INTERNATIONAL INDIAN SCHOOL, RIYADH

WORKSHEET 2019-2020 (YEARLY)

CLASS: VIII SUBJECT: MATHEMATICS

CHAPTER: 3 UNDERSTANDING QUADRILATERALS

1. The adjacent angles of a parallelogram are ------------.

2. The sum of the exterior angles of an equilateral triangle

is ---------------- .

3. ----------------- is an example of a regular polygon with four

sides.

4. In a parallelogram ABCD < B = 600 then <C = ------------.

5. The bisectors of two adjacent angles of a parallelogram

at ----------------.

6. Name the following

(a) A quadrilateral which is equilateral but not equiangular.

(b A quadrilateral which is equilateral as well as equiangular

(c) A quadrilateral whose both pair of opposite angles are

equal.

7. Draw the example of each of the following

(a) Curves that are neither simple nor closed.

(b) Curves that are closed but not simple.

(c) Curves that are both closed and simple.

8. If the perimeter of a rectangle is 70cm and one of its sides is

15cm long, then find the length of the other sides.

9. Can there be a parallelogram ABCD in which

(i) AB =BC = 5cm and AD = DC = 6cm?

(ii) < A = < C = 400 and< D =< B = 600?

(iii) < A = < C = 750 ?

(iv) O is the midpoint of diagonal AC, BO = 5cm and

DO = 2cm?

(v) AB = 6cm and DC = 6cm

10. If one of the angles of a rhombus is 600 , what are the

measures of the remaining angles?

11. Can there be a polygon with measure of each exterior

angle as the following? If yes, find the name and the

number of sides of the polygon.

(i) 720 (ii) 1400 (iii) 450 (iv) 250 (v) 600

12. Find the number of sides of a regular polygon if the

measure of each of its interior angles are

(i) 900 (ii) 1200 (iii) 1500 (iv) 1440

13. If one angle of a parallelogram is two – thirds of its

adjacent angle, find the angles of the parallelogram.

14. Two adjacent angles of a parallelogram are (5x - 3)0

and (5x – 67) 0. Find all the angles of the parallelogram.

15. If the opposite angles of a parallelogram are (3x – 3)0

and (6x – 69)0, find all the angles of the parallelogram.

ANSWERS – CHAPTER - 3

1) Supplementary 2) 3600 3)square 4) 1200 5) 900

6) Rhombus,Square,Parallelogram 8) 20cm 10) 60,120,60,120

11) (i)yes, regular pentagon,5 (ii) no (iii) yes, regular octagon,8

(iv)no (v)yes, regular hexagon,6 12)(i) 4(ii) 6(iii) 12(iv) 10

13) 72,108,72,108 14) 122,58,122,58 15) 63,117,63,117

CHAPTER 7 CUBE AND CUBE ROOTS

1. Cube of an even number is ---------------------.

2. -----------is the smallest Hardy – Ramanujan number.

3. Cube of an odd number is ----------------.

4. ------------ is the inverse operation of cube.

5. -------------- is the one’s digit of the cube of 5027.

6. What is the smallest number by which the following must be

multiplied to obtain a perfect cube?

(a) 864 (b) 500 (c) 1323

7. Find the smallest number by which each of the following must be

divided to obtain a perfect cube.

(a) 625 (b) 243 (c) 704

8. Which of the following are perfect cubes.

(a) 343 (b) 1029 (c) 6400

9. Amit makes a cuboid having sides 3cm, 2cm, 3cm. How many such cuboids

will be required to form a cube?

10. Find the cube root of the following by prime factorisation method. (a) 216

(b) 3375 (c) 21952

11. Find (a) √343729

3 (b) √144𝑋96

3

ANSWERS

(1) Even number (2) 1729 (3) odd number (4) cube root (5) 3

(6) 2, 2, 7 (7) 5, 9, 11 (8) 343 (9) 12 (10) 6, 15, 28 (11)7/9, 24

CHAPTER-- 11 MENSURATION

1. The curved surface area of a 10m high cylinder is 440m2. Find the volume of

the cylinder.

2. The rectangular vessel of dimensions 20cm by 15cm by 11cm is full of water.

If the water is poured into an empty cylindrical vessel of radius 10cm, find the

height of water in the cylindrical vessel.

3. Find the volumes, the curved surface area and the total surface area of the

cylinders having dimensions:

(a) r= 5cm, h=21cm (b) r= 8.5cm,h= 35cm (c) r=12cm,h=4cm

4. The volume of a 5cmlong cylindrical iron rod is 6930cm3. Find its diameter.

5. The circumference of a base of a cylinder is 176cm and its height is 60cm,

find the volume of the cylinder.

