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TABLE OF CONTENTS 8 DATA HANDLING 1 8.1 RECORDING AND ORGANIZATION OF DATA 1 8.2 REPRESENTATION OF DATA 3 8.3 BAR GRAPH 9 9 INTRODUCTION TO ALGEBRA 13 9.1 PATTERNS –MAKING RULES 13 9.2 EXPRESSIONS WITH VARIABLES 17 9.3 RULES FROM GEOMETRY AND SIMPLE EQUATIONS 19 10 PERIMETER AND AREA 23 10.1 PERIMETER 23 10.2 AREA 27 11 RATIO AND PROPORTION 31 11.1 COMPARING QUANTITIES WITH DIFFERENT UNIT 31 11.2 RATIO IN DIFFERENT SITUATIONS 34 11.3 DIVISION OF A GIVEN QUANTITY IN A GIVEN RATIO 38 11.4 PROPORTION AND UNITARY METHOD 40 13 PRACTICAL GEOMETRY 43 13.1 A LINE SEGMENT 43 13.2 CONSTRUCTION OF A CIRCLE 46 13.3 PERPENDICULARS 48 13.4 CONSTRUCTION OF ANGLES USING PROTRACTOR 51 13.5 CONSTRUCTING ANGLES OF SPECIAL MEASURES 53 PROJECT BASED QUESTIONS 55 ADDITIONAL AS BASED PRACTICE QUESTIONS 56

CHAPTER 8 DATA HANDLING EXERCISE 8.1 RECORDING AND ORGANIZh{pvu OF DATA 8.1.1 Key Concepts i. Data is a collection of numbers gathered to give some information. ii. To get a particular information from a given data, it can be arranged in a tabular form using tally marks. 8.1.2 Additional Questions Objective Questions 1. [AS3] A collection of information is called . (A) Information (B) Data (C)Frequency (D)Tally marks 2. [AS3] The number of times a particular value occurs in the data is called its . (A) Frequency (B) Data (C)Information (D)Range 3. [AS3] If represents 10 books, then represents books. (A) 3 (B) 40 (C) 100 (D) 1000 EXERCISE 8.1. RECORDING AND ORGANIZATION OF DATA 1

4. [AS3] The representation of data using pictures or symbols is called a (A) Histogram (B) Bargraph (C) Pictograph (D)Frequency table 5. [AS3] The width of the bars in a bar graph for all bars. (A) Remains the same (B) Is different (C)Increases from left to right (D)Decreases from left to right Long Answer Type Questions 6 [AS5] The following observations show the number of children present for daily sports practice during the month of August. Arrange the data as a frequency distribution. 35 40 40 38 40 40 36 39 40 40 38 37 40 35 38 39 40 38 40 37 35 39 35 36 37 38 35 40 35 38 7 [AS5] The weight (in g) of 36 oranges picked at random from a basket are as follows. 65 73 68 73 71 66 70 72 66 72 70 65 73 65 65 70 71 67 68 69 68 67 70 69 68 67 69 67 72 70 70 67 68 67 73 70 Arrange the data in a suitable frequency distribution. EXERCISE 8.1. RECORDING AND ORGANIZATION OF DATA 2

EXERCISE 8.2 REPRESENTATION OF DATA 8.2.1 Key Concepts i. Data that has been organized and presented in frequency distribution tables can also be presented using pictographs and bar graphs. ii. A pictograph represents data in the form of pictures, objects or parts of objects. It can be drawn using symbols to represent a certain number of items or things. 8.2.2 Additional Questions Objective Questions 1. [AS3] If represents 90 trees, then represents trees. (A) 30 (B) 40 (C) 20 (D) None 2. [AS3] The number that the symbol represents is ________. (A) 4 (B) 5 (C) 6 (D) None EXERCISE 8.2. REPRESENTATION OF DATA 3

3. [AS5] The pictograph shows the capacity of 4 containers. The container that has a capacity of 1 litre is ______. 2 Bottle Flask Mug Glass Key: represents 100 ml (A) Bottle (B) Flask (C) Mug (D) Glass 4. [AS3] If the symbol represents 150 trees, then the number of trees represented by is _______. (A) 600 (B) 700 (C) 750 (D) 500 EXERCISE 8.2. REPRESENTATION OF DATA 4

5. [AS5] If represents 15 students, the group of symbols that represents 90 students is ______. (A) (B) (C) (D) Long Answer Type Questions 6 [AS5] The table shows the number of TV sets sold at Diwakar’s store. Make a pictograph by using pictures. Month Sales January 20 February 40 March 25 April 30 7 [AS5] The table given shows the number of students playing four different games: Games Football Hockey Cricket Badminton No. of 200 140 100 50 students Present this information as a pictograph. EXERCISE 8.2. REPRESENTATION OF DATA 5

8 [AS5] The pictograph shows the pocket money that six pupils get each week. represents 5 rupees (Rs. 5). Study the pictograph and answer the questions that follow. Rani – Sunder – Keerthana – Sravani – Sita ram – Ramakanth – (i) Who gets exactly Rs. 45? (ii) How much money did they get altogether? (iii) Who gets the maximum pocket money? (iv) Who gets the minimum pocket money and how much? (v) How many students got equal money? EXERCISE 8.2. REPRESENTATION OF DATA 6

9 [AS5] The pictograph shows the money spent by six pupils on buying notebooks. Radha Satish John Nirmala Rashid Vinay Using the given pictograph, answer the following questions. (i) Without counting, ﬁnd the pupil who spent the least amount on buying notebook. (ii) How much money did they spend altogether? (iii) Who spent exactly Rs. 40? (iv) How much money did Nirmala spend? (v) Who spent the maximum amount? EXERCISE 8.2. REPRESENTATION OF DATA 7

