MATHEMATICS ASSIGNMENT -2016-17
CLASS-VIII
1. Parikshit makes a cuboid of plasticine of sides 5cm,2cm,5cm. How many such
cuboids will he need to form a cube ?
2. Find the cube root of 17576 through estimation.
3. Find the cube root of each of the following numbers by prime factorisaton method.
I)512 II)10648 III)13824
4. State true or false
1. Cube of any odd no. is even.
2. A perfect cube does not end with two zeros.
3. If square of a no. ends with 5 ,then its cube ends with 25
4. There is no perfect cube which ends with 8.
5. The cube of two digit no. may be a 3 digit no. .
6. The cube of two digit no. may have seven or more digits.
7. The cube of single digit no. may be single digit no. .
5. You are told that 1331 is a perfect cube. Can you guess without factorization what is its cube
root? Similarly, guess the cube root of 4913, 12167,32768.
6. Add
i) ab-bc,bc-ca,ca-ab
ii) 2𝑝2 𝑞 2 − 3𝑝𝑞 + 4 , 5 + 7𝑝𝑞 − 3𝑝2 𝑞 2
7. Subtract
i) 4𝑎 − 7𝑎𝑏 + 3𝑏 + 12 from 12𝑎 − 9𝑎𝑏 + 5𝑏 − 3
ii) 3xy + 5yz − 7zx from 5𝑥𝑦 − 2𝑦𝑧 − 2𝑧𝑥 + 10𝑥𝑦𝑧
8. Obtain the volume of rectangular boxes with the following length , breadth and height
respectively.
i) 5𝑎, 3𝑎2 , 7𝑎4
ii) 𝑥𝑦, 2𝑥 2 𝑦, 2𝑥𝑦 2
9. Obtain the product of
i) 𝑥𝑦, 𝑦𝑧, 𝑧𝑥
ii) 𝑎, 2𝑏, 3𝑐, 6𝑎𝑏𝑐
iii) 𝑚, −𝑚𝑛, 𝑚𝑛𝑝
10. Find the product
i)
ii)
2
3
−
9
𝑥𝑦 × (− 10 𝑥 2 𝑦 2 )
10
3
6
𝑝𝑞 3 × (5 𝑝2 𝑞)
11. Simplify 3𝑥 4𝑥 − 5 = 3 and find its value for
1
(i) x=3 (ii)x=2
12. Add
i) 𝑝 𝑝 − 𝑞 , 𝑞 𝑞 − 𝑟 , 𝑟(𝑟 − 𝑝)
ii) 2𝑥 𝑧 − 𝑥 − 𝑦 , 2𝑦(𝑧 − 𝑦 − 𝑥)
13. Subtract
i) 3𝑙(𝑙 − 4𝑚 + 5𝑛) from 4𝑙(10𝑛 − 3𝑚 + 2𝑙)
14. Multiply
i) 2𝑝𝑞 + 3𝑞 2 and 3𝑝𝑞 − 2𝑞 2
ii) 𝑎 + 3𝑏 and (𝑥 + 5)
15. Find the product
i) 5 − 2𝑥 (3 + 𝑥
ii) 𝑝2 − 𝑞 2 (2𝑝 + 𝑞)
16. Simplify
i) 𝑡 + 52 (𝑡 2 − 5)
ii) 𝑥 + 𝑦 2𝑥 + 𝑦 + 𝑥 + 2𝑦 (𝑥 − 𝑦)
iii) 𝑥 + 𝑦 (𝑥 2 − 𝑥𝑦 + 𝑦 2 )
iv) 𝑎 + 𝑏 + 𝑐 (𝑎 + 𝑏 − 𝑐)
17.
i)
ii)
iii)
iv)
Use a suitable identity to get each of the following products.
2𝑦 + 5 (2𝑦 + 5)
2𝑎 − 7 (2𝑎 − 7)
𝑎2 + 𝑏 2 (−𝑎2 + 𝑏 2 )
(7𝑎 − 9𝑏)(7𝑎 − 9𝑏)
18. Use the identity 𝑥 + 𝑎 𝑥 + 𝑏 = 𝑥 2 + 𝑎 + 𝑏 𝑥 + 𝑎𝑏 to find the following product
i) 𝑥 + 3 (𝑥 + 7)
ii) 4𝑥 + 5 (4𝑥 − 1)
iii) (𝑥𝑦𝑧 − 4)(𝑥𝑦𝑧 − 2)
