectangle is proportional to [1]

a) the class size of the corresponding class b) cumulative frequency of the corresponding
interval class interval

c) the class mark of the corresponding class d) frequency of the corresponding class
interval interval
Section B
p
41. Express the decimal 0.3178 in the form
¯
¯¯¯¯¯¯
¯

q
, where p, q are integers and q ≠ 0. [2]
0 0

42. Evaluate:
2 +7

0
. [2]
5

43. Find the value of k, if x - 1 is a factor of p(x) : p(x) = x

2
+ x+ k . [2]

44. Factorise : 27x3 + y3 + z3 - 9xyz. [2]

45. Factorise: x2 + 9x + 18 [2]

46. In which quadrant will the point lie, if : [2]

(i) The y-coordinate is 3 and the x-coordinate is –4?
(ii) The x-coordinate is –5 and the y-coordinate is –3?
(iii) The y-coordinate is 4 and the x-coordinate is 5?
(iv) The y-coordinate is 4 and the x-coordinate is –4?
47. Name the quadrant in which the point lies :(i) A(1, 1) (ii) (–2, –4) (iii) C(1, –2). [2]
48. Find four solutions for the following equation: x + y = 0 [2]
S
49. Write two solutions of the equation 4x - 5y = 15. [2]
BP

Section C
50. In fig. write the Co-ordinates of the points and if we join the points write the name of fig. formed. Also write [3]
Co-ordinate of intersection point of AC and BD.

51. In fig find the vertices' co-ordinates of △ABC [3]

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52. In figure, if PQ || ST, ∠ PQR = 110o and ∠ RST = 130o, find ∠ QRS. [3]

53. In figure, AB || CD, find the value of x [3]

Section D
S
54. The length of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the [5]
triangle and the height corresponding to the longest side
BP

55. Two sides of a triangular field are 85 m and 154 m in length and its perimeter is 324 m. Find the area of the [5]
field.
56. An iron pillar consists of a cylindrical portion 2.8 m high and 20 cm in diameter and a cone 42 cm high is [5]

surmounting it. Find the weight of the pillar, given that 1 cm3 of iron weighs 7.5 g.
57. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the [5]
hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.
58. A tent is in the shape of a cylinder, surmounted by a conical top. If the height and diameter of the cylindrical part [5]
are 3.5 m and 6 m, and slant height of the top is 4.2 m, find the area of canvas used for making the tent. Also,
find the cost of canvas of the tent at the rate of ₹ 500 per m2.
59. In a study of diabetic patients in a village, the following observations were noted: [5]

Age in years 10-20 20-30 30-40 40-50 50-60 60-70

Number of
2 5 12 19 9 4
patients

Represent the above data by a frequency polygon.

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