10 [AS5] The librarian of a school prepared a record of the number of library books borrowed by students on each day of a week. Then she made the pictograph given to show this information. Number of library books borrowed Monday – Tuesday – Wednesday – Thursday – Friday – Each represents 25 books. Using the given pictograph, answer the following questions. (i) On which day were the least number of books borrowed and how many? (ii) On which day were the maximum number of books borrowed and how many? (iii) How many books were borrowed on Tuesday? (iv) Altogether how many books were borrowed on the ﬁrst three days of the week? (v) How many books in all were borrowed during the week? EXERCISE 8.2. REPRESENTATION OF DATA 8

EXERCISE 8.3 BAR GRAPH 8.3.1 Key Concepts i. Data can be represented by means of a bar diagram or a bar graph. ii. In a bar graph, bars of uniform width are drawn horizontally or vertically with equal spacing between them. iii. The length of each bar corresponds to the respective frequency. 8.3.2 Additional Questions Objective Questions Using the given bar graph, choose the correct option in the questions given. 1. [AS5] Cars of _______colour is the least common among the cars parked. (A) Black (B) White (C) Red (D) Grey 2. [AS5] The colours of the same number of cars parked are _______. (A) Black and Grey (B) White and Black (C)White and Red (D)Grey and White EXERCISE 8.3. BAR GRAPH 9

3. [AS5] The total number of cars in the parking lot is ________. (A) 20 (B) 35 (C) 50 (D) 40 4. [AS5] The fraction of the number of red cars to that of white cars is _______. (A) 5 (B) 2 2 5 (C) 3 (D) 1 1 3 5. [AS5] The colour of the cars that are the maximum in number is _______. (A) Black (B) White (C) Red (D) Grey Very Short Answer Type Questions 6 [AS3] Fill in the blanks. (i) In a pictograph, if represents 20 apples, the representation of is . (ii) If each represents 3 ﬂowers, then represents . (iii) The symbol represents . (iv) The tally mark representation for ‘10’ is . (v) In a bargraph, the height of a bar represents its . EXERCISE 8.3. BAR GRAPH 10

Long Answer Type Questions 7 [AS5] The number of passengers arriving into a city during six months of a year is given. Draw a horizontal bar graph to represent the data taking 1 cm for every 5000 passengers. Month No. of passengers July 40,000 Aug 80,000 Sep 60,000 Oct 40,000 Nov 50,000 Dec 20,000 8 [AS5] The number of votes obtained by ﬁve contestants for the post of class representative in a 6th class election is as given. Draw a vertical bar graph for the data. Student Shanker Joseph Pallavi Santosh Anoop Votes 15 25 20 10 30 obtained 9 [AS5] Survey of the favourite ice–cream ﬂavour of 23 boys is as given. Represent it as a bar graph. –crIceeam Vanilla Chocolate Almond Pista Others 6 5 2 8 2 Favourite ice–cream of boys EXERCISE 8.3. BAR GRAPH 11

10 [AS5] The following table shows the marks secured by Sumit in the annual examination. English Maths Hindi Sanskrit Science Social 50 40 60 70 50 55 Draw a vertical bar graph to show the given information. EXERCISE 8.3. BAR GRAPH 12

CHAPTER 9 INTRODUCTION TO ALGEBRA EXERCISE 9.1 PATTERNS – MAKING RULES 9.1.1 Key Concepts i. Patterns follow a specific rule. By observing the pattern, we can extend it further. For example, if we need 3 match sticks to make a triangle, then we need (2 × 3) = 6 match sticks to make 2 triangles, (3 × 3) = 9 match sticks to make 3 triangles and so on. Continuing similarly, we can extend the pattern. Here, n × 3 gives the number of match sticks needed to form ’n’ number of triangles in the pattern. 9.1.2 Additional Questions Objective Questions 1. [AS3] One centimetre equals 0.3937 inches. The expression which gives the number of inches in x centimetres is _________. (A) 0.3937 − x (B) 0.3937 + x (C) 0.3937 x (D)0.3937 ÷ x 2. [AS3] The verbal expression that does not represent a − 8 is ________. (A) 8 less than a (B) a decreased by 8 (C)Take away 8 from a (D) a subtracted from 8 3. [AS1] The value of the expression 3ab, for a = 4 and b = 2 is _______. (A) 24 (B) 12 (C) 8 (D) 6 EXERCISE 9.1. PATTERNS – MAKING RULES 13

4. [AS1] The value of a2 + 2a − 3 for a = 2 is _______. (A) 11 (B) 6 (C) 5 (D) 4 5. [AS1] The expression that is not equal to 18 is ________. (A) 2t, for t = 9 (B) t – 5, for t = 23 (C)3t + 3, for t = 5 (D) 9t ÷ 3, for t = 5 Short Answer Type Questions 6(i) [AS1] If a = 6 and x = 2, ﬁnd the values of: a + 6x b) 2ax + 7x − 10 4ax − 3a − 2 a) 5a − 3x (ii) [AS1] Evaluate: a) pq(p + 3) + r f or p = 2, q = 3 and r = 1 b) 12p(q – r) for p = 1, q = 4, r = 2 c) 1 – x + y for x = − 2, y = − 7 7 [AS3] Write the algebraic expressions for: (i) Four times the sum of y and seven (ii) 25 decreased by four times ‘e’ (iii) Take away the product of 15 and t from 60 8 [AS4] The score of Manisha in mathematics is 25 more than two–third of her score in science. If she scored x marks in science, determine her score in mathematics. 9(i) [AS5] Find the rule which gives the number of match sticks required to make the following letters: a) T b) N (ii) [AS5] Observe the following pattern: How many line segments does each such shape contain? 14 EXERCISE 9.1. PATTERNS – MAKING RULES