6. A cylindrical tank has a capacity 9240cm3. If its depth is 15cm. then find its

diameter.

7. A rectangular piece of paper of dimensions 88cm by 5cm is rolled along the

length to form a cylinder. Find the volume of the cylinder formed.

8. Find the volume of the cube whose side is

(a) 5cm (b) 6.5cm (c) 14cm (d) 1.2cm

9. The ratio of the length, breadth and height of a cuboid is 5:3:2. If its volume

is 3750cm3, find the length, breadth and height of the cuboid.

10. The bottom of the tank of a water cooler is rectangular in shape. It is 90cm

X 60cm.How high it must be made so that it can hold 162 litres of water?

11. A beam of wood is 5m long and 36cmthick. It is made of 1.35m3 of wood.

What is the width of the beam?

12. The volume of a room is 378m3 and the area of its floor is 84m2.Find the

height of the room.

13. A swimming pool is 260m long and 140mwide. If 54600 cubic metres of

water is pumped into it, find the height of the water level in it.

14. Find the volume of wood used to make a closed box of outer dimensions

80cm x45cm x32cm, the thickness of wood being 2.5cm all around.

15. Find the volume of iron required to make an open box whose external

dimensions are 36cm x25cm x16.5cm, the box being 1.5cm thick throughout. If

1cm3 of iron weighs 8.5grams, find the weight of the empty box in kilograms.

16. A box with a lid is made of wood which is 3cm thick. Its external length,

breadth and height are 56cm, 39cm and 30cm respectively. Find the capacity

of the box. Also find the volume of wood used to make the box.

17. The external dimensions of a closed wooden box are 62cm, 30cm and

18cm. If the box is made of 2cm thick wood, find the capacity of the box.

18. A closed wooden box 80cm long, 65cm wide and 45cmhigh is made of

2.5cm thick wood .Find the capacity of the box and its weight if 100cm3 of

wood weighs 8g.

19. Find the volume, lateral surface area and the total surface area of a cube

each of whose edges measures: (a) 7m (b) 5.6cm (c) 8dm5cm

20. The surface area of a cube is 1176cm2. Find its volume.

21. The volume of a cube is 729cm3. Find its surface area.

22. The dimensions of a metal block are 2.25m by 1.5m by 27cm. It melted and

recast into cubes, each of side 45cm. How many cubes are formed?

23. If the length of each edge of a cube is doubled, how many times does its

volume become? How many times does the surface area become?

ANSWERS (MENSURATION)

(1)1540 cm3, (2)10.5cm (3)1650cm3, 660cm2, 817.14 cm2 (ii) 7947.5cm3,

1870cm2, 2324.14cm2(iii) 1810.28cm3,

301.71cm2, 1206.85cm2(4)42cm,(5)147840 (6)28cm (7)3080cm

(8)125,274.625,2744,1.728cm(9)25,15,10

(10)30cm,(11)75cm(12)4.5cm (13)1.5m (14)34200cm (15)42.9165kg

(16)39600, 25920(17)21112cm

(18)54000cm, 4320g (19)343,196,294(ii) 616,125.44, 188.16(iii) 614.125,

289,433.5 (20)2744(21)486cm2

(22)10 (23) 1: 8, 1: 4

CHAPTER- 9 ALBEBRAIC EXPRESSIONS AND IDENTITIES

1. Multiply the following:

(a) 11x2y and 2x2y2 (b) 3y2 and 7y5 (c) 5x3 and 4x9 (d)-9xy and 4x2z

2. Find the products of:

(a) (-2xy2)(5y)(-3z2) (b ) (ab)(bc)(ca) (c) (6a2b)(-2b2c)(3ac2)

(d)(5/9ab)(9/7bc)(-7/5ca)

3. Find the value of (3p2q) x (8q3), when p=1 and q= (- ¼).

4. Find the value of (-8x2y3) x (1/5 xy2), when x= (-1) and y =2.

5. Find the product of (3a2b3), (-7a2) and (5a2b2), and then verify the result for

a=2 and b=3.

6. Find the product of (-3/4xy2z) and (-2z2) then verify the result for x=1, y=2

and z=3.

7. Verify a2b2c2 = (ab) x (bc) x (ca) for a=3 and b=4

8. Find the product and then verify the following for a=2 and b= (-5)

(i) a (a2 – ab2) (ii) 2/7a (ab – 7/6ab2)

9. Find the product of the following

(i) 2x (3x+y2) (ii) (-3y) (x2+3xy)

(iii) 3a2 (4a-5a2) (iv) -8a2b (-3a2-2b)

(v) -5/9abc (18/15a2bc – 3/10abc2) (vi) 7a( 0.1a2-0.5b)

10. Multiply 5/9y2z, 7/10x2 and (-3xz2), and verify the result for x=1/2, y=1/3

and z=1/4.

