Mrs. Jyoti Kohli, TGT (Mathematics) Don Bosco …...6 Chapter 10 – Practical Geometry Construction of a line parallel to a given line, through a point not on the line Constructing

PREFACE

I take great pleasure in presenting this Mathematics Assignment Booklet for

Class 7 for the academic session 2019-2020. This booklet has been written in

accordance with the CBSE and NCERT pattern. Through this Booklet, I want

to supplement the teaching material in the textbook. This booklet is aimed at

providing ample practice to the students in the various mathematical concepts

so that they may grasp these concepts and effectively apply them, with

sufficient drill and practice. I also hope this booklet will stimulate the students‟

mind and interest in Mathematics.

One of the unique features of this booklet is the variety of exercises that have

been incorporated. The questions have been presented in a lucid manner so

as to arouse the interest of the students in mathematics and to develop

problem-solving skills in them along with logical and lateral thinking. These

worksheets will help the students to quickly test their knowledge and skills.

The booklet especially aims to make Mathematics enjoyable through activities,

crosswords, and enrichment exercises that appeal to students. Keeping in

mind that the level of understanding of each student may differ at any point of

time, an effort has been made to introduce questions progressively such that

each student gains confidence and learns concepts in an organized manner.

The Sample test papers at the end of the booklet will help better equip

students for their exams as they self-administer these tests to simulate

examination conditions.

I would also like to take the opportunity to express my sincere appreciation to

Fr. Babu Varghese, our school Principal, for his constant support, guidance

and encouragement. I am also grateful to Mr. Baiju Mathew, our subject

coordinator for Mathematics, for believing in me and for his support and

suggestions in preparing this booklet.

I welcome any suggestions for improvement and I shall acknowledge and

incorporate them in the subsequent edition.

Thank you!

Mrs. Jyoti Kohli, TGT (Mathematics)

Don Bosco School, Alaknanda, New Delhi

- 2 -

CONTENTS

S.No. Topic Page Number

1) Syllabus

2) Assignment 1 – Integers…………………………….…. 7

3) Assignment 2A – Fractions and Decimals…..…………. 9

4) Assignment 2B – Fractions and Decimals…..…………. 11

5) Assignment 3 – Data Handling ………………………… 13

6) Assignment 4 – Simple Equations……..……………… 16

7) Assignment 5 – Lines and Angles……….…………….. 18

8) Assignment 6 – The Triangle and Its Properties…….. 21

9) Assignment 7 – Congruence of Triangles..…………… 25

10) Assignment 8 – Comparing Quantities ……………….. 27

11) Assignment 9 – Rational Numbers ……………………. 30

12) Assignment 10 – Practical Geometry ..…………………. 33

13) Assignment 11 – Perimeter and Area ..………………… 34

14) Assignment 12 – Algebraic Expressions ……………… 37

15) Assignment 13 – Exponents and Powers …………….. 40

16) Assignment 14 – Symmetry……………………………… 43

17) Assignment 15 – Visualising Solid Shapes ……………. 46

18) Sample Paper 1 – PT1……………………………………... 48

19) Sample Paper 2 – PT2……………………………………… 50

20) Sample Paper 3 – PT3……………………………………… 54

3

Syllabus Academic Session 2019-20

Periodic Test 1

Chapter 1 – Integers

Properties of addition and subtraction of integers

Multiplication and Division of integers

Properties of multiplication and division of integers

Making Multiplication Easier

Simplification using different kinds of Brackets and BODMAS Rule

Chapter 2 – Fractions and Decimals

Revision of Fraction addition and subtraction

Multiplication and Division of fractions

Reciprocal of a fraction

Revision of Decimal addition and Subtraction

Multiplication and Division of Decimal numbers

Multiplication and division of Decimal Numbers by 10, 100 and 1000

Simplification involving Fractions, decimals and BODMAS rule.

Chapter 14 – Symmetry

Lines of symmetry for regular polygons

Rotational symmetry

Line symmetry and rotational symmetry

Syllabus for Half Yearly Examination

Periodic Test 2

Chapter 1 - Integers (Assignment 1)

Chapter 2 – Fractions and Decimals (Assignment 2A and 2B)

Chapter 3 – Data Handling

Representative values - Arithmetic Mean, Median, Mode

Range

Use of bar graphs

Drawing Double Bar Graph

Chance and probability

4

Chapter 4 – Simple Equations

Setting up of an equation

Solving an Equation

From solution to equation

Applications of simple equations to practical situations

Chapter 5 – Lines and Angles

Related angles - Complementary Angles, Supplementary Angles, Adjacent

Angles,

Linear Pair, Vertically Opposite Angles

Pairs of lines - Intersecting Lines, Transversal.

Angles made by a Transversal - Interior angles, Exterior angles, Corresponding

angles, Alternate interior angles, Alternate exterior angles, Interior angles on the

same side of the transversal

Transversal of Parallel Lines

Checking for parallel lines

Chapter 6 – Triangle and Its Properties

Medians of a triangle

Altitudes of a triangle

Exterior angle of a triangle and its property

Angle sum property of a triangle

Two special triangles : equilateral and isosceles

Sum of the lengths of two sides of a triangle

Right-angled triangles and Pythagoras property

Chapter 13 – Exponents and Powers

Exponents

Laws of Exponents

Miscellaneous examples using the laws of exponents

Decimal number system

Expressing large numbers in the standard form

Chapter 14 – Symmetry (Assignment 14)

5

Syllabus for Periodic Test 3

Chapter 7 – Congruence of Triangles

Congruence of plane figures

Congruence among line segments

Congruence of angles

Criteria for congruence of triangles – SSS, SAS, ASA, RHS Congruence rules

Chapter 8 – Comparing Quantities

Equivalent ratios and Proportions

Percentage

Converting Fractional Numbers and Decimals to Percentage

Converting Percentages to Fractions or Decimals

Converting Percentages to “How Many”

Ratios to Percents

Increase or Decrease as Per Cent

Prices related to an item or buying and selling

Profit or Loss as a Percentage

Simple interest

Chapter 9 – Rational Numbers

Equivalent rational numbers

Positive and negative rational numbers

Rational numbers on a number line

Rational numbers in standard form

Comparison of rational numbers

Rational numbers between two rational numbers

Operations on rational numbers

Syllabus for Annual Examination

Chapter 4 – Simple Equations (Assignment 4)

Chapter 7 – Congruence of Triangles (Assignment 7)

Chapter 8 – Comparing Quantities (Assignment 8)

Chapter 9 – Rational Numbers (Assignment 9)

6

Chapter 10 – Practical Geometry

Construction of a line parallel to a given line, through a point not on the line

Constructing a triangle when the lengths of its three sides are known (sss

criterion)