Long Answer Type Questions 10 [AS1] Find the values of the following expressions for a = 4 and b = 2. (i) a + b (ii) a – b (iii) ab (iv) a b (v) 3ab (vi) a + 5b (vii) 3ab – 4b + 5 (viii) 5a − 2b 4ab − 8 11 [AS3] Write the algebraic expressions: (i) Radhika has 3 books more than twice the books with Rakesh. Write the relationship using the letter y. (ii) The cost of one pen is Rs. 7. What is the rule to ﬁnd the cost of ‘n’ pens? (iii) The cost of 9 books is Rs.23. Find the rule to buy 'n' books where n < 9 and then ﬁnd the price of one book. (iv) Venu says that he has two books less than what Laxmi has. Write the relationship using the letter x. (v) A teacher distributes 6 pencils per student. How many pencils are needed for a given number of students? (Use ‘z’ for the number of students.) 12 [AS3] (i) How many weeks are there in ‘d’ days? Write an algebraic expression for it. (ii) A man has 350 watches. He sells ‘w’ watches everyday. Write an algebraic expression to show the number of watches he would be left with after ‘t’ weeks . EXERCISE 9.1. PATTERNS – MAKING RULES 15

13 [AS4] (i) Raja is 10 years older than Ravi. If Ravi’s age is x years, what is Raja’s age? (ii) A ball and a kite cost Rs. 65. If the ball costs Rs. b, what is the cost of the kite? 14 [AS4] (i) Each boy eats 5 toffees. How many toffees do ‘n’ boys eat? (ii) Sandy scores 8 marks in long answer type questions. For short answer questions, 2 marks are given for each correct answer. What is Sandy’s total score if she answers x short answer questions correctly? EXERCISE 9.1. PATTERNS – MAKING RULES 16

EXERCISE 9.2 EXPRESSIONS WITH VARIABLES 9.2.1 Key Concepts i. A variable takes different values. Its value is not ﬁxed. ii. We may use any letter a, b, m, n, p, q, x, y, z etc. to represent a variable. iii. A variable allows us to express relations in any practical situation. iv. Variables are numbers, although their value is not ﬁxed. We can do operations on them just as in the case of ﬁxed numbers. v. We can form expressions with variables using different operations. Some examples are 2 - m, 3s + 1, 8p, x etc. 3 9.2.2 Additional Questions Objective Questions 1. [AS3] ‘a’ increased by twice ‘b’ is written as______. (A) a + 2b (B) 2(a + b) (C)b + 2a (D)a + b 2. [AS3] “3 times the difference of 30 and c” is written as________. (A) 3(30) − c (B) 3(30 − c) (C)30 − 3c (D)3c –30 3. [AS3] “70 increased by the quotient of x and y” can be written as__________. (A) 70 − x (B) 70 × x y y (C) 70 + x (D) 70 ÷ x y y 4. [AS3] “3p + 5” can be written as________. (B) 5 more than 3 times p (A) 5 times product of 3 and p (D)5 times 3 times 3 and p (C)5 less than product of 3 and p EXERCISE 9.2. EXPRESSIONS WITH VARIABLES 17

5. [AS3] 6n –1 can be written as_________. (B) One less than six times ‘n’. (A) One and six times ‘n’. (D)One time six times ‘n’. (C)One more than six times ‘n’. Short Answer Type Questions 6 [AS3] 'n' represents any integer. Write the expression that represents any multiple of 3. 7 [AS3] Represent the numbers in terms of n, where 'n' represents any integer. (i) The square of any multiple of 5. (ii) The cube of any even number. Long Answer Type Questions 8 [AS3] Write each of the following statements as an expression. (i) n is increased by thrice m. (ii) Three times the sum of 30 and C. (iii) 70 decreased by the quotient of y and x. (iv) Length in centimetres that is 4 cm longer than y metres. 9 [AS3] The symbol ‘n’ represents any integer. Write the statement for the following expressions. (i) 3n (ii) 2n + 1 (iii) n − n 3 (iv) 2 n − 8 5 EXERCISE 9.2. EXPRESSIONS WITH VARIABLES 18

EXERCISE 9.3 RULES FROM GEOMETRY AND SIMPLE EQUATIONS 9.3.1 Key Concepts i. Variables allow us to express many common rules of geometry and arithmetic in a general way. ii. An equation is a condition on a variable. Such a condition limits the values the variable can have. iii. An equation has two sides, LHS and RHS on either side of the equality. iv. The LHS of an equation is equal to its RHS only for deﬁnite values of the variable in the equation. Such a value of the variable is called the solution of the equation. v. To get the solution of an equation, one of the methods used is the Trial and Error method. 9.3.2 Additional Questions Objective Questions 1. [AS3] 8 less than total number of students x is thirty. The equation that representsthe given statement is ________. (A) 8 − x = 30 (B) 30 − 8 = x (C) x + 30 = 8 (D) x − 8 = 30 2. [AS1] The solution of the equation –6 + a = 12 is_________. (A) –6 (B) 18 (C) 6 (D) –18 3. [AS3] The inverse of “Multiply by –3” is ________. (A) Divide by 3 (B) Multiply by 3 (C)Divide by –3 (D) Multiply by 1 3 EXERCISE 9.3. RULES FROM GEOMETRY AND SIMPLE EQUATIONS 19

4. [AS1] The solution of the equation “the difference between n and 16 is 5” is________. (A) 11 (B) –11 (C) 21 (D) –21 5. [AS1] The equation that does not have m = 42 as a solution is _______. (A) m = 6 (B) m = 1 7 42 (C) m = 13 (D) m = 2 4 21 Very Short Answer Type Questions 6 [AS3] Answer the following questions in one sentence. (i) Write any two simple equations and give their LHS and RHS. (ii) Identify LHS and RHS of the following equation. a + 7 = 12 (iii) Write the LHS and RHS of the equation 2z + 3 = 5z + 10. (iv) Write an equation for the statement ‘5 times a number ‘a’ equals to 20’ and identify its LHS and RHS. (v) Write an equation for the statement ‘14 more than a number ‘n’ equals 20’ and identify its LHS and RHS. Short Answer Type Questions 7(i) [AS1] Find the solution of the equation x – 4 = 2 by trial and error method. (ii) [AS1] Solve the equation 3x − 5 = 7 − x by trial and error method. EXERCISE 9.3. RULES FROM GEOMETRY AND SIMPLE EQUATIONS 20