19. Find the following squares by using the identities
i)(6𝑥 2 − 5𝑦)2
ii)(2𝑥𝑦 + 5𝑦)2
20. Simplify
i)(𝑎𝑏 + 𝑏𝑐)2 − 2𝑎𝑏 2 𝑐
ii)(𝑚2 − 𝑛2 𝑚)2 + 2𝑚3 𝑛2
21. Show that
i)(3𝑥 + 7)2 − 84𝑥 = (3𝑥 − 7)2
ii) 𝑎 − 𝑏 𝑎 + 𝑏 + 𝑏 − 𝑐 𝑏 + 𝑐 + 𝑐 − 𝑎 𝑐 + 𝑎 = 0
22. Using identities, evaluate
i) 712
ii) 9982
iii) 297 × 303
iv) (5.2)2
v) (8.9)2
23. Using 𝑎2 −𝑏 2 = 𝑎 + 𝑏 (𝑎 − 𝑏) , find.
i) 512 −492
ii) (1.02)2 − (0.98)2
24. Using 𝑥 + 𝑎 𝑥 + 𝑏 = 𝑥 2 + 𝑎 + 𝑏 𝑥 + 𝑎𝑏 ,find
i) 103 × 104
ii) 9.8 × 9.7
25. Is a square prism same as a cube? Explain.
i)Verify Euler’s formula for these
i)
ii)
ii)Using Euler’s formula find the unknown
Faces
?
5
20
Vertices
6
?
12
Edges
12
9
?
iii) Can a polyhedron have 10 faces , 20 edges and 15 vertices ?
26. Find m so that (−3)𝑚 +1 × (−3)5 = 𝑥(−3)7
27. Simplify and express the result un power notation with exponent
i) (3−7 ÷ 3−10 × 3−5
ii) 2−3 × (−7)−3
28. Find the value of m for which 5𝑚 ÷ 5−3 = 55
29. Find the value of
i) (30 +4−1 ) × 22
ii) (3−1 × 4−1 × 5−1 )0
30. Simplify
i)
ii)
25×𝑡 −4
5−3 ×10×𝑡 −8
(t≠0)
3−5 ×10 −5 ×125
5−7 ×6−5
31. Express in standard form.
i) 6020000000000000
ii) 0.00000000837
32. Express in usual form .
i) 3.02 × 10−6
ii) 3.61492 × 106
33. Express the no.s appreaing in the statement in standard form .
i) Size of a plant cell is 0.00001275 m
34. In astack there are 5 books each of thickness 2mm and 5 paper sheets each of thickness
0.016mm . What is the total thickness of the stack.
35. Find the common factors of the given terms .
i) 16𝑥 3 , −4𝑥 2 , 32𝑥
ii) 3𝑥 2 𝑦 3 , 10𝑥 3 𝑦 2 , 6𝑥 2 𝑦 2 𝑧
Factorise from Q.36 to 41
36. i) 15𝑥𝑦 − 6𝑥 + 5𝑦 − 2
ii) 𝑎𝑥 + 𝑏𝑥 − 𝑎𝑦 − 𝑏𝑦
37.i) 𝑎2 + 8𝑎 + 16
ii) 𝑝2 − 10𝑝 + 25
38. i) 63𝑎2 − 112𝑏 2
ii) 16𝑥 5 −144𝑥 3
39. i) 2𝑥 3 + 2𝑥𝑦 2 + 2𝑥𝑧 2
ii) 𝑎𝑚2 + 𝑏𝑚2 + 𝑏𝑛2 +𝑎𝑛2
40. i) 𝑝4 − 81
ii) 𝑥 4 − (𝑦 + 𝑧)4
41. 𝑝2 + 6𝑝 + 8
42. Divide 44 𝑥 4 − 5𝑥 3 − 24𝑥 2 by 11𝑥(𝑥 − 8)
43. Divide 𝑧 5𝑧 2 − 80 by 5𝑧(𝑧 + 4)
44. Divide
i) (5𝑥 2 − 6𝑥) ÷ 3𝑥
ii) (𝑝3 𝑞 6 − 𝑝6 𝑞 3 ) ÷ 𝑝3 𝑞 3
45. i) 10𝑦(6𝑦 + 21) ÷ 5(2𝑦 + 7)
ii) 9𝑥 2 𝑦 2 (3𝑧 − 24) ÷ 27𝑥𝑦(𝑧 − 8)
46. Divide as directed
i)5 2𝑥 + 1 3𝑥 + 5 ÷ (2𝑥 + 1)
ii) 26𝑥𝑦 𝑥 + 5 (𝑦 − 4) ÷ 13𝑥(𝑦 − 4)
47. Factorise the expression and divide them as directed.
i) 𝑦 2 + 7𝑦 + 10 ÷ (𝑦 + 5)
ii) 𝑚2 − 14𝑚 − 32 ÷ (𝑚 + 2)
48. Find and correct the errors in the following mathematical statement.
(2𝑥)2 + 4 2𝑥 + 7 = 2𝑥 2 + 8𝑥 + 7
49.
2𝑎 + 3𝑏 𝑎 − 𝑏 = 2𝑎2 − 3𝑏 2
50.