11. Find the following products and verify the results for x= (-1) and y= (-2)

(i) (3x2+2y2) (x+y) (ii) (x2 –y2) (x2 +y2)

(iii) (3x2 +1/3 y2) (2y -3x2) (iv) (x4 – y4) (x+y)

(v) (1/2x –y) (3/5x +y) (VI) (0.7x – 0.6y) (2.3 x – 2y)

12. Find the products of the following

(i) (3x -2) (5x2 + 6x +2) (ii) (x2 + y2 +z2) (xy + yz)

(iii) (x+ y) (x2 –xy + y2) (iv) (5x2 +y) (3x + 2y)

(v) (x3 + y3) (x2 – xy + y2 ) (vi)( 3/5 x2 – 3y + 2) (1/3 x – y)

13. Simplify : (3y + 2) (y-2) – (7y+3) (y- 4)

CHAPTER: 12 EXPONENTS AND POWERS

1. Evaluvate the following

(a) (9/10)-4 ÷ (9/10)-6 (b) (-1/4)-3 ÷ (-1/4)-5 (c) (3-7 ÷ 3-10)x 3 -3

2. Evaluvate the following

(a) [( 3/2)2]-2 (b) [(3/2)-2]-2 (c) {[(-1/5)-1]2}-1

3. Simplify the following

(a) (3/2)2 x (4/5)2 (b) (-1/3)3 x (-1/2)3 (c) (2/3)-4 ÷ (1/3)-4

4. Find the value of the following

(a) (1/3)-2 + (1/4)-2 + (1/5)-2 (b) (30 + 2 -1) ÷ 2-2 (c) (2-1 x 4-1) ÷ 2-4

5. Express the numbers in the following statements in standard form

(a) The average size of a red blood cell is 0.000007 m.

(b) 1 micron = 1/1000000 m.

(c) The charge of an electron is 0.0000000000000000016 Coulomb.

(d) The radius of a wire on a computer chip is 0.0000015

6. According to 2011 census, male population in India is 623700000 and female

popution is 586500000. Express the difference between the two in a standard

form.

7. Express the following numbers in usual form

(a) 1.02 x10-4 (b) 9.82 x 10-6 (c) 6.75 x 10-8 (d) 9.5 x 10-10

(e) 8.8 x 107 (f) 4.534906 x 105

8. If the diameter of the Sun is 1.4 x 109 m and that of the Earth is 1.275 x 104m.

Compare the two.

9. Express the following numbers in standard form: (a)0.0072 (b)972008.045

(c) 0.0000067 (d) 0.000000193 (e)0.00000008436

10. Find the value of a/b for which (2/5)-5 x (15/7)-5 =( a/b)-5

11. Find the value of x for which ( -3/4) 6 ÷ ( -3/4 )2 =( -4/3) x.

12. Find the value of x for which (2/5)4 x (2/5)-7=(2/5 )2x+1

13. Find the value of x for which 710 ÷ 78 =( 1/7) x

ANSWERS

1.(a)( 9/10)2 (b) (-1/4)2 (c) 1 (2) (a) (2/3)4 (b) (3/2)4(c) 1/5)2(3) (a)36/25 (b)

1(1/216 (c) 1/16(4)(a) 50 (b)2 (c) 6 ( 5) (a) 7x 10-6m (b)10-6m(c) 1.6x 10-18

(d)1.5x10-6 (6)3.72x107 (7)0.000102,

0.00000982,0.0000000675,0.00000000095,88000000,4534906

(8)1.39998725x109(9)7.2x10-3,9.72008045x105,6.7x10-6,

1.93x10-7,8.436x10-8 (10) 6/7 (11)(-4) (12)(-2) (13) (-2)

------------- xxxxxx ---------------

CHAPTER – 14 FACTORISATION

1.Find the greatest common factors for the given monomials

(a) 14m3n3, 21m5n2, 35m6n6 (b) p2q5r3, - p6q7r3, pq5r2

(c) 24a2b, -16abc (d) 32a2b2c3, 36ab2c2 (e) 38x5y3, 57 x4y2

2.Factorise the following

(a) 6x2 – 9x2y + 12xy2 (b) 8x4y + 2xy4 – 24x4y3 + 18x3y2

(c) 10xy – 15x2y2 (d) 3x (x – 3y) + 6 (x – 3y)