8(i) [AS1] Complete the patterns given: x 2468 2x + 5 9 29 a 13 6 7 1 58 3a − 2 p 5 10 15 20 25 26 5p + 1 (ii) [AS1] The next term in the sequence 1, 10, 20, 31 is . 9(i) [AS3] a) Find the general rule for the perimeter of a rectangle. Use variables ‘l ’ and ‘b’ for length and breadth of the rectangle respectively. b) Find the general rule for the area of a square by using the variable ‘s’ for the side of a square. c) What is the rule for perimeter of an isosceles triangle? (ii) [AS3] a) Find an expression for the area (A) of a rectangle whose length is 'l' and breadth is 'b'. b) Express the perimeter of a triangle ‘p’ as an expression, when its sides are 'a', 'b' and 'c'. c) The perimeter of a plot is 4a. If it is in the shape of a square, what is its side? Long Answer Type Questions 10 [AS1] Solve the following equations: (i) 2x + 1 = 5 (ii) 3a – 3 = 9 (iii) 5z – 1 = 24 (iv) 2q + 5 = 17 (v) 8b + 6 = 22 EXERCISE 9.3. RULES FROM GEOMETRY AND SIMPLE EQUATIONS 21

11 [AS3] State which of the following are equations. (i) x + 3 = 7 (ii) r + 5 >8 (iii) 3x – 5 < 2 (iv) 2a – 4 = 3 (v) 3z – 27 > 3 12 [AS3] Write the LHS and RHS of the following equations: (i) x + 5 = 11 (ii) 2p – 6 = 10 (iii) 4a + 1 = 8 (iv) 3z + 9 = 16 (v) 2b – 4 = 8 EXERCISE 9.3. RULES FROM GEOMETRY AND SIMPLE EQUATIONS 22

CHAPTER 10 PERIMETER AND AREA EXERCISE 10.1 PERIMETER 10.1.1 Key Concepts i. Perimeter is the distance covered along the boundary forming a closed ﬁgure when you go around the ﬁgure once. ii. a. Perimeter of a rectangle = 2 × (length + breadth) b. Perimeter of a square = 4 × length o f its side c. Perimeter of an equilateral triangle = 3 × length o f any side iii. a. Figures in which all sides and angles are equal are called regular closed ﬁgures. b. The perimeter of a regular ﬁgure is equal to the number of sides multiplied by the length of each side. 10.1.2 Additional Questions Objective Questions 1. [AS1] The perimeter of a square with side 8 cm is ______. (A) 2 cm (B) 32 cm (C)64 cm (D)16 cm 2. [AS1] The length of the side of a square if the perimeter is 48 cm is ______. (A) 8 cm (B) 4 cm (C)12 cm (D)16 cm EXERCISE 10.1. PERIMETER 23

3. [AS4] A wire in the shape of an equilateral triangle of side 10 cm is bent into a regular pentagon. Each side of pentagon so formed is _______. (A) 8 cm (B) 4 cm (C)6 cm (D)12 cm 4. [AS1] The perimeter of an equilateral triangle with side 5 cm is ______. (A) 15 cm (B) 20 cm (C)25 cm (D)60 cm 5. [AS3] The perimeter of a rectangle whose length is ’l’ units and breadth is ’b’ units is units. (A) 2(l –b) (B) lb (C) l (D)2(l + b) b Very Short Answer Type Questions . 6 Fill in the blanks. . (i) [AS3] The length of the boundary of a ﬁgure is called its . (ii) [AS3] The perimeter of an equilateral triangle . (iii) [AS1] If the perimeter of a regular pentagon is 10 cm, its side is (iv) [AS2] If the side of a square is doubled, its perimeter is (v) [AS3] Side of square = perimeter. Short Answer Type Questions 7 [AS1] Find the perimeter of following: (i) A table with sides 30 cm, 15 cm, 30 cm, 15 cm. (ii) Your mathematics textbook. 8(i) [AS4] a) A rectangular ﬁeld is 50 m by 40 m. Mahesh goes ten times around it. What is the distance covered by him? b) Find the breadth of the rectangular ﬁeld whose length is 70 cm and perimeter is 200 cm. EXERCISE 10.1. PERIMETER 24

(ii) [AS4] The length of a rectangular ﬁeld is twice its breadth. A man jogged around it 5 times and covered a distance of 3 km. What is the length of the ﬁeld? 9 [AS4] A rectangular park of sides 100 m and 70 m has to be fenced with a barbed wire. The cost of the wire is Rs. 20 per metre. Find the length of the wire required for fencing and also the cost of fencing the park. Long Answer Type Questions 10 [AS5] Find the perimeters of the following ﬁgures. (i) (ii) 11 [AS1] Find the length of the side of: (i) a square if its perimeter is 48 cm. (ii) an equilateral triangle if its perimeter is 36 cm. (iii) a regular pentagon if its perimeter is 65 cm. 12 [AS4] A wire in the shape of an equilateral triangle of side 16 cm is bent into a regular octagon. Find the length of each side of the octagon. EXERCISE 10.1. PERIMETER 25

13 [AS1] (i) Find the perimeter of a rectangle which is 54 m long and 36 m wide. (ii) Find the length of a rectangle whose perimeter is 80 cm and breadth is 12 cm. (iii) Find the breadth of a rectangle whose perimeter is 120 m and length is 36 m. 14 [AS4] A piece of string is 120 cm long. What will be the length of each side if the string is bent to form: (i) a square? (ii) an equilateral triangle? (iii) a regular pentagon? (iv) a regular hexagon? 15 [AS4] Mr. Varma has an orchard of length and breadth 280 m and 200 m respectively. He wants to fence it with 4 rounds of barbed wire. Find the cost of fencing at Rs. 35 per metre. EXERCISE 10.1. PERIMETER 26

