INTERNATIONAL INDIAN SCHOOL, RIYADH

VIII STD MATHEMATICS

CHAPTER - 12 EXPONENTS AND POWERS- WORK SHEET

Answer for Chapter – 121. [i] 81/100 [ii] 1/16 [iii] 1 [2] [i]16/81 [ii]81/16 [iii]1/625 [3][i]36/25 [ii]1/216 [iii]1/16

4.[i]5/6 [ii]10 [iii]1 [5][i] 50 [ii] 6 [iii]2 [iv] 6 [v] 36/25 [vi] 7/8 [6] [i]2/3 [ii]144a 7. x = -

2 [8] x = - 2 [9] x = -1 [10] a/b = 6/7 [11] 3.72 X 107

12.diameter of the sun is about 100 times the diameter of the earth

13. [i] 7.2 X 10-3 [ii] 9.72 X10-4 [iii] 6.7 X 10-6 [iv] 1.93 X10-7 [v] 8.436 X 10-8 [vi] 8.04X10-1

14.[i] 0.000102 [ii] 0.00000982 [iii]0.0000000675 [iv]0.00000000095[v]0.00000088

[vi]0.0000208 [15] [i] 7 X 10-8 [ii] 1 X 10-6 m [iii] 1.6 X 10 -19 coulomb [iv] 1.5 X 10 -6 m.

Chapter - 13 DIRECT AND INVERSE PROPORTIONS WORK SHEET

1. A car can cover a distance of 210 km in 5 hrs. How long it takes to cover a distance of 546 km.

2. If a per son deposit Rs.1000 and gets RS.250 as interest for 3 years, how much interest would a deposit of Rs.3600 earn in 3 years with the same rate of interest.

3.68 boxes of a certain commodity require a shelf length of 13.6m.How many boxes of the same commodity would occupy a shelf length of 20.4m?

4.13 men can dig 117 m long trench in one day. How many men should be employed for digging 225m long trench in one day?

5. The length of the, which is 72m high casts a shadow of 80m at a particular time on a day. Find the height of an electric pole, which casts a shadow of 10m under similar conditions.

6. Find the values of a, b, and c in each of the following tables given that x and y are direct proportion

(I)

X 6 15 24 b 21Y 10 a 40 47.

5c

(Ii)

X 8 a 6 2Y 20 17.5 b c

7. If the thickness of a pile of 18 coins is 40mm, find the thickness of a pile of 450 coins.

8.22 men can dig 13 ½ m long trench in one day. How many men should be employed for digging 54m long trench of the same type in one day?

9. If 2/3 piece of iron has a mass of 6 kg weight, then what would be the mass of 5/6 of the iron piece?

10. The speed of two trains are in the ratio 4: 5.If the speed of the first train is 64km/h, what is the speed of the other train?

11. The monthly earnings and monthly saving of Shamali are in the ratio 4:1. If Shamali s monthly Salary is Rs 75000, how much is her annual saving?

12. In 7 days a machine cleans 5. 6 X 10 7 kg weight of iron ore. How much iron ore will it clean in 45 days?

13. Complete the following table by finding the vales of a, b , c and d if x and y vary in Inverse proportion

(I)

(ii)

X 40 a 16 10 dY 2 4 b c 32

X 60 72 b 180 dY 300 a 150 c 90

14. If 18 workers can do a work in 180 days. If two more workers join this work, the work will be completed in how many days?

15. If y is directly proportional to x 2, and y = 8 when x = 4, then find y when x = 5?

16. A swimming pool can be filled in 8 hrs. by 4 equal pumps. How many such pumps are required if the pool is to be filled in 5 1/3 hours?

17. If a sum of money is divide equally among 36 persons, they will get Rs.25 each. How much money would each get, if the number of persons is reduced by 6?

18. At a camp there is sufficient food for 500 scouts for 21 days. If 250 more scouts join the camp, how long would the food last?

19. If 9 taps of the same size empty a tank in 36 minutes, how long will it take to empty the tank If 5 taps go out of order?