Constructing a triangle when the lengths of two sides and the measure of the

angle between them are known. (sas criterion)

Constructing a triangle when the measures of two of its angles and the length of

the side included between them is given. (asa criterion)

Constructing a right-angled triangle when the length of one leg and its hypotenuse

are given (rhs criterion)

Chapter 11 – Perimeter and Area

Perimeter and Area of squares and rectangles

Area of Triangles and Parallelogram

Circumference and area of a Circle

Conversion of units

Applications

Chapter 12 – Algebraic Expressions

Terms of an expression, Factors of a term, Coefficients

Like and unlike terms

Monomials, binomials, trinomials and polynomials

Addition and subtraction of algebraic expressions

Finding the value of an expression

Using algebraic expressions – formulas and rules

Chapter 13 – Exponents and Powers (Assignment 13)

Chapter 15 – Visualising Solid Shapes (Assignment 15)

Plane figures and solid shapes

Faces, edges and vertices

Nets for building 3-d shapes

7

Integers

Assignment 1

1 (a) Write a pair of integers whose difference gives −6.

(b) What is the difference between the temperature 15 degrees above zero and 20

degrees below zero?

(c) Solve : −12 +( −3) − ( - 5) . 2.

2 Which of the following statements is true and which is false? Justify each false statement

with an example/reason.

(a) The collection of integers is closed under division.

(b) The product of four positive integers is positive.

(c) The product of four negative integers is negative.

3 Find suitable pairs of integers:

(i) Write a positive integer and a negative integer whose sum is a negative integer.

(ii) Write a positive integer and a negative integer whose sum is a positive integer.

(iii) Write a positive integer and a negative integer whose difference is a negative integer.

(iv) Write a positive integer and a negative integer whose difference is a positive integer.

(v) Write two integers which are smaller than – 5 but their difference is – 5.

(vi) Write two integers which are greater than – 10 but their sum is smaller than – 10.

(vii) Write two negative integers whose difference is 7.

(viii) Write two integers such that one is smaller than –11, and other is greater than –11

but their difference is –11.

(ix) Write two integers whose product is smaller than both the integers.

(x) Write two integers whose product is greater than both the integers.

4 Find each of the following products:

(a) (–18) × (–10) × 9 (c) (–20) × (–2) × (–5) × 7

(b) (–1) × (–5) × (– 4) × (– 6)

5 Find: (a) (–81) ÷ 9 (b) 125 ÷ (–25) (c) (–201) ÷ (–3)

6 Simplify each of the given expressions:

(a) 25 – [ - 15 – ( 23 - 4 of 7 + 10)] (b) 17 + [18 ÷ 3 ( - 2 – 4) + 1]

(c) −125 + 250 † 5 x 10 - 325 (d) (5 – 2 x 3) – [ - 2 – { - 10 + (3 + 10 ÷ 2)}]

(e) 7 – [13 – {–2 – 6 (6 of –5)}] (f) {(-10) – (-5)} + {(-22) + (-40)}

7 Simplify each of the following using a suitable property:

(a) 15 x 93 +15 x ( -73) (b) 80 × 665 × (−125)

(c) − 124 x 25 – 25 x ( - 24) (d) −42 × (−98)

(e) 56 x ( -23) – 56 x 76 – 56 (f) (-13) x (-19) + 13

8 The sum of two integers is – 71. If one of them is – 32, find the other?

8

9 Subtract (-128) from the sum of 55 and (-38).

10 If a = - 5, b = -6 and c = 8 Then show that

(i) (a + b) + c = a + (b + c) (ii) (a – b) (b - a).

11 A boy flung a pebble 18 metres high in the air which fell and settled at the bottom of a

pond 14 metres deep. By how much distance did the pebble fall?

12 A certain freezing process requires that room temperature be lowered from 45° C at a

rate of 6°C every hour. What will be the room temperature 8 hrs after the process

begins?

13 In a test (+4) marks are given for every correct answer and (-2) marks for every wrong

answer. Rohit answered 25 questions correctly and scored 68 marks. How many

questions did he attempt incorrectly?

14 Poonam is an enthusiastic student in her diving class. On the first day, she managed to

dive to a depth of 5m. From second day onwards, she managed to dive five meters

deeper than the previous day, and so on. How far did she dive on the fifth day?

15 A manufacturer is producing two products A and B. He earns a profit of Rs 36 per unit on

product A and a loss of Rs 8 per unit on product B. If he sells 3000 units of product A

and 2500 units of product B, find his overall profit or loss.

16 Suppose we represent the distance above the ground by a positive integer and that

below the ground by a negative integer, then answer the following:

(i) An elevator descends into a mine shaft at the rate of 5 meters per minute. What will be

its position after one hour?

(ii) If it begins to descend from 15 m above the ground, what will be its position after 45

minutes?

17 A shopkeeper earns a profit of Re 1 by selling one pen and incurs a loss of 40 paise per

pencil while selling pencils of her old stock.

(i) In a particular month she incurs a loss of Rs 5. In this period, she sold 45 pens. How

many pencils did she sell in this period?

(ii) In the next month she earns neither profit nor loss. If she sold 70 pens, how many

pencils did she sell?

18 In a true-false test containing 50 questions, a student is to be awarded 2 marks for every

correct answer and –2 for every incorrect answer and 0 for not supplying any answer. If

Yash secured 94 marks in a test, what are the possibilities of his marking correct or

wrong answer?

9

Fractions and Decimals

Assignment 2A

1. Solve

(i) 3 - 3

5 𝑖𝑖 5 +

4

7 (iii)

1

3 +

2

5

𝑖𝑣 2

3 +

4

5 +

7

10 (v) 4

1

2 + 5

1

3 (iv) 6

1

4 – 5

1

2

2. Which is greater : 4

5 or

4

7 (ii)

3

8 or

2

5

3. Arrange the following in ascending order : 3

7,

4

5,

9

10,

1

2.

4. Fill in the blanks

(i) 25

7 x ______ = 1

(ii) 1 3

4 x

4

7 = ______

(iii) 55

220 reduced to the lowest form = _______

(iv) 1

4 of 1 kg = _________ grams

(v) 7

5 =

42

…

5. Riya gave 2

5 of cake to Raman and

1

3 of it to Aman. What fraction of the cake is

left?

6. Find 3

7 of a collection of (i) 70 balls (ii) 42 birds

7. In a class of 80 students one-fifth are girls and the remaining are boys (i) Find the fraction of boys. (ii) Find the number of girls and boys.

8. Find the following products and express them as mixed fractions

(i) 4 x 4

5 (ii) 3 x 1

1

2 (iii) l

3

7 x 7 (iv) 4

1

11 x 33

9. Find (i) 1

3 of 2

2

5 (ii)

2

9 of 7

1

2

10. From a container having 160 litres of oil, 3

5 of the quantity leaked. Find the

remaining quantity of oil.