EXERCISE 10.2 AREA 10.2.1 Key Concepts i. The amount of surface enclosed by a closed ﬁgure is called its area. ii. To calculate the area of a ﬁgure using a squared paper, the following conventions are adopted. a. Ignore portions of the area that are less than half a square. b. Count more than half a square in the region as one square. c. Take the exact half square as ½ sq. unit. iii. Area of a rectangle = length × breadth iv. Area of a square = side × side v. The area of a square is more than the area of a rectangle having the same perimeter as that of a square. 10.2.2 Additional Questions Objective Questions 1. [AS1] The area of a square with perimeter 28 cm is _____. (A) 7 cm2 (B) 49 cm 2 (C)784 cm 2 (D)196 cm2 2. [AS1] The area of a square whose perimeter is equal to perimeter of a rectangle with length 10 cm and breadth 6 cm is ______. (A) 64 cm2 (B) 8 cm 2 (C)16 cm 2 (D)32 cm2 3. [AS2] If the length of a rectangle is doubled, the area of the new rectangle formed_______. (A) Remains the same (B) Is doubled (C)Becomes four times (D)Is halved EXERCISE 10.2. AREA 27

4. [AS1] The side of a square of area 256 cm2 is ________. (A) 12 cm (B) 16 cm (C)18 cm (D)20 cm 5. [AS1] The length of a rectangle of area 135 cm2 and breadth 9 cm is ________. (A) 11 cm (B) 12 cm (C)13 cm (D)15 cm Short Answer Type Questions 6 [AS1] In a rectangle, if l = 40 cm and its perimeter, P = 130 cm, find the breadth, b and the area, A of the rectangle. 7(i) [AS1] A rectangle has a perimeter of 20 cm. If the measures of sides are whole numbers in centimetres, ﬁnd the four possible pairs of values for the length and the width of the rectangle. (ii) [AS1] Convert: a) 2.45 m2 to cm2 b) 365 mm 2to cm 2 8 [AS1] If the area of a square of side 16 cm is same as that of a rectangle of length 64 cm, what is the breadth of the rectangle? 9 [AS2] What will happen to the area of a rectangle if: (i) its length is doubled and breadth is trebled? (ii) its length and breadth are doubled? 10 [AS2] What will happen to the area of a square if its side is: (i) doubled? (ii) halved? 11(i) [AS4] Find the cost of distempering four walls of a room at the rate of Rs. 20 per sq. m, if each wall is square shaped of side 4 m. (ii) [AS4] A tile measures 10 cm × 10 cm. How many such tiles are required to cover a wall of dimensions 4 m × 2.5 m? 12 [AS4] Find the perimeter of a rectangular ﬁeld whose length is four times its width and which has an area 30976 sq. cm? EXERCISE 10.2. AREA 28

13 [AS4] It costs Rs. 1000 to fence a square ﬁeld at Rs. 2.50 per metre. Find (i) the length of the side of the square. (ii) the area of the square. 14(i) [AS4] A play ground measures 300 m by 170 m. Find the cost of planting grass on this at the rate of Rs. 80 per hectare. (ii) [AS4] A square piece of ground is 75 m long. Find the cost of erecting a fence around it at Rs. 4 per metre. Long Answer Type Questions 15 [AS1] (i) The area of a rectangle is 240 cm2 . If its length is 20 cm, ﬁnd its breadth. (ii) Find the perimeter of a rectangle whose area is 650 cm2 and breadth is 13 cm. 16 [AS1] Find the perimeter of a square whose area is 2500 m2 . 17 [AS2] What happens to the area of a rectangle when: (i) its breadth is doubled, the length remaining the same? (ii) its length and breadth both are doubled? 18 [AS2] What will happen to the area of a square if its side is trebled? 19 [AS4] The area of a square ﬁeld is 100 hectares. Find its side and perimeter. 20 [AS4] Four square ﬂower beds each of side 1.5 m are dug on a piece of land 8 m long and 5 m wide. What is the area of the remaining part of the land? 21 [AS4] The length of a rectangular plot of land is twice its breadth. If the perimeter of the plot is 300 m, ﬁnd its area. 22 [AS4] What is the area of a square shaped handkerchief of side 40 cm? 23 [AS4] The sides of a rectangular ground are 300 m and 120 m. Find its area in hectares. 24 [AS4] Find the area in hectares of a rectangular ﬁeld whose length is 240 m and breadth is 110 m. 25 [AS4] How many envelopes can be made out of a sheet of paper 125 cm by 85 cm, if each envelope requires a piece of paper of size 17 cm by 5 cm? EXERCISE 10.2. AREA 29

26 [AS4] A farmer has a rectangular ﬁeld which measures 350 m by 240 m. He hopes that by sowing a variety of wheat, the yield will be 25 quintals per hectare, and it will sell in the market at Rs. 160 per quintal. What is his expected income? 27 [AS4] The length and breadth of a playground are 52 m 20 cm and 34 m 8 cm respectively. Find the cost of levelling it at Rs. 1.50 per square metre. 28 [AS4] Two plots of land have the same perimeter. One is a square of side 60 m, while the other is a rectangle whose breadth is 1.5 m. Which of the plots has greater area and by how much? 29 [AS4] A room is 12 m long and 8 m broad. It is surrounded by a verandah which is 2 m wide all over. Find the cost of ﬂooring the verandah with marble at Rs. 25 per square metre. 30 [AS4] A person walks at 4 km/h. How long will he take to go round a square ﬁeld 4 times, if its area is 900 m2 ? 31 [AS4] A rectangular court yard is 3 m 78 cm long and 5 m 25 cm broad. It is desired to pave it with square tiles of the same size. What is the largest size of the tile that can be used? Also ﬁnd the number of such tiles. 32 [AS5] (i) Find the area of the following ﬁgure by counting the squares. (ii) Find the area of the following ﬁgure by counting the squares. EXERCISE 10.2. AREA 30