20. Amal walks to her school at a speed of 4 .5 km/hr. and takes 40 minutes to reach the school. One day she reached the school five minutes late. Find her speed on that day assuming that she started in time from home.

21.800 men can finish a stock of food in 60 days. How many more men should join them to finish the same stock in 40 days?

22. Danish spent his entire pocket money buying 20 paperback books at Rs.22.50 per book. If he had Bought hard cover books at Rs.30 per book instead of paperback books, then how many books could he have purchased with his pocket money?

23. If x and y vary inversely as each other, and x = 15 when y = 6 then find y when x = 10.

24. At constant temperature the pressure of a gas is inversely proportional to its volume. If certain Amount of a gas occupies a volume of 30cc and exerts a pressure of85 g/cm 2, then find the decrease. In its pressure when the same amount of gas occupies a volume of 75cc.

25.630 chocolates were packed equally in 21 boxes. If 18 chocolates had to be paced in each box, find the number of boxes required.

26. If x varies inversely as the square of y, then k = ________________.

27. If the cost of 5 pens is Rs.37.50, then the number of pens which can be bought for Rs.52.50 is _______________.

29. 234 km / hr is equivalent to ___________ m /sec.

30. A cyclist travels 12 km in 3 hours. In__________ hours he will travel 20km.

ANSWERS; [1] 13hrs [2]Rs.900 [3] 102 [4] 25 [5] 9m [6] [i]a =25, b= 28.5, c =35[ii]a = 7,b = 15 [7]100cm [8] 88 men [9] 7.5kg [10] 80km/hr [11] Rs.18750 [12] 3.6 X 108 [13][i] a = 250, b =120, c = 100, d= 200 [ii] a = 20, b= 5, c = 8, d = 3.2 [14] 20days [15] 12.5 [16] 6 [17] Rs.30 [18] 14 day [19] 1hr 4 minutes 48seconds [20] 4km/hr [21] 400 [22] 15 books [23] y = 9 [24] 51g/cm2 [25] 35 boxes

Chapter- 14 FACTORISATION WORK SHEET CLASS VIII

1. Find the greatest common factors for the given monomials

[i] 14m3n3, 21m5n2, 35m6n6 [ii] p2q5r3, --p6q7r3, pq5r2

[iii] 24a 2b, --16abc [iv] 32a2b2c3, 36ab2c2 [v] 38 x5y3, 57x4y2

2. Factorize the following:

[i] 6x2 – 9x2y + 12xy2 [ii] 8x4y + 2xy4 – 24x4y3 + 18x3y2

[iii] 10xy -- 15x2y2 [iv] - 3 [ x – 3y ] + 6 [ x – 3 y ]

3. Factorize:

[i] m2 -10m + 25 [ii] 49 x2 _ 14x + 1

[iii] x2y2 – 6xyz + 9z2 [iv] x2/4 + x + 1 [v] 16x2 - 81y2

[vi] 625 – p 2 [vii] 16 [ x + y ]2 – 81 [x – 2y ]2

[viii] 1 – x2 + 2xy - y2 [ix] x2 + y2 + 2xy - z2

[x] 45 x2 - 20 [xi] 15x5 - 135x3

[xii] 4a2 + 12 ab + 9b2 - c2 [xiii] x2 +25x – 54

[xiv] p2 + 9p – 36 [xv] x2 – 8x - 33

[xvi] m2 - - 26m + 120 [xvii] s2 -19s – 92 [xviii] y2 + y – 72

4. Divide the following algebraic expressions:

[i]- 35 x5y3 ÷7xy

[ii] 196 m4n6÷ 14 m2n3

[iii] [7x - 35 ] ÷ 7 [iv] 6x + 33 ] ÷ [ 2x + 11 ]

[v] 75xyz [4x – 8 ] [5y – 15] ÷ 125 [ x – 2 ] [ y- 3 ]

[vi] 72ab[a + 5] [b – 4 ] ÷ 36a [b – 4 ]

[vii] 28[x + 3 ][x2 + 3x + 7] ÷ 7[x + 3] [viii] x2 – 11x +30 ÷ x – 5 [ix]2x2 + 6x ÷ [x + 3]