3. Factorise

(a) m2 -10m +25 (b) 49x2 – 14x +1 (c) x2y2 – 6xyz +9z2

(d) x2/4 + x +1 (e) 4a2 + 12ab +9b2 – c2 (f) x2 + 25x – 54 (g) s2 – 19s -92

(h) p2 + 9p -36

4. Divide the following algebraic expressions

(a)(- 35x5y3) ÷ 7xy (b) 196m4n6 ÷ 14m2n3 (c) [ 7x – 35] ÷ 7

(d) [6x + 33] ÷ [2x + 11]

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

(g) x2 – 11x + 30 ÷ (x – 5)

(h)2x2+6x ÷ [x+3]

5. Factorise completely

(a)25-4x2-12xy-9y2 (b) x2 – a2 + 10ab – 25b2

ANSWERS

1. (a) 7m3n2 (b) pq5r2 (c) 8abc (d) 19x4y2

2. (a)3x(2x-3xy+4y2) (b)2xy(4x3+y3-12x3y2+9x2y)

(c) 5xy (2 – 3xy) (d) (x – 3y) ( 3x + 6)

3. (a) (m-5)2 (b) (7x-1)2 (c) (xy-3z)2 (d) (x/2+1)2

(e) (2a+3b+c)(2a+3b-c) (f) (x+2)(x-2) (g) (s-23)(s+4),

(h) (p+12) (p-3)

4. (a) -5x4y2 (b) 14m2n3 (c) (x-5) (d) 3 (e)12xyz (f)(x-6) (g) 2x

5. (a) (5+2x+3y)(5-2x-3y) (b) (x+a-5b)(x-a+5b)

CHAPTER -- 4 PRACTICAL GEOMETRY

1. Construct a quadrilateral ABCD, given that EF = 7 cm, EH = 6 cm, EG = 7.5

cm, FH = 6.5 cm, and FG = 4.5cm.

2. Construct a quadrilateral WISE, given WI = 5 cm, SE = 6cm, SE = 5.5cm, WS

= 4 cm and IE = 10 cm.

3. Construct a quadrilateral GEAR, given that GE = 4 cm, EA = 3.5 cm,GA = 5 cm,

AR = 6 cm and GR = 4.3 cm.

4. Construct a quadrilateral MARS, given that MA = 3cm, AR = 4 cm, RS = 2 cm,

MS = 3.5 cm and MR = 5cm.

5.Construct a quadrilateral FAST , given that FA = 5.5 cm, AS = 4 cm, ST =6cm,

˂ F = 600 and ˂ A = 1200 .

6.Construct a quadrilateral SAIL given that SA = 5.5 cm, SL = 4.5 cm, AI = 5.5

cm ˂ S = 1350 and ˂ L = 450.

7.Constuct a quadrilateral GAIN given that GA = 6 cm, IL = 4 cm ˂ G = 450, ˂ A =

900, ˂ I = 1200 .

8.Construct a quadrilateral FACE, given that FE = 5 cm, CE = 7 cm, ˂ F = 1250, ˂

A = 1050 ˂ C = 1000 .

9.Construct a rhombus ABDC, given diagonals are 6.6 cm and 5cm.

10.Construct a parallelogram PQRS with ˂ P = 750 ,PQ = 6 cm, QR = 4cm.

CHAPTER 8 COMPARING QUANTITIES

1. If 72% of 250 students in a class are interested in Mathematics, how

many students are

Interested in Mathematics?

2. Amal paid Rs.214 for a pair of shoes worth Rs.200. What is the rate of

VAT charged?

3. An article marked at Rs.50 is sold for Rs.45. What is the rate of discount?

4. A shirt was sold for Rs.880 including 10% VAT. What was its price before

VAT was added?

5. What is the difference between S.I. and C.I. on a sum of Rs.1000 at 10%

for 2 years?

6. A machine worth Rs.12000 is depreciated by 10% per year .What will be

its value after 2 years?

7. By what percent is 2000 less than 2400 ?

8. A car was sold for Rs.510000 after allowing 15% discount. What wa its

actual selling price ?

9. Find the compound interest on Rs. 3000 at 5 % per annum, compounded

annually for 2 years

10. A dealer offers 8 % discount on all his goods and still makes a profit of 15

%.If an item is marked Rs. 500, find its cost price.

11. Find the rate of discount being given on a calculator whose selling price

is Rs.630 after deducting a discount of Rs,420 on its marked price.

12. After allowing a discount of 25 % on the marked price of a shirt, it is sold

for Rs.480. Find the Marked price of a shirt.

13. A merchant bought two scooters for Rs.30000 each. On one he gained

20% on the other he lost

14. 20 %.Find the loss or gain percent in the whole transtaction.