CHAPTER 11 RATIO AND PROPORTION EXERCISE 11.1 COMPARING QUANTITIES WITH DIFFERENT UNITS 11.1.1 Key Concepts i. A type of comparison where we compare things or quantities by division is called ratio. ii. When we compare two quantities, we have to take care of the order of the quantities. iii. In general, the ratio of two quantities a and b is written as a : b and we read it as a is to b. iv. a : b b : a unless a = b. 11.1.2 Additional Questions Objective Questions 1. [AS3] In 13 : 17, 17 is called the . (A) Antecedent (B) Consequent (C)Middle term (D)Extreme 2. [AS1] If a = 2b, then a : b = . (A) 2 : 1 (C)3 : 4 (B) 1 : 2 (D)4 : 3 3. [AS1] The ratio of Rs. 2.50 and Rs. 3.75 is . (A) 3 : 2 (B) 4 : 5 (C)6 : 7 (D)2 : 3 EXERCISE 11.1. COMPARING QUANTITIES WITH DIFFERENT UNITS 31

4. [AS1] If 2x = 5y, then x : y is . (A) 5 : 2 (C)3 : 4 (B) 2 : 5 (D)5 : 9 5. [AS1] The ratio 384 : 480 in its simplest form is . (A) 3 : 5 (B) 5 : 4 (C)4 : 5 (D)2 : 5 Very Short Answer Type Questions 6. [AS3] Match the statements on ratio under column A with the appropriate answers given undercolumn B. Column A units. Column B i. A ratio has a. 2500 : 1 ii. The ratio of 2 cm to 10 mm b. order of quantities iii. The ratio of 5 g to 2 mg c. 2 : 1 iv. In a ratio is very important. d. “is to” ( : ) v. The symbol for ratio e. No Short Answer Type Questions 7 [AS4] John has 25 pens and Abhishek has 5 pencils. Find the ratio of the number of pens that John has to the number of pencils that Abhishek has. EXERCISE 11.1. COMPARING QUANTITIES WITH DIFFERENT UNITS 32

8 [AS5] In the ﬁgure, ﬁnd the ratio of number of white squares to the number of black squares and also write their number. Long Answer Type Questions 9 [AS4] Rani bought 5 kg of rice, Asha bought 4 kg of oil and Naresh bought 50 grams of cashew nuts. Find the ratio of rice to oil and cashew nuts. EXERCISE 11.1. COMPARING QUANTITIES WITH DIFFERENT UNITS 33

EXERCISE 11.2 RATIO IN DIFFERENT SITUATIONS 11.2.1 Key Concepts i. A ratio is said to be in the simplest form or in the lowest terms when it is written in terms of whole numbers with no common factors other than 1. For example, the simplest form of 35 : 40 is 7 : 8 (∵ 35 = 7×5 = 7 ) 40 8×5 8 11.2.2 Additional Questions . Objective Questions (B) 2 : 6 1. [AS1] A ratio equivalent to 2 : 3 is (A) 4 : 3 (C)6 : 9 (D)10 : 9 2. [AS1] The angles of a triangle are in the ratio 1 : 2 : 3. The measure of the largest angle is . (A) 30◦ (B) 60◦ (C) 90◦ (D) 120◦ 3. [AS4] The length and the breadth of a ﬁeld are in the ratio 5 : 3. If the breadth of the ﬁeld is 42 m, then its length is (A) 50 m (B) 70 m (C)60 m (D)90 m 4. [AS4] Rahul has 3 marbles more than the number of marbles with Rajesh. If Rajesh has 12 marbles, then the ratio of marbles with Rajesh and Rahul is . (A) 4 : 5 (B) 5 : 4 (C)6 : 7 (D)7 : 6 EXERCISE 11.2. RATIO IN DIFFERENT SITUATIONS 34

5. [AS4] The ratio of boys and girls in a school is 12 : 5. If there are 840 girls in the school, then the number of boys is . (A) 1190 (B) 2016 (C) 2856 (D) 2142 Very Short Answer Type Questions (B) 3 : 5 6 [AS1] Choose the correct answer. (D)5 : 4 (i) The simplest form of 16 : 20 is _______. (B) 5 : 4 (A) 3 : 2 (D)3 : 4 (C)4 : 5 (B) 6 : 5 (ii) The simplest form of 18 : 24 is_______. (D)4 : 7 (A) 6 : 4 (C)4 : 4 (B) 3 : 4 (D)1 : 4 (iii) The simplest form of 12 : 28 is ________. (A) 7 : 5 (B) 7 : 11 (C)3 : 7 (D)4 : 9 (iv) The simplest form of 15 : 20 is ________. (A) 5 : 4 (C)2 : 4 (v) The simplest form of 21 : 33 is ______. (A) 3 : 5 (C)5 : 3 EXERCISE 11.2. RATIO IN DIFFERENT SITUATIONS 35

Short Answer Type Questions 7 [AS4] Let us assume that there are 56 students in a class of which 26 are girls. Find (i) The ratio of number of boys to number of girls. (ii) The ratio of number of boys to total number of students. (iii) The ratio of number of girls to total number of students. 8(i) [AS5] Finding the ratio among different quantities of chocolates: The given figure shows two boxes: One is Rani’s and the other is Priya’s. Observe the two boxes and write the ﬁrst quantity and second quantity. Also compare them using a statement. Find the ratio between these two boxes of chocolates. (ii) [AS4] Rajesh got 50 marks in Hindi, 75 marks in Maths and 80 marks in Social, each out of 100 marks. Find the ratio of marks scored by Rajesh in the three individual subjects. 9(i) [AS4] In a school, there are 22 boys and 33 girls. Find the ratio of number of boys to the number of girls and express in the simplest form. (ii) [AS4] In an exam, Raghu got 95 marks in Mathematics and 100 marks in Science out of 100 marks individually. Find the ratio of marks in Mathematics to Science and express it in the simplest form. 10(i) [AS4] The ratio of male and female employees in a multinational company is 5 : 3. If there are115 male employees in the company, then ﬁnd the number of female employees. (ii) [AS4] Sunitha earned Rs. 40,000 and paid Rs. 5000 as income tax. Find the ratio of a) Income tax to income. b) Income to income tax. EXERCISE 11.2. RATIO IN DIFFERENT SITUATIONS 36