11. Cost of 1 m of cloth is Rs 25 1

5. Find the cost of 4

2

3 m of cloth.

12. Find the perimeter and area of a rectangle whose length and breadth are 12 1

3 m and 8

1

5 m respectively.

10

13. Find

(i) 15 ÷ 3

5 𝑖𝑖

2

5 ÷ 2

1

2 𝑖𝑖𝑖 55 ÷ 3

2

3 (iv) 3

3

7÷ 8

14. Find the reciprocal of (i) 5

8 (ii)

11

9 (iii) 8 (iv)

1

12 (v) 1 (vi) 0

15. Cost of 10 pens is Rs 75 1

5. Find the cost of one pen.

16. Priya had 17 1

4 m long tape. She cut it into 3 equal pieces. Find the length

of each piece.

17. Find the perimeter of a triangle whose sides are 12 1

2 m, 11

1

3 m and 9

1

4 m.

18. How much is (i) half of half (ii) half of one-fourth (iii) half of one-sixth

19. The capacity of a tank is 80 1

4 litres. If it is three-fourth full, how much water

does it contain?

20. Find the perimeter of a square whose each side is 11 1

4 m.

21. Srishti cycles a distance of 24 1

2 km in 2

1

3 hours. Calculate the distance

covered by her in one hour.

22. A farmer divided his field in three parts. On half of his field he grew wheat. Of the remaining half he used one-third to grow rice and the rest to grow vegetables. What fraction of the field is used to (i) grow rice (ii) grow vegetables

23. How many pieces of length 3 1

4 metres can be cut from a plank of wood of

length 16 1

4 metres?

11

Decimals

Assignment 2B

1) Find the following products (i) 0.005 x 10 (ii) 0.005 x 100

2) Which is greater (i) 0.2 or 0.02 (ii) 0.57 or 0.5 (iii) 0.09 or 0.1 (iv) 1.23 or 2.13

3) Express using decimal : (i) 3352 g as kg (ii) 826 cm as m (iii) 700 g as kg

(iv) 2512 ml as litre (v) 4213 m as km (vi) 9 paisa as Rs (vii) 5 kg 50 g as kg (viii) 1750 gm as kgs (ix) 4 Rs 6 p as Rs

4) Multiply

(i) 253 x 0.06 (iv) 0.627 x 0.4 (ii) 0.04 x 1.8 (v) 132.54 x 8.204 (iii) 55.57 x 8.5 (vi) 0.155 x 0.15

5) Find the product

(i) 0.4 x 0.02 x 0.12 (ii) 2.34 x 0.54 x 0.05 (iii) 8.1 x 0.05 x 0.043 (iv) 2.2 x 0.2 x 0.02

6) If 253 x 12 = 3036, find the following products without actual multiplying (i) 2.53 x 12 (ii) 2.53 x 1.2 (iii) 25.3 x 12 (iv) 25.3 x 1.2

7) The cost of 1 metre of cloth is Rs 35.20. Find the cost of (i) 15 metres of cloth (ii) 20.5 metres of cloth

8) Ticket for a bus-journey comes at the rate of Rs 17.40 per kilometre. How much will Angad have to pay for travelling 125 km ?

9) A bottle of medicine can hold 25 ml of quantity. How much medicine can be stored in1500 bottles? Give the answer in litres.

10) Find the quotient (i) 574.25 ÷ 10 (ii) 574.25 ÷1000

(iii) 574.25 ÷ 100 (iv) 574.25 ÷10000

11) If 32.48 ÷ 16 = 2.03, find the value of (i) 324.8 ÷ 16 (ii) 32.48 ÷ 1.6 12) Divide

(i) 9.6 by 4 (ii) 179.2 by 32 (iii) 0.25 by 5 (iv) 5135.68 by 35.2 (v) 21.14 by 7 (vi) 0.07525 by 2.15

12

13) Hardik covered a distance of 655.2 kilometres in 12 hours. How much did he travel in one hour?

14) 29 books when placed together on a shelf cover a length of 100.05 cm. Find the thickness of each book.

15) Simplify using BODMAS rule:

(i) 4

7 ÷ [1

2

7 -

3

14 ]

(ii) 7 + {1

3 +

2

9 × (

7

4 -

5

12) }

(iii) {(10 1

3 -

2

9 ) ÷

5

18 } of (

3

8 +

1

4 )

(iv) 15

21 of

45

3 –

1

15 ÷

3

7

(v) 3

16 +

13

16 ÷ 2

9

15 ÷ 1

1

3

(vi) 3

4 of

16

27 +

23

14 +

12

18

(vii) 19.05 - [2.06 + {2.57 + (9.91 - 5.09 - 0.76)}]

(viii) 18 - 4.2 ÷ 6 + 1.3 × 0.4

(ix) 6.4 ÷ 1.6 of 5 + 1.3 × 3.1 - 0.07

(x) 50.3 - 5.6 ÷ 0.7 × 1.6 of 3.5

(xi) 23.6 - 0.6 of (9.4 - 5.6) + 0.6 × 3.06

27.08 - [5.6 + 3 of (6.5 - 0.5 × 2.01)]

13

Data Handling

Assignment 3

1) The marks obtained by a group of students in a science test are76, 85, 90, 72, 89, 95, 56, 48, and 75, then what is the range of the marks obtained?

2) What is the mean of the first 9 whole numbers?

3) A batsman scored the following number of runs in six innings: 36, 35, 50, 46, 60, 55 Calculate the mean runs scored by him in an inning.

4) The ages in years of 10 teachers of a school are: 32, 41, 28, 54, 35, 26, 23, 33, 38, 40 (i) What is the age of the oldest teacher and that of the youngest teacher? (ii) What is the range of the ages of the teachers? (iii) What is the mean age of these teachers?

5) Following are the margins of victory in the football matches of a league. 1, 3, 2, 5, 1, 4, 6, 2, 5, 2, 2, 2, 4, 1, 2, 3, 1, 1, 2, 3, 2, 6, 4, 3, 2, 1, 1, 4, 2, 1, 5, 3, 3, 2, 3, 2, 4, 2, 1, 2. Find the mode of this data.

6) Find the mode of (i) 2, 6, 5, 3, 0, 3, 4, 3, 2, 4, 5, 2, 4, (ii) 2, 14, 16, 12, 14, 14, 16, 14, 10, 14, 18, 14

7) Heights (in cm) of 25 children are given below: 168, 165, 163, 160, 163, 161, 162, 164, 163, 162, 164, 163, 160, 163, 16, 165, 163, 162, 163, 164, 163, 160, 165, 163, 162

What is the mode of their heights? What do we understand by Mode here?