5. For each of the following polynomial in variable x , state [a] the degree of the polynomial

[b]coefficient of x [c]coefficient of y2

[i] 17y2 – 8x +15 [ii] – Y2 + y + 8 [iii] x5 + 3xy2 – 15y -20x + 4

6. Factorise completely:

[a] 25 – 4x2 – 12xy – 9y2 [b] x2 – a2 + 10ab – 25b2

Answers:1. [i]7m3n2 [ii]pq5x2 [iii]8ab [iv]4ab2c [v] 19x4y2

2.[i] 3x[2x – 3xy + 4y2] [ii]2xy[4x3 + y3 – 12x3y2 + 9x2y] [iii] 5xy [2 -3xy] [iv] 3[x -3y] [2x- 6y – 1]

3. [i][m -5] 2 [ii][7x – 1]2 [iii][xy – 3z]2 [iv] [x/2 + 1]2 [v] [4x + 9y] [4x –9y] [vi] [25 – p] [25 + p] [vii] [13x – 14y ][22y – 5x] [viii] [1 + x- y] [1- x + y] [ix][x + y +z ][x + y – z] [x] 5[3x -2][3x + 2] [xi] 15x3[x + 3][x – 3] [xii][2a + 3b +c][2a + 3b –c] [xiii][x +27][x – 2]

[xiv][p +12][p- 3] [xv][x- 11][x + 3] [xvi][m -20][m- 6] [xvii][s – 23][s + 4] [xviii] [y + 9][y – 8]

4. [i] -7x4y2 [ii]14m2n3 [iii]x – 5 [iv] 2 [v]12xyz [vi] -2b[a + b] [vii]4[x2 + 3x + 7] [viii] [x – 6] [ix]2x2- 5x + 3 [x]3 + 3x + x2 [xi] 2x

Chapter -15 INTRODUCTION TO GRAPHS

Work sheet Class VIII

1.Write the abscissa and y-coordinate of each of the following points.

[i] [3,4] [ii] [ - 5, - 7] [iii] [9, - 5] [iv] [ - 2, 0] [v][ 0,7]

2. Plot the following points on a graph sheet. Verify if they lie on a line

[i] A [2,3], B[0,1], C[ - 2, - 1], D[ -3, - 2]

[ii] S [3,6], M[0,3], I[ -1, 2], L[ -2,1], E[2,0]

[iii] P[5,7], Q[3,5], R[2,3] S[0,3]

3. Draw the line passing through [1,6] and [3,2].Find the coordinates of the points at which this line meets the x-axis and y- axis.

4.Plot the following points on a graph sheet using the same pair of axes and the same scale for each: [i] [ -3,4] [ii][2, -3] [iii] [ 4,5] [iv] [- 8, - -2] [v] [- 5, - 9] [vi] [1,2]

5. Draw the graph for the following table of values, with suitable scales on the axes.

Interest on deposits for a year

Deposit in [Rs.] 5000 10000 15000 20000 25000

Simple interest in[Rs] 325 650 975 1300 1625

[a]Does the graph pass through the orgin

[b]Use the graph to find the interest on Rs.12500 for a year.

[ c]To get an interest of Rs.1462.50 per year, how much money should be deposited?

6.Draw a linear graph

[i] X 1 2 3 4 5 [ii] x 2.5 3 3.5 4 4.5

y 7 14 21 28 35 Y 10 12 14 16 18

7.Fill in the blanks:

[i] The horizontal axis is called ---------------------.

[ii]The coordinate axes divide the Cartesian plane into four parts known as the --------------------.

[iii]The point of intersection of the coordinate axes is called the -------------.

[iv]The coordinates of the orgin are ---------.

8.Draw the line passing through [1,2] and [2,1].Find coordinates of the points at which this line

Meets the x- axis and y- axis.

9.Plot the points a[3,1], B [-3, 3], C [ -3, 6], D [2, -3] in a rectangular coordinate system.

10.The following table gives the price of television sets

Size in inches 14 20 29 35 52

Price in Rs.1000 6 10 14 20 50