(Practice Worksheet) MATHEMATICS

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Jemima Hensley
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1 BIRLA PUBLIC SCHOOL, DOHA- QATAR (Practice Worksheet) MATHEMATICS CLASS 8 CHAPTER 1- RATIONAL NUMBERS I. Fill in the blanks: 1. If a is reciprocal of b, then reciprocal of b is. 2. The product of a rational number and its multiplicative inverse is. 3. The reciprocal of a reciprocal of a number is. 4. The product of 2 rational numbers is always.. The reciprocal of a negative rational number is always. II. Find the multiplicative inverse of the following 1) - 8 X ) 0 3 3) III. Find the Additive inverse of the following: 1) 2 3 X 9 4 2) IV. Name the property of multiplication of rational numbers for the following: X 16 1 = 16 1 X X( )= 7 4 X X -3 12

2 V. Simplify using properties: x x x X X X 1 14 VI. Answer the following questions 1. By what number should be multiply -1 - so the product may be 28 7? 2. The cost of metres of rope is Rs Find cost per metre Is every whole number a rational number? Is the converse true? 4. Is zero a rational number? If yes give 2 examples. Is 0. the multiplicative inverse of 2 2?Why or Why or not? 6. Represent -6 6, 6 6, and on a number line (Use same number line for all) Multiply the reciprocal of 9-18 by the additive inverse of Find the additive inverse of the multiplicative inverse of the expression ( -3 x-10) 9. Find 10 rational number between the additive inverse of the sum 2 and 1 and the 3 product of 6 21 and What should be added to ( ) to get 4? CHAPTER 2- LINEAR EQUATIONS IN ONE VARIABLE 1. Solve the following equations: a) x-11=3x+9 b) 3y+4=7-2y c) 9-2(x-) =x+10

3 d) (y-1) =3(2y-) -(1-3y) e) 2(x-1)-6x=10-2(x-4) f) g) h) i) ( ) x 3 - x ( x -3) 4 ( x -3) 4 ( - 7x) 2 + 4x = 7 3 ( + x -1 ) ( + x -1 ) ( ) = -8 7 ( - x - 2 ) =1 3 ( - x - 2 ) =1 3 j) 1(x-)-3(x-9) +(x+6) =0 k) x = x The sum of two numbers is 2. One of the numbers exceeds the other by 9. Find the numbers. 3. Length of rectangle is 4 m less than 3 times its breadth. If the perimeter of rectangle is 32 m. Find its length and breadth 4. Rhea s mother is four times as old as she is now. In twenty years the mother will be twice as old as her daughter then. Find their present ages.. The sum of three consecutive multiples of is. Find the multiples. 6. The sum of the digits of a 2-digit number is 8. The number obtained by interchanging the digits exceeds the original number by 18. Find the original number 7. The sum of three consecutive numbers is 243. Find the numbers. 8. The length of a rectangle is twice its breadth. If the perimeter is 72 metre, find the length and breadth of the rectangle.

4 9. Tarun s father is 28 years younger than Tarun s grandfather and 30 years older than Tarun. If sum of ages of all three is 106 years, find the age of each of them. 10. The sum of the digits of a two-digit number is 7. If the number formed by reversing the digits is less than the original number by 27, find the original number. CHAPTER 3: UNDERSTANDING QUADRILATERALS 1. Which of the following is a formula to find the sum of interior angles of a quadrilateral of n-sides? (i) (ii) (iii) (iv) (n 2) Sum of the measures of the exterior angles of a polygon with any number of sides is ? (i) 180 (ii) 360 (iii) 720 (iv) The interior angle of a regular polygon exceeds its exterior angle by The number of sides of the polygon is ? (Hint: Let each exterior angle be x 0 ) (i) 14 (ii) 18 (iii) 1 (iv) Which of the following quadrilaterals has all sides equal and diagonals bisect each other at right angle? (i) square (ii) rectangle (iii) rhombus (iv) trapezium. II. State whether True or False.. (a) All rectangles are squares. (b) All rhombuses are parallelograms. (c) All square are rhombuses and also rectangles. (d) All squares are not parallelograms. (e) All kites are rhombuses.

5 (f) All rhombuses are kites. (g) All parallelograms are trapeziums. (h) All squares are trapeziums. III. Find the following: 6. In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1: 2: 3: 4. Find the measure of each angle of the quadrilateral. 7. The interior angle of a regular is 108. Find the number of sides of the polygon. 8. The exterior angle of a regular polygon is one-fifth of its interior angle. How many sides have the polygon? 9. The measures of two adjacent angles of a parallelogram are in the ratio 4:. Find the measure of each of the angles of the parallelogram. 10. If an exterior angle of a regular polygon is 4, then find the number of its sides. 11. If an interior angle of a regular polygon is 162, then find the number of its sides. 12. Find the measure of an interior angle of a regular polygon having 1 sides. 13. In the rhombus ABCD, BCD = 4. Find ABC? 14. One angle of a quadrilateral is 111 and the remaining three angles are equal. Find three angles. IV. Do as directed: 1. The ratio of each exterior angle of a regular polygon to each of its interior angle is 2:3. Find the number of sides of the polygon? 16. A playground is in the shape of a convex quadrilateral. Two of its interior angles are right angles. If the remaining two angles are in the ratio 4:, find the measure of all interior angles. 17. PQRS is a parallelogram such that m R = 110, then find m P and m S.