11(i) [AS5] In the given ﬁgure, ﬁnd the ratio of the number of: a) shaded parts to unshaded parts b) unshaded parts to shaded parts (ii) [AS5] In the following ﬁgure, express the ratio of shaded parts to unshaded parts in the simplest form. 12 [AS5] Draw a four sided closed ﬁgure and divide it into the same number of equal parts horizontally and vertically. Shade the ﬁgure with any colour so that the ratio of shaded parts to unshaded parts is 1 : 7. EXERCISE 11.2. RATIO IN DIFFERENT SITUATIONS 37

EXERCISE 11.3 DIVISION OF A GIVEN QUANTITY IN A GIVEN RATIO 11.3.1 Key Concepts i. The ratio of two quantities ‘a’ and ‘b’ can be given in any one of the following ways: a. Symbolic form: a : b b. Fractional form: a b c. Verbal form: ‘a’ is to ‘b’ 11.3.2 Additional Questions Objective Questions 1. [AS1] If A, B and C divide Rs.1200 among themselves in the ratio 2 : 3 : 5, then B’s share is . (A) Rs. 240 (B) Rs. 300 (C)Rs. 350 (D)Rs. 360 2. [AS4] A bag of 88 marbles is shared between Raghu and Harish in the ratio 3 : 5. How many marbles does Harish receive? (A) 33 (B) 35 (C) 55 (D) 65 3. [AS4] 65 chocolates are divided between Manisha and Shravya in the ratio 5 : 8. Then the number of chocolates Manisha gets is . (A) 25 (B) 40 (C) 38 (D) 52 EXERCISE 11.3. DIVISION OF A GIVEN QUANTITY IN A GIVEN RATIO 38

4. [AS4] When some amount is divided between Nishanth and Suresh in the ratio 4 : 5, Nishanth got Rs. 8000. Then Suresh’s share is . (A) Rs. 18,000 (B) Rs. 10,000 (C)Rs. 15,000 (D)Rs. 13,000 5. [AS1] Two numbers are in the ratio 5 : 6. If the sum of the numbers is 198, then the two numbers are . (A) 100, 98 (B) 80, 118 (C)120, 78 (D)90, 108 Short Answer Type Questions 6(i) [AS4] Rahul, Ravi and Sunil divide Rs. 24,000 among themselves in the ratio 1 : 3 : 4. Find the share of each. (ii) [AS4] A box of 25 pencils is shared between Akshay and Aditya in the ratio 2 : 3. a) How many pencils does Aditya receive? b) How many pencils does Akshay receive? EXERCISE 11.3. DIVISION OF A GIVEN QUANTITY IN A GIVEN RATIO 39

EXERCISE 11.4 PROPORTION AND UNITARY METHOD 11.4.1 Key Concepts i. Equalities of ratios is called proportion. In general, if the ratio of a and b is equal to the ratio of c and d, we say that they are in proportion. This is represented as a : b :: c : d. 11.4.2 Additional Questions Objective Questions 1. [AS1] If 4, a, a and 36 are in proportion, then a = . (A) 16 (B) 18 (C) 20 (D) 12 2. [AS3] If a, b, c and d are in proportion, then . (A) ab = cd (B) ac = bd (C)ad = bc (D)None of these 3. [AS3] If 14, 36, x and 72 are in proportion, then the value of x is . (A) a2 = bc (B) 28 (C)c2 = ab (D)None of these 4. [AS4] If the cost of 5 pens is Rs. 30, then the cost of one dozen pens is (A) Rs. 60 (B) Rs. 120 (C)Rs. 72 (D)Rs. 140 EXERCISE 11.4. PROPORTION AND UNITARY METHOD 40

5. [AS1] The ﬁrst, second and fourth terms of a proportion are 16, 24 and 54 respectively. The third term is . (A) 32 (B) 48 (C) 28 (D) 36 Very Short Answer Type Questions 6. [AS1] Match the ratios in column A with their corresponding terms in column B. Column A Column B i. 2 : 3 : : 16 : a. Product of means ii. The costof 6 erasers when the cost b. Proportion of 5 erasers is Rs. 20 c. 10 iii. Equality of two ratios iv. In a proportion, product of extremes = d. Rs. 24 v. 5 : 7 : : : 14 e. 24 Short Answer Type Questions 7(i) [AS2] Mahesh and Sai added their money and bought 20 eggs. Mahesh contributed Rs.12 and Sai Rs.18. They wanted to distribute the eggs between them. Sai said 10 eggs for each and Mahesh said 12 eggs for Sai and 8 eggs for him. Who is correct? Justify your answer. (ii) [AS4] If three oranges cost is Rs. 30, how much would 5 oranges cost? Long Answer Type Questions 8 [AS4] A farmer has sheep and cows in the ratio of 7 : 4. (i) How many sheep does the farmer have, if he has 240 cows? (ii) Find the ratio of number of sheep to the total number of animals the farmer has. (iii) Find the ratio of the total number of animals with the farmer to the number of cows with him. EXERCISE 11.4. PROPORTION AND UNITARY METHOD 41