8) Which statement is false in the following statement? (a) The data 1, 2, 1, 1, 2, 1, 3, 4, has mode 1 (b) The data 4, 6, 6, 4, has mean 5 (c) The median is always one in a data (d) Mean = (number of observation) / sum of all observation

9) Let us consider the following examples:

(a) You have to decide upon the number of chapattis needed for 25 people called for a feast. (b) A shopkeeper selling shirts has decided to replenish her stock. (c) We need to find the height of the door needed in our house. (d) When going on a picnic, if only one fruit can be bought for everyone, which is the fruit that we would get. In which of these situations can we use the mode as a good estimate?

10) Your friend found the median and the mode of a given data. Median = 42, Mode = 32. Describe and correct your friend‟s error if any: 35, 32, 35, 42, 38, 32, 34.

11) Find the median of the data: 24, 36, 46, 17, 18, 25, 35

14

12) Sale of English and Hindi books in the years 1995, 1996, 1997 and 1998 are given below: Draw a double bar graph and answer the following questions:

(a) In which year was the difference in the sale of the two language books least? (b) Can you say that the demand for English books rose faster? Justify.

13) The bar chart shows the result of a survey to test water resistant watches made by different companies. Each of these companies claimed that their watches were water resistant. After a test the above results were revealed.

(a) Can you work a fraction of the number of watches that leaked to the number tested for each company? (b) Could you tell on this basis which company has better watches?

14) Consider the statements; (i) The Sun coming up from the West (ii) An ant growing to 3 m height. (iii) If you take a cube of larger volume its side will also be larger. (iv) If you take a circle with larger area then it‟s radius will also be larger. (v) India winning the next test series.

15) If a container has 5 red balls and 9 white balls and if a ball is pulled out without seeing, what are the chances of getting a red ball.

16) A box has 10 balls. 3 balls are yellow, 2 balls are red and the remaining are green. Find the probability that a ball drawn is a) Red b) Yellow c) Green.

17) What is the probability of getting an ace from a well shuffled pack of cards?

18) There are 5 marbles in a box with numbers from 1 to 5 marked on each of them, then what is the probability of drawing a marble with number 5.

19) What is probability of getting (a) 3 on a dice (b) a number greater than 4?

15

ACTIVITY ON PROBABILITY

1) Describe the chance of happening of each of the following events:

(a) If today is 8th December, tomorrow will be 9th December. (b) A hundred people can fit into a car. (c) You throw a tail with a coin. (d) You throw a 3 with a die. (e) Throwing an odd number with a die. (f) You throw a number greater than 7 with a die. (g) A red marble is picked up from a bag containing 7 red & 3 green marbles. (h) If you work hard, you will pass the examination. (i) Three lines intersect at 4 points. (j) We can draw a triangle whose angles add up to 180 degrees.

2) There are 10 whole numbers.

(a) Write all the possible outcomes of picking an odd number from first 10 whole numbers. (b) What is the probability of picking 5?

3) Consider the letters from the word GAMES:

(a) Write all the possible outcomes of picking any letter from the word GAMES. (b) Find the probability of selecting the letter E.

4) Write the probability of picking a vowel from the English alphabets.

5) Find the probability of picking the letter M from the word MATHEMATICS.

6) What is the probability of drawing a black card from a deck of cards?

7) Tell whether the probability will be 0 or 1:

(a) If today is Friday then yesterday was Thursday. (b) A die when thrown shall land up with number 0. (c) You are younger today than tomorrow.

8) List the outcomes you can see in this experiment:

(a) Spinning the following wheel. Also, write the probability of getting D

(b) Tossing two coins together. (c) Picking an integer from –7 to 3. Also, what is the probability of getting a positive integer? (d) Getting a multiple of 3 from 20 to 45. Also, what is the probability of getting an even

number?

A

D C

D B

A

16

Simple Equations

Assignment 4

1) Express as equation

(a) The sum of numbers x and 4 is 9

(b) Seven times m plus 3 you 38

(c) If you add 3 to one third of Z, you get 30

2) Write the equation in the statement form

(a) 3p +6 = 21

(b) 𝑦

4 – 5 = 12

3) Solve for the variable in the following equations :

(a) 𝑎

3 =

7

4

(b) 2q + 6 = 12 (c) (5p - 2) = (1 + 2p)

(d) ( 3x - 7

2 ) = ( x +

3

2)

(e) 2p –1 = 23 + p

(f) 3p –1 = 23 and 6m – 2 = 34

(g) 3(b + 2) – (b – 8) = 3(b + 8)

(h) 7𝑥

3 –

4

3 =

𝑥

2 +

3

2

(i) 2y + 7

2 =

39

2

(j) 4 + 3(t + 2) = 10.

(k) - 8 (x - 5) = 16.

(l) 3n +15 = 37.

(m) 2x - 1

3 =

1

6 - x

(n) 2 ( x – 2) + 3 ( 4x – 1 ) = 0

(o) 0.5 x – (0.8 – 0.2x) = 0.2 – 0.3x

4) Solve the equation, 3 x + 5 = 11 by trial and error method.

5) Find the number/numbers: (a) one third of number when added to 5 gives 6

17

(b) 4 is added to a number and the sum is multiplied by 5. If 20 is subtracted from the product and the difference is divided by 8, the result is equal to 10.

(c) One number is 3 less than the two times of the other. If their sum is increased by 7, the

result is 37.

(d) Laxmi takes away 7 from 5

2 of the number and the result is

11

2.

(e) Twice a number when decreased by 7 gives 45.

6) Isha subtracts twice the number of notebooks she has, from 47. She gets 5 as the result. What is the number of notebooks?

7) If two supplementary angles are differ by 44° then what are the angles?

8) The sum of 4 consecutive integers is 70. Then what number is the greatest among them?

9) The total cost of three prizes is Rs. 2790. If the value of the second prize is twice the first and the value of 3rd prize is three times the second prize, find the value of the first prize.

10) The present age of A is twice that of B. 30 years from now, age of A will be times that of B. Find the present ages of A and B respectively.

11) The average of 11, 12, 13, 14 and x is 13. What is the value of x? 12) In an isosceles triangle, the base angles are equal and the vertex angle is 50°. What are the

values of base angles of the triangles? 13) The teacher tells the class that the lowest marks obtained by a student in her class is one-

forth the highest marks plus 8 and equals to 33. What is the highest score?

14) Sachin says that he has 6 books more than the 6 times of the books Priyanka has. Sachin has 42 books. How many books does Priyanka have?

15) A shopkeeper sells mangoes in two types of boxes, one small and one large. A large box

contains double as many as small boxes plus 6 loose mangoes. The number of mangoes in a large box is given to be 100. Then what is the number of mangoes in small box?