6 18. Two opposite angles of a parallelogram are (x 8 ) and (2x + 82). Find the measures of each angle of the parallelogram. 19. Find the value of x in the following figure: 20. JKLM is a parallelogram. If m J = 70, then find all other angles. Suggested Videos:

7 CHAPTER 4: PRACTICAL GEOMETRY Construct the following quadrilaterals: 1. A rhombus DOHA such that the length of two diagonals are 6cm and 8 cm respectively. 2. Construct a parallelogram PQRS such that PQ = 6cm, PS = cm and the distance between the parallel sides PQ and SR is 4cm. (Hint: Video 2: See the steps of construction, when one side, a diagonal and height is given.) 3. Construct a kite PQRS such that QS = 8cm, PS = cm and RS = 6 cm. 4. Construct a rectangle ABCD such that AB 4 cm and diagonal BD is cm.. Construct a square DEAR such that one of its side is cm. 6. Construct a quadrilateral ABCD such that AB = cm, BC = cm, ABC = 80 0, AD =. 0 and CD = 6cm. 7. Construct the quadrilateral MATH such that AT = 4. cm, TH = cm, MH=. cm, diagonal MT =. cm and diagonal AH = 7cm. 8. Construct a quadrilateral MIST such that MI = 3. cm, IS = 6. cm, M =7 0, I=10 0 and S = Suggested Videos: (Video 1) (Video 2) (Video 3) (Video 4)

Chapter : Data Handling 1. A die is thrown once. What is the probability of getting a multiple of 3. 2. A letter of English alphabet is chosen at random.

8 Chapter : Data Handling 1. A die is thrown once. What is the probability of getting a multiple of A letter of English alphabet is chosen at random. Find the probability that the letter chosen is a vowel. 3. There are 2 red,3 blue and black balls in a bag. A ball is drawn from the bag without looking into the bag. What is the probability of getting a non-red ball? 4. If Rs. 3,600 is 360 degrees. Use the following pie chart to find the amount, of rupees spent on food is Clothing Rent 0 70 E 20 O t h e r s d u c a t i o Food n. The following histogram shows the weekly wages (in Rs.) of workers in a factory. Y W o r k e r s o f m b e r N u X' 2 1 Y' Monthly Wages (in Rupees) X

(i) In which wage group are the largest number of workers being kept? What is their numbers? (ii) What is the amount which is received by the least number of workers? 6.

9 (i) In which wage group are the largest number of workers being kept? What is their numbers? (ii) What is the amount which is received by the least number of workers? 6. During lunch break, sale of the south Indian dishes in a canteen is given below. Prepare a pie chart. Name of the dish Quantity sold Plain dosa 4 Masala dosa 6 Idli sambhar 8 Sambhar rice Uttappam Observe the histogram and answer the following questions: a) Find the number of women between years. b) Find the number of women whose age is less than 28 years? c) Find the number of women whose age is more than 31 years?

10 8. The following pie chart represents the number of valid votes obtained by four candidates who contested an election for the post of chairman. The total number of valid votes polled was 720. (Hint 720=360 degrees) C B A D a) What are the number of votes polled by the winning candidate? b) What are the number of votes polled by the losing candidate? c) What are the number of votes of the candidate who made a century? 9. Three dice were thrown, the outcomes noted. Four players played the game 10 times each. Their scores were:,7,9,8,6,4,6,12,1,18,17,12,10,3,13,7,11,17,10,,4,6,8,16,18,14,6,18,9,10,1,14,3,7, 9,17,11,4,12,16. Prepare a grouped frequency table. Divide this data into class intervals of size 3 and draw a histogram. Chapter 6: Squares and Square roots 1. What is the least number of four digits which is a perfect square? 2. Find the square root of 76 by prime factorization. 3. Find the square root of 929 by division method 4. Find the square root of by division method.. Find the smallest square number which is divisible by each of the numbers 6,9 & 1.

11 6. Find the least number which when added to 220 makes it a perfect square. Also find square root of number obtained. 7. Find the least number which when subtracted from 634 to make it a perfect square. Also find square root of number obtained. 8. Find the square root of by prime factorization. 9. Find the smallest number by which 292 should be divided to make it a perfect square and find square root of number obtained 10. Find the smallest whole number by which it should be multiplied to get a perfect square number. Also find the square root of the number so obtained. (i) 2028 (ii) The cube root of 12 is Chapter 7: Cubes and Cube roots 2. If a number is written as Find the smallest number by which this is to be multiplied to form a perfect cube. 3. Is 392 a perfect cube? If not, find the smallest natural number by which 392 must be multiplied so that the product is a perfect cube. 4. Find the cube root of 1776 through prime factorization. What is the side of a cube whose volume is 4666 cm³ 6. Is 3240 a perfect cube. Find the smallest number by which 3240 should be divided to get a perfect cube. Find cube root of the perfect cube obtained 7. Find the smallest number by which 392 should be multiplied to get a perfect cube and find cube root of perfect cube obtained. ****THE END****

CLASS 8 (Mathematics) -EM

1 CLASS 8 (Mathematics) -EM 1.RATIONAL NUMBER - Natural, Whole, Integers (positive and negative), rational numbers. Properties of Rational Numbers- Closure, Commutativity, Associativity with example The