(iv) How many animals did the farmer have in all? (v) Find the ratio between the number of cows and the number of sheep that the farmer has. 9 [AS4] The cost of 7 boxes of apples is Rs. 280. What is the cost of 4 boxes of apples? 10 [AS4] A box of fruits contains apples and oranges. For every 2 apples, there are 6 oranges. Complete the table based on the given information. Apples 24 6 Oranges Total no. of fruits 6 12 24 24 40 (i) What is the ratio of the number of apples to that of oranges? (ii) If you have 8 apples, how many oranges will you have? (iii) If there are 32 fruits in a medium-sized box, how many will be apples? (iv) In the super fat box, there are 40 fruits. How many will be oranges? (v) In the box, there are 12 apples. How many fruits are there in the box? 11 [AS4] (i) A train journey of 75 km costs Rs. 215. How much will a journey of 120 km cost? (ii) If the sales tax on a purchase worth Rs 60 is Rs. 4.20, what will be the sales tax on the purchase worth Rs. 150? EXERCISE 11.4. PROPORTION AND UNITARY METHOD 42

CHAPTER 13 PRACTICAL GEOMETRY EXERCISE 13.1 A LINE SEGMENT 13.1.1 Key Concepts i. The geometrical instruments used to construct shapes: a. A graduated ruler b. The compass c. The divider d. Set–squares e. The protractor 13.1.2 Additional Questions Objective Questions 1. [AS3] A line segment has a deﬁnite . (A) Length (B) Breadth (C)Height (D) None of these 2. [AS3] The distance between the points A and B is called the of AB. (A) Breadth (B) Length (C)Height (D)None of these 3. [AS1] If AB = 6.7 cm and C is the mid–point of AB, then AC = . (A) 3.5 cm (B) 3.25 cm (C)3.35 cm (D)3.15 cm EXERCISE 13.1. A LINE SEGMENT 43

4. [AS3] Line segment AB is line segment BA. (A) Equal to (B) Not equal to (C)Perpendicular to (D)None of these 5. [AS3] The length of a line segment is the distance between its two end points. (A) Maximum (B) Shortest (C)Congruent (D)None of these Short Answer Type Questions 6(i) [AS1] Given that AB = 12 cm, AD = 18 cm and AE = 20 cm, ﬁnd BC, CD and DE. The distance between BC and CD are equal as shown in the ﬁgure. (ii) [AS1] Given that PQ = 6 cm, mark a point R on PQ. Find the length between PR and QR and assume R is about 5 cm away from P on the line. 7(i) [AS5] If AB = 7.5 cm and CD = 2.5 cm, construct a line segment whose length is equal to a) AB − CD b) 2AB (ii) [AS5] Draw a line segment CD. Produce it to CE such that CE = 3CD. 8 [AS5] Draw a line segment AC of length 5 cm. Mark a point B on AC and ﬁnd the length between AB and BC. Assume that ‘B’ is the midpoint of AC. 9(i) [AS5] By using ruler, construct a line segment of length 5.9 cm. (ii) [AS5] Construct a line segment RS such that it is three times that of PQ which is 2 cm. 10 [AS5] Construct a line segment CD of length 12 cm. Mark a point ‘O’ on it at a distance of 6 cm from C. Measure CO and OD. What do you observe? EXERCISE 13.1. A LINE SEGMENT 44

11(i) [AS5] Construct a line segment of length 7.2 cm using compass. (ii) [AS5] PQ = 2.4 cm. Construct RS using compass such that the length of RS is four times that of PQ. EXERCISE 13.1. A LINE SEGMENT 45

EXERCISE 13.2 CONSTRUCTION OF A CIRCLE 13.2.1 Key Concepts i. Every point on the boundary of a circle is equidistant from its centre. 13.2.2 Additional Questions Objective Questions 1. [AS3] The geometrical instrument we use to construct a circle is________. (A) A ruler (B) A compass (C) A divider (D)A protractor 2. [AS3] A set of points in a plane which are at the same distance from a ﬁxed point is called a . (A) Rectangle (B) Rhombus (C)Square (D)Circle 3. [AS3] The distance between the centre of a circle and any point on it is called its . (A) Radius (B) Diameter (C) Chord (D) Tangent 4. [AS3] A circle can have radii. (A) Two (B) Three (C) Five (D)Inﬁnitely many EXERCISE 13.2. CONSTRUCTION OF A CIRCLE 46

5. [AS3] Two circles having the same radii are called circles. (A) Concentric (B) Congruent (C)Similar (D)None of these Very Short Answer Type Questions 6 [AS3] Answer the following questions in one sentence. What is meant by concentric circles? 7 [AS5] Answer the following questions in one sentence. (i) Construct a pair of concentric circles of radii 3 cm and 5 cm. (ii) Construct a set of concentric circles of radii 3 cm, 4 cm and 5 cm. (iii) Construct a pair of concentric circles of radii 2.5 cm and 5 cm. (iv) Construct a set of concentric circles of radii 4 cm, 5 cm and 6 cm. Short Answer Type Questions 8(i) [AS5] Construct a circle with centre ‘O’ and radius 2.5 cm. (ii) [AS5] Construct a circle with centre ‘P’ and radius 3 cm. 9(i) [AS5] Construct three circles in such a way that the circles intersect at four points. (ii) [AS5] Construct 5 circles in such a way that the circles intersect at 8 points. EXERCISE 13.2. CONSTRUCTION OF A CIRCLE 47

EXERCISE 13.3 PERPENDICULARS 13.3.1 Key Concepts i. Two lines are said to be perpendicular if they intersect such that the angles formed between them are right angles. 13.3.2 Additional Questions Objective Questions 1. [AS3] If two lines intersect at right angles, then they are called . (A) Parallel lines (B) Perpendicular lines (C)Transversal lines (D)None of these 2. [AS3] The symbol for ‘is perpendicular to’ is . (A) = (B) ⊥ (C) (D)None of these 3. [AS3] A divides a line segment into two equal parts. (A) Bisector (B)Perpendicular (C)Divider (D)None of these 4. [AS3] The line which is perpendicular to the given line segment and also passes through its mid–point is called its . (A) Perpendicular bisector (B) Angular bisector (C)Median (D)None of these EXERCISE 13.3. PERPENDICULARS 48

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