𝑎 + 4 𝑎 + 2 = 𝑎2 + 8
51.
𝑎 − 4 𝑎 − 2 = 𝑎2 − 8
52. Draw the line passing through (2,3) and (3,2) . Find the coordinates of the points at which
this line meets the x–axis and y-axis .
Draw the graph with suitable scales .
53. Distance travelled by a car.
Time ( in hours )
6 am
7 am
8 am
9 am
Distance ( in km )
40
80
120
160
i) How much distance did the car cover during the period 7:30 am to 8:30 am?
ii) What was the time when the car had covered a distance of 100 km since its start?
54. Is it a linear graph?
Side of square ( in cm )
Area ( in 𝑐𝑚2 )
2
4
3
9
4
16
5
25
6
36
55. Is it a linear graph?
Side of a square ( in cm ) 2
Perimeter ( in cm )
8
3
12
3.5
14
5
20
6
24
56. Find the values of the letters in each of the following and reasons for the steps involved .
i)
4A
ii) 1 A
iii) A B
+ 9_8
+XA
+ X5
C B_3
9A
CAB
57. If 31z5 is multiplied with 9, where z is a digit, what is the value of z ? You will find that there
are two answers for this problem. Why is this so?
58. If 24x is a multiple of 3, where x is a digit , what is the value of x?
59. The shape of a garden is rectangular in the middle and semi-circular at the ends as shown
in the diagram. Find the area and perimeter of this garden.
7cm
mcc
60. A flooring
20mtile has the shape of a parallelogram whose base 24cm and the correspornding
height is 10cm. How many such tiles are required to cover a floor of area 1080 m2 ?
61. Find the area of a rhombus whose diagonals are of length 10cm and 8.2cm?
62. The area of a trapezium shaped field is 480m2, the distance between two parallel sidesis
15m and one of the parallel side is 20m. Find the other parallel side.
63. The area of rhombus is 240cm2 and one of the diagonals is 16 cm. Find the other diagonal.
64. Length of the fence of a trapezium shaped field ABCD is 120 m. If BC=48 m, CD=17 m and
AD=40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.
65. Find the area of rhombus whose side is 5 cm and whose altitude is 4.8 cm. If one of its
diagonals is8 cm long, find the length of the other diagonal.
66. The floor of a building consists of 3000 tiles, which are rhombus shaped and each of its
diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor if cost per m2
is Rs 4.
67. In a building there are 24 cylindrical pillars. The radius of each pillar is 28 cm and height is 4
m . Find the total cost of painting the curved surface area of all pillars at the rate of Rs8 per m2.
68. Find the height of a cylinder whose radius is 7 cm and the total surface area is 968 cm2.
69. A suitcase with measures 80 cm * 48 cm* 24 cm is to be covered with tarpaulin cloth. How
many meters of tarpaulin of width 96 cm is requires to cover 100 such suitcases?
70. Find the side of a cube whose surface area is 600 cm2?
71. Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of
15m, 10m and 7mrespectively.From each can of paint 100 m2 of area is painted. How many
cans of paint will she need to paint the room.
72. A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How
much sheet of metal is required?
73. The lateral surface area of a hollow cylinder is 4224 cm2. It is cut along its height and
formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet ?
74. A road roller takes 750 complete revolutions to move once over to level a road. Find the
area of the road if the diameter of a road roller is 84 cm and length is 1m.
75. Find the height of a cuboid whose volume is 275 cm3 and base area is 25 cm2.
76. A godown is in the form of a cuboid of measures 60m*40m*30m. How many cuboidal
boxescan be stored in it if the volume of one box is 0.8m3?
77. A rectangular paper or width 14 cm is rolled along its width and a cylinder of radius20 cm is
formed. Find the volume of the cylinder.
78. A rectangular piece of paper 11cm*4cm is folded without overlapping to make a cylinder of
height4 cm. Find the volume of the cylinder.
79. Find the height of a cuboid whose base area is 180cm2 and volume is 900 cm3 ?
80. A cuboid is of dimensions 60cm*54cm*30cm. How many small cubes with side 6 cm can be
placed in the given cuboid ?
81. Find the height of the cylinder whose volume is 1.54m3 and diameter of the base is140 cm.
82. A milk tank is in the form of cylinder whose radius is 1.5m and length is 7 m. Find the
quantity of milk in liters that can be stored in the tank ?
83. A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in
five hours ?
84. In a model of a ship, the mask is 9cm high, while the mask of the actual ship is 12 m high. If
the length of the shipis 28m, how long is the model ship ?
85. Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72
km. What would be her distance covered in the map ?
86. A loaded truck travels14 km in 25 minutes. If the speed remains the same how far can it
travel in 5 hours?
87. There are 100 students in a hostel. Food provision for them is for 20 days. How long will
these provisions last, if 25 more students join the group ?