16) Vidya‟s mother‟s age is 5 years more than the three times of Vidya‟s present age. Find Vidya‟s present age, if her mother is 44 years old.

17) The sum of 2 consecutive integers is 11. Find the greater among them.

18) The length of a rectangular field is twice its breadth. If the perimeter of the field is 150m.

Find its length and breadth.

18

Lines and Angles

Assignment 5

1) Fill in the blanks:

(a) If two lines intersect at a point, then the vertically opposite angles are always

________

(b) A line that intersects two or more lines at distinct points is called _____________

(c) If two adjacent angles are supplementary, then they form __________________

(d) If l ‖ m, then, ∠1 = ∠2, because they _________________ angles

(e) In the figure, pair of alternate interior angles are _______ and _______

2) Which of the following statements are true and which are false?

(a) Two obtuse angles can be supplementary.

(b) Adjacent angles can be complementary.

(c) Adjacent angles can be supplementary.

(d) An angle is greater than 45°, its complement will be less than 45°.

(e) An angle is less than 90°, its supplement will also be less than 90°.

(f) Two complementary angles always form a linear pair.

(g) Two acute angles can form a refex angle.

(h) Two acute angles can form a linear pair.

(i) Two right angles can form a linear pair.

(j) Two supplementary angles form a linear pair.

(k) Two obtuse angles can be adjacent angles.

(l) An acute angle can be adjacent to an obtuse angle.

3) Do 110⁰ and 70⁰ form a pair of complementary angles?

4) Are 120⁰ and 70⁰ a pair of supplementary angles?

5) What is the measure of the complement of 41°?

6) Find the supplement of (a) 28⁰ (b) 145.5⁰ (C) ½ right angle

7) Find the angle which is equal to its complement.

8) Find the angle which is equal to its supplement.

19

9) Two complementary angles are in the ratio 2 : 7. Find these angles.

10) Two complementary angles are (x + 2) ⁰ and (4x – 12) ⁰. Find the value of x.

11) Two supplementary angles are (3x – 8) ⁰ and (x + 48) ⁰. Find the angles.

12) State true or false. Justify each false statement with an example/reason.

(a) Two angles forming a linear pair are supplementary.

(b) Two supplementary angles form a linear pair.

(c) If two lines are intersected by a transversal, then pairs of corresponding angles are

equal.

(d) If a transversal cuts two lines such that the co-interior angles are supplementary, then

the lines are parallel.

13) Name the angles : C

(a) Adjacent to ∠ AOB B

(b) Vertically opposite of ∠ DOE D O A

(c) All linear pairs

E

14) Refer to the figures and find the value of x, if given lines are parallel.

Fig (i) Fig. (ii)

Fig. (iii) Fig. (iv)

15) Two lines PQ and RS intersect at O. If ∠POR = 50°, then what is the value of ∠ROQ?

20

16) In the given figure, decide whether l is parallel to m.

17) In the figure, AB ‖ CD, ∠APQ = 50°, ∠PRD = 127°, find the value of x and y respectively.

18) Two complementary angles are in the ratio 4 : 5. Find the angles.

21

The Triangle and its Properties

Assignment 6

1) The measures of the sides of some triangles and some of the angles of the triangle are

given. Classify the triangles according to their sides or angles. (a) 4.2 cm, 4.2 cm, 4.2 cm. (b) 4 cm, 4cm, 3 cm. (c) 3.5 cm, 4cm, 3 cm. (d) 30⁰, 50⁰, 100⁰ (e) 60⁰, 30⁰, 90⁰ (f) 50⁰, 60⁰, 70⁰ (g) Two sides are equal and one angle is 90°.Name the sides opposite to angle ABC and

angle ACB of Δ ABC

2) Fill in the blanks :

(a) The line segment joining a vertex of a triangle to the midpoint of its opposite side is

called ______________ of a triangle.

(b) An altitude of a triangle is a ______________ drawn from a vertex to the opposite

side.

(c) The number of possible medians in a triangle are ________.

(d) In an _____________triangle all the altitudes lie in the interior of the triangle.

(e) In an ________________triangle two attitudes lie in the exterior of the triangle.

(f) In a _______________triangle two altitudes are the two sides of the triangle.

(g) The altitudes of a right triangle meet at

________________________________________

(h) The angle opposite to the side LM of ΔLMN is ______________.

(i) Side opposite to the vertex Q of ΔPQR is _________

(j) The vertex opposite to the side RT of ΔRST is ____________.

(k) The longest side of a Right angled triangle is called ______________.

3) In a triangle PQR, PQ = PR. If angle PQR = 54°, find the measure of the other two

angles of the triangle.

4) One of the base angles of an isosceles triangle is 45°. Find the measures of the other two angles. What kind of triangle is it?

5) Three angles of a triangle are in the ratio 5 : 7 : 3. Find the measures of all the angles of the triangle.

6) The vertical angle of an isosceles triangle is two times the sum of its base angles. Find the measure of each angle.

7) Two angles of a triangle are of 60⁰ and 55⁰. Find the measure of the third angle.

22

8) If the angles of a triangle are in the ratio 2 : 3 : 4, determine the three angles

9) In an isosceles triangle one of the base angles is 65⁰. Find the vertical angle.

10) In a right-angled triangle one of the acute angles is 55⁰. Find the other angle.

11) One of the angles of a triangle is equal to the sum of the other two. What is that angle?

12) Can a triangle have :

(a) (a) All angles greater than 60⁰ (b) All angles less than 60⁰ (c) All angles equal to 60⁰ (d) Two obtuse angles (e) Two right angles (f) Two acute angles

13) Each of the two equal angles of an isosceles triangle is twice the third angle. Find all the

three angles.

14) ABCD is a quadrilateral. Is AB + BC + CD + DA > AC + BD?

15) In triangle PQR, angle R = angle Q = 70⁰. Name the pair of sides which are equal.

16) Can you construct a triangle whose angles are : (a) 45⁰, 72⁰ and 50⁰? (b) 75⁰, 45⁰ and 60⁰?

17) Can these measurements denote the lengths of the sides of a triangle? (Give reasons)

(a) 8 cm, 7 cm, 1 cm (b) 5.2 cm, 2.1 cm, 8.4 cm (c) 4 cm, 4 cm, 4 cm. (d) 5 cm, 10 cm, 4 cm.

18) The exterior angle of a triangle is 110⁰ and one of the interior opposite angles is 30. Find

the measure of other two angles.

19) The hypotenuse of a right triangle is 17 cm long. If one of the remaining two sides is 8 cm in length, then what is the length of the third side?

20) The diagonals of a rhombus measure 16 cm and 12 cm. Find the perimeter of the rhombus.

21) In an isosceles triangle ABC, angle ABC = 45⁰ and BC = CA, then calculate angle C.