15. I gave a certain person Rs. 8000 at simple interest for 3 years at 5 %.

How much more should I have gained had I given it at compound

interest.

16. Find the difference between compound interest on Rs. 10000 for 1 1

2

years at 10 % per annum,

17. According as the interest is paid yearly or half yearly.

18. A loan of Rs. X is cleared after I year 4 months. The rate of compound

interest is 6 % per annum. What sum is paid to clear the debt?

19. Reem paid 10 % of her salary as income tax. If she is left with Rs 8520,

after paying income tax. Find her salary.

ANSWERS

1.70 2.7% 3.10% 4.800 5.10 6.9720 7.20 8.60000 9.307.50 10.

11.331

3% 12.1640 13.3500

14.61 15.1760 16. 17. 18. 19.

CHAPTER 11 MENSURATION

1. Find the surface area of a cube whose edge is 12.5 cm.

2. Find the cost of painting the outer surface of a closed box which is 60 cm

long 40 cm broad and 30 cm high at the rate of 50 paisa per square

centimeter.

3. The paint in a certain container is sufficient to paint an area equal to

9.375m2 .How many bricks of dimensions 22.5 cm X 10 cm X 7.5 cm can be

painted out of this container?

4. A hall is 150 m long and 25 m wide. If its height is 6 m, find the area of the

four walls of the hall.

5. Find the surface area of a cubical box whose each side is 1 m, assuming

that the box has no lid.

6. The radius of a right circular cylinder is 5 cm and its height 9 cm. Find the

curved surface area and the total surface area.

7. The walls and ceiling of a room are to be painted. If the length , breadth

and height of the room are respectively 4.5 m, 3 m and 3.5 m find the area

to be painted.

8. How will the surface area of a cube change if the length of its edge is :

( a ) doubled ( b) halved

9. The curved surface area of a cylinder is 1320 cm2 and its volume is 2640

cm2 . Find its height.

10. Curved surface area of a right circular cylinder of height 14 cm is 924 cm2

.Find the radius of the base.

11. How many bricks will be required to construct a wall 10 m long 4m wide

and 3 m high if each brick measures 25 cm X 12 cm X 8 cm.

12. The volume of a cuboid is 528 cm3 and the area of its base is 88 cm2 . Find

the height

13. The perimeter of one face of a cube is 20 cm. Find the volume of the cube.

14. The volume of a cuboid is 3600 cm3 and its height is 12 cm. If the length

and breadth are in the ratio 4 : 3, find its length and breadth.

15. A box which measures 70 cm X 36 cm X 12 cm is to be covered with

canvas. How many meters of canvas of width 80 cm would be required to

cover 150 such boxes.

ANSWERS :

1.937.5 2.3300 3.100 4.2100 5.5m2 6.440 7.52.5 8.4 times of the original

area ,b)1

4 times of the original area 9.r=4 , h=52.5 10.r=10.5 11.50000

12.6 13.125 14.l=20, b=15 15.567

CHAPTER- 15 INTRODUCTION TO GRAPHS

1. Write the abscissa(x-coordinate)or ordinate(y-coordinate)

of each of the following points.

[3,4] [-5,-7] [9,-5] [-2,0] [0,7]

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

lie on a line

(a) [2,3] [0,1] [-2,-1] [-3,-2]

(b) [3,6] [0,3] [ -1,2] [-2,1] [2,0]

© [5,7] [3,5] [2,3] [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

(a) [-3,4] (b) [2,-3] (c) [4,5] (d) [-8,-2] (e) [-5,-9] (f) [1,2]

5. Plot the points P[3,3] , Q[-3,3] and join OP,OQ,PQ.What

figure do you obtain?

6. The following table gives the quantity of an item and its

Cost

Quantity (in kg) 5 8 11 14 17

Cost (in Rs) 130 280 360 400 440

Plot a graph to show the data. Find

(i) The amount needed to buy 15 kg of the item

(ii) The quantity of the item, which can be bought for Rs230

7. Write the coordinates of the point whose:

(i) abscissa = -6 and ordinate = 0

(ii) ordinate = 7 and abscissa = -12

8. State whether the following points lie on the x-axis or

Y – axis (i) [0,7] (ii) [-5,0] (iii) [18,0] (iv) [2,0]

9. Draw the graph for the following table of values, with

suitable scales on the axis. Interest on deposits for a year.

Deposite in [Rs] 5000 10000 15000 20000 25000

Simple interest in [Rs] 325 650 975 1300 1625

(a) Does the graph pass through the origin?

(b) Use the graph to find the interest on Rs 12500 for a

year.

(c) To get an interest of Rs 1450 per year, how much money

should be deposited ?