23

22) Look at the figure and find angle ACD and angle AED A 35⁰ E 45⁰ 45⁰ B C D

23) In the following figure find (a) angle ACD (b) angle ADC (c) angle DAE

A E 50⁰ 45⁰ 115⁰ B C D

24) In a triangle ABC, BC is produced both ways such that exterior angle ACD = 110⁰ and exterior angle ABE = 120⁰. What is the measure of angle BAC? A 120⁰ 110⁰ E B C D

25) In a triangle ABC, AB = AC and angle A = 72⁰. Determine angle B and C.

26) If the angle made by the equal sides of an isosceles triangle is 68⁰, find the other two equal angles.

27) The lengths of two sides of a triangle are 13 cm and 17 cm. Between what two measures should the length of the third side fall?

28) ΔABC is right-angled at C. If AC = 5 cm and BC = 12 cm, find the length of AB.

29) In a triangle , BC is produced to D to make an exterior angle of 110⁰. EF is drawn parallel to BC through A such that angle EAB = 50⁰. Find the value of angle x, angle y and angle z.

E A F 50⁰ x y z 110⁰ B C D

24

30) In a triangle ABC, BC is produced to D, such that angle ACD = 120⁰. CA and BA are produced to E and F respectively such that angle EAF = 45⁰. Find the measure of angles x, y and z.

E F 45⁰ A x y z 120⁰ B C D

31) In the figure, triangle ABC is isosceles with AB = AC. If angle A = 50⁰, what are the measures of angle 1 ad angle 2?

B 1 3 A 50⁰ 2 4 C

25

Congruence of Triangles

Assignment 7

1) Fill in the blanks with correct answers:

(a) Two figures are congruent, if they have the same _____________ and ____________.

(b) AB = 5 cm and EF = 6 cm. Are they congruent? _______________

(c) Two angles are congruent if they have the same __________________

(d) Two circles are congruent if their ____________ are the same.

(e) Two squares are congruent if they have equal _____________.

(f) If ∆ABC and ∆PQR are congruent, then in the symbolic form we write it as ___________

(g) The matching parts of the two triangles are also called the __________________ parts.

(h) The corresponding parts of congruent triangles are ______________.

(i) If ∆ ABC ≅ ∆ DEF, ∠A = 100° and ∠B = 45°, then ∠F = ________

(j) If ∆ABC ≅ ∆DEF, then

AB = _______ BC = _______ AC = _______

∠A = ________ ∠B = _______ ∠C = ________

2) Which of the following cannot be used to prove that two triangles are congruent? (a) AAS congruence (c) SAS congruence (b) SSS congruence (d) AAA congruence

3) Which pair of triangles shows congruency by the SAS Congruence criterion?

(a) Figure D (b) Figure B (c) Figure C (d) Figure A

4) In ∆ABC, CD is the perpendicular bisector of side AB. Draw the figure and answer the question.

(a) State the three pairs of matching parts (b) Is ∆ADC ≅ ∆BDC? Why?

5) ABCD is a rectangle. Find the three corresponding equal parts which make ∆ABD ≅ ∆CDB. Draw

figure and answer the question.

26

6) Which of the following is true?

(a) ΔABC ≅ ΔQRP (b) ΔABC ≅ ΔRPQ (c) ΔABC ≅ ΔPQR (d) ΔABC ≅ ΔPRQ

7) In the following pair of triangles, the equal corresponding parts have been marked similarly. Write the pairs of corresponding equal parts and the congruence of the two triangles.

(a)

(b)

8) ABCD is a rectangle and AC is a diagonal.

(i) Show three pairs of equal parts giving reasons, in ∆ ABC and ∆ ADC.

(ii) Is ∆ ABC ≅ ∆ ADC ? Give reason.

(iii) Is BAC = DAC? Give reason.

9) In the figure PQ and XY bisect each other at O.

(i) Show three pairs of equal parts in ΔPOX and ΔQOY

(ii) Is ΔPOX ≅ ΔQOY? Give reasons.

(iii) Is ∠X = ∠Y? Give reasons.

10) In the figure, O is the midpoint of BC and ∠B = 90°, ∠C = 90°.

By using ASA Congruence rule, Show that Δ AOB ≅ Δ DOC

The three pairs of congruent parts are:

(i)_____________________________________

(ii)_____________________________________

(iii)_____________________________________

Δ______ ≅ Δ_______ ( _______ Congruence Rule)

The three pairs of congruent parts are:

(i)_____________________________________

(ii)_____________________________________

(iii)_____________________________________

Δ______ ≅ Δ_______ ( _______ Congruence Rule)

O

D

C

A

B

X

Y Z

W

27

Comparing Quantities

Assignment 8

1) 75% of what number is 15?

2) What is 2% of 1hr?

3) Write 45% as a fraction in simplest form.

4) What is the decimal value of 55%?

5) Write 1

6 as a percentage.

6) Convert the following into fraction and Decimal

(i) 241

2 %

(ii) 39.2%

7) Calculate the following (i) 12% of 120 (ii) 30% of 300

8) A basket is full of fruits mangoes, oranges and apples. If 60% are mangoes, 10% are oranges than what is the percentage of apples.

9) In a survey of 40 students, 25% of students liked to play football. What is the number of students who like to play football?

10) What is the ratio of 40 days to 40 hrs?

11) Convert each part of the ratio 4 :1 into percentage.

12) If 5% of it is 600 then what is the whole quantity?

13) Which is the correct statement : (a) amount = principal interest. (b) amount = principal + interest. (c) amount = principal - interest. (d) amount = principal/interest.

14) There are 25 radios. 16 of them are damaged. What is the percentage of damaged radios?

15) If 75% of students in a class have a bicycle then what is the percent of the student who do not have bicycles?

16) Rajesh‟s salary in the year 2007 was Rs. 30,000 and in the previous year it was Rs. 25,000.

What was the percentage of increase in salary?

17) Ramesh bought a tape recorder for Rs. 4,000 and sold it for Rs. 5,000. Find how much was

his gain percent.

28

18) By selling a TV set at a profit of Rs. 600, a shopkeeper made a profit of 20%. Find the cost

price.

19) A house was purchased for Rs. 8,00,000 and sold at a gain of 20%. Find the selling price.

20) A car was purchased for Rs. 4,50,000 and sold at a loss of 15%. Find the selling price.

21) A man lost 12% by selling a tape for Rs. 4,400. Find the cost price of the tape.

22) If the principal amount is Rs 1.200 at 10% p.a. then what would be the amount to be paid at

the end of 3 yrs?

23) If Manohar pays an interest of Rs 750 for 2 years on a sum of Rs 4,500, find the rate of

interest.

24) (a) Divide 126 cm long wire in the ratio 4 : 3.

(b) Convert each part of the ratio to percentage.

25) A fan costing Rs. 480 was sold for Rs. 540. Find the gain percent.

26) Ramlal sold a cow at a profit of 12% with SP Rs. 850. Find the cost price.

27) Sharad bought an old car for Rs. 75,000 and spent Rs. 10,000 on its repairing. He sold this

car to Abdul at a gain of 15%. What did Abdul pay for the car?

28) If the weight of one iron ball is 16kg then what is the weight of 8 such iron balls?

29) One person divides his income in two parts if he gives 2 parts to Ram and 1 part to Shyam. What percentage of money he gives to Ram and Shyam separately.

30) Ramesh and Satish contested the Delhi assembly elections. Ramesh scored 11,484 votes which was 44% of the total votes. Satish scored 26% of the votes. Calculate the number of votes cast in the village and the number of voters who did not vote for either Ramesh or Satish.

31) Raju borrowed Rs 18000 from a moneylender at 12 % per annum for 5 years and Sanju borrowed the same amount at 8% per annum from the bank for 6 years. Who paid more interest and by how much?

32) Nikhil borrowed some money from a moneylender at 10% per annum. He paid Rs 3000 as interest after two years. How much money did he borrow?

29

PERCENTAGE CROSSWORD

1 2 3 4

5

6 7

8 9

ACROSS DOWN

1. 25% of 128 = ____________ 1. 6% of 600 = __________

3. n% of 12 is 3, then n = ___________

2. 5% of n = 12.5, then n = __________

5. 12% of n = 7.8, then n = ___________

4. n% of 18 is 9.9, then n = __________

7. 66 2

3 % of 42 = ___________ 6.

3

5 % of 2500 = ____________

8. n% of 208 = 108.16, then n = _______

9. 0.4% of n = 1.024, then n = _________

30

Rational Numbers

Assignment 9

1) Express 3

17

with positive denominator.

2) Which of the following is a positive rational number? 9

7

or

9

4

.

3) Reciprocal of 19

17 = _____________

4) Which rational numbers are equal to their reciprocal? 5) The reciprocal of which rational number does not exist?

6) Simplify 9

7

+ 4

3

.

7) Subtract 3

2

from 6

5

.

8) Express −12

28 in the standard form.

9) Simplify and express in standard form 16

9 x

27

64

.

10) Find the value of

35

16 ÷

14

15 and express as a rational number in standard form.

11) Subtract −1

2 from

4

5

12) Write the following rational numbers in ascending order: −3

7,

−3

2,

−3

4

13) Arrange in descending order : 3

2

, 7

4

, 3

8

, 9

6

.

14) Find two rational numbers between −3

8 and

2

1.

15) Find four rational numbers between −3

5– and

−1

3.

16) Express 119

68

in the standard form.

17) Represent the following rational numbers on number line.

31

18) Write down the additive inverse of following rational numbers:

19) −3

5 x

35

7 x

−1

9 = ?

20) Write the integer (-8) as a rational number.

21) Identify the greatest rational number : 450

−7,

−3

21,

5

7,

29

14

22) Write −2

3 as rational number with denominator -30.

23) What is the product of a rational number with its reciprocal always equal to?

24) Find x such that −3

7 and

𝑥

−21 are equivalent rational numbers.

25) Find the value of x if 𝑥

−11 = -3

26) Write the rational number −7

−6 with denominator 6.

27) Given a = 3

5 and b =

−2

5 prove that a + b = b + a.

28) Sum of two rational numbers is –8, one number is 3

4 , find the other.

29) Product of two rational numbers is −8

9 , one is

−10

3, find the other.

30) Find the sum of:

(i) −8

13 and

−3

11

(ii) 7

3 and

−4

5

31) Solve:

(i) 29

4 -

30

7 (ii)

5

13 -

−8

26

32) Find the product of:

(i) −4

5 and

−5

12

(ii) −22

11 and

−21

11

33) Simplify:

(i) 3

7 ÷

21

−55

(ii) 1 ÷ −1

2

32

CROSSWORD PUZZLE ON RATIONAL NUMBERS

5 𝟏

𝟑

𝟔

𝟕 + =

𝟗

𝟏𝟒

X - x =

−𝟓

𝟔 - =

−𝟏

𝟒

= = = x -

6 = 1 𝟏

𝟏𝟒 ÷

=

= 𝟕

𝟗 + - 1

33

Practical Geometry

Assignment 10

1) Draw a line AB and take a point outside it. Draw a line CD parallel to AB and passing through the

point P.

2) Draw a line AB and draw another line CD parallel to AB at a distance of 5.5 cm from it.

3) Draw a line „l‟ and draw another line „m‟ parallel to „l‟ at a distance of 4.3 cm from it.

4) Construct a triangle ABC, given that AB = 5 cm, BC = 6 cm and AC = 7 cm.

5) Draw Δ PQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?

6) Construct Δ ABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠B.

7) Construct ΔXYZ if it is given that XY = 6 cm, m∠ZXY = 30° and m∠XYZ = 100°.

8) Examine whether you can construct Δ DEF such that EF = 7.2 cm, m∠E = 110° and m∠F = 80°.

Justify your answer.

9) Construct Δ LMN, right angled at M, given that LN = 5 cm and MN = 3 cm.

10) Construct a right angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long.

11) Construct an isosceles right angled triangle ABC, where m∠ACB = 90° and AC = 6 cm.

12) Construct a triangle ABC in which AB = AC = 4.8 cm and BC = 5.3 cm. Measure ∠B and ∠C.

13) Construct an equilateral triangle each of whose sides measures 6.2 cm. Measure each of its angles.

14) Construct a right angled triangle, whose hypotenuse measures 5.6 cm and one of whose acute

angles measure 30°.

15) Construct a ΔABC , in which ∠B = 70°, AB = 4.8cm and BC = 5.2 cm.

16) Construct a right angle triangle PQR in which ∠Q = 90o, PR = 6cm and QR = 4cm. 17) Construct a triangle ABC such that AB = 5cm, BC = 4.6cm and AC = 4.3cm. 18) Construct a triangle ABC such that CB = 6.5cm, CA = 4.2cm and BA = 5.1cm. 19) Construct an isosceles triangle ABC such that AB = AC = 5cm and ∠A = 60o. 20) Construct an isosceles triangle ABC such that AC= CB, AB = 6cm and base angle = 45o . 21) Construct an isosceles triangle PQR where the non-equal side PQ = 4.2 cm and base angles are 30o

each . 22) Construct a right angled triangle ABC where AB = 4.5 cm, AC = 5.8 cm and angle A = 90o. 23) Construct an isosceles triangle ABC such that AB = BC = 4 cm angle BAC = 60o.

34

Perimeter and Area

Assignment 11

1) Find the area of the parallelogram ABCD if DX AB, BY AD, BY = 30 cm, DX = 20 cm and AD = 25 cm. Also find the length of AB.

2) The area of a parallelogram ABCD is equal to that of another parallelogram PQRS. In ABCD, AB = 40 cm and the corresponding altitude DE = 18 cm whereas in PQRS, QR = 36 cm. Find the corresponding altitude PM.

3) PQR is right angled at P. PS is perpendicular to QR. If PQ = 8 cm, QR =17 cm and PR =

15 cm, find the area of PQR. Also find the length of PS.

4) A garden in the form of a right angled triangle has an area of 72 sq m. If the two sides comprising the right angle are equal, what could be the possible lengths of these sides?

5) The area of a parallelogram is420 sq m. If the distance between two parallel sides is 15 m, find the length of these sides.

6) If the perimeter of a parallelogram is 140 m, the distance between a pair of opposite sides is 7 m and its area is 210 sq m, find the length of two adjacent sides of the parallelogram.

7) To fence a circular garden, the total cost is Rs 26,400 at the cost of Rs 50 per metre. Find the radius of the circle.

8) A rectangular garden is 200m long and 160m broad. In its middle, there is a circular tank of

radius 28m. Find the cost of covering the remaining portion of the garden with grass at the

rate of 50 paise per sq.metre. (Take = 22/7)

9) If the length of the minute hand of a clock is 14cm, find the area swept by it in half an hour.

10) There are two concentric circles. The radius of the outer circle is 10 cm & the radius of the

inner circle is 4 cm. Find the area of the shaded portion.(Take = 22/7)

11) The area of square and a rectangle are equal. If the side of the square is 40 cm and the breadth of the rectangle is 25 cm, then find the perimeter of the rectangle.

12) If the area of the triangle ABC is 36 cm2 and the height AD is 3 cm then calculate the length of its base.

13) Find the area of the triangle, having base of 4 cm and altitude of 3 cm.

14) Two cross road each 3m wide, cut at right angles through the center of a rectangular park 72m by 56 m, such that each is parallel to one of the sides of the rectangle. What will be the area of the remaining portion of the park?

15) A sheet of paper measures 30 cm by 20 cm. If a strip of 4 cm wide is cut from it all around then find the area of the remaining sheet.

35

16) A rectangular garden is 65cm long and 50cm wide. Two cross paths each 2m wide are to be

constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.

17) A field has four square corners, each of side 8 m, as shown in the figure. The dimensions of

the field are 45 m by 58 m. Find the perimeter excluding the square corners.

18) Shelly wants to frame a rectangular painting. If the perimeter is 56 cm and its width is 13

cm then find the length of the painting. 19) A school campus is rectangular in shape. Its length and breadth are 50m and 30m,

respectively. There is a 2 m wide path inside the campus all around it. What is the area of the path in square metres?

20) A garden is in the shape of a rectangle. If the perimeter of the garden is 196 m and its length is 56 m then calculate the width of the garden.

21) A rectangular field has a perimeter of 92 m and its length is 25 m. Find the area of the field. 22) If the area of a rectangle is 7820 m2 and its width in 85 m then what is its length?

23) What is the circumference of a circle of diameter 10cm (Take 𝜋 = 3.14).

24) Find the area of a circle of radius 15cm (use 𝜋 = 3.14).

25) A rectangular garden is 65cm long and 50cm wide. Two cross paths each 2m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.

26) Find the perimeter of the given shape. The side of the square inside is 14 cm.(Take 𝜋 = 22

7)

36

Fun and Interesting Facts About Pi

1) The mind-boggling ratio of a circle‟s circumference to its diameter is called pi. Being an irrational mathematical entity it doesn‟t reveal itself in fraction. Its decimal representation neither ends nor does it repeat a permanent pattern! It‟s an enigma. It has captivated the human intelligence for millennia.

2) The symbol for Pi has been in use for over 250 years. The symbol was introduced by William Jones, an Anglo-Welsh philologist in 1706 and made popular by the mathematician Leonhard Euler, who adopted the symbol and it quickly became a standard notation.

3) Pi is the 16th letter of the Greek alphabet.

4) Since the exact value of pi can never be calculated, we can never find the accurate area or circumference of a circle.

5) Although Pi day is celebrated on March 14 (3/14), the exact time for celebration is 1:59 pm so that the exact number 3.14159 can be reached.

6) Pi is just another weird mathematical number. It is a part of Egyptian mythology. People in Egypt believed that the pyramids of Giza were built on the principles of pi. The vertical height of the pyramids have the same relationship with the perimeter of their base as is the relationship between a circle‟s radius and its circumference. The pyramids are phenomenal structures and so having π as the core principle makes it really special for architects.

7) The number of digits in the number pi is a phenomenon in itself. Humans can never find all the digits of number pi because of its very definition. Babylonian civilization used the fraction 3 ⅛, the Chinese used the integer 3. By 1665, Isaac Newton calculated pi to 16 decimal places. It was in the early 1700s that Thomas Lagney calculated 127 decimal places of pi reaching a new record. In But this record was broken to a whole new level in 2017 when a Swiss scientist computed more than 22 trillion digits of pi which took more than a hundred days.

8) Many genius minds have a relation with the Pi day. Albert Einstein was born on Pi day. Stephen Hawkings died on 3/14, Pi day at the age of 76.

9) There is no zero in the first 31 digits of Pi.

10) To remember lesser number of digits there is an easier technique. Remember the sentence where the number of letters of each word coincide with the digits of pi.

How I wish I could recollect pi easily today! (= 3.14159265) May I have a large container of coffee, cream and sugar? (= 3.1415926535)

37

Algebraic Expressions

Assignment 12

1) Draw a tree diagram for the expression 5xy - 10.

2) Fill in the blanks: (a) The coefficient of x2 in -7x3 + 4 x2 – 10 x is __________. (b) The terms of the expression -15x3 – 4 y3 + 10 x3 y3are ______, _______ and _______. (c) 3x2y and -2yx2 are ________terms. (d) If 3x = -18, then 5x = ________. (e) The coefficient a2 in -21a2b3c is _________.

3) What are the terms in the following expressions? 8y + 3x2, 7mn – 4, 2x2y.

4) Identify, in the following expressions, terms which are not constants. Give their numerical coefficients: xy + 4, 13 – y2, 13 – y + 5y2, 4p2q – 3pq2 + 5

5) What are the coefficients of x in the following expressions? 4x – 3y, 8 – x + y, y2x – y, 2z – 5xz

6) What are the coefficients of y in the following expressions? 4x – 3y, 8 + yz, yz2 + 5, my + m

7) Group the like terms together from the following: 12x, 12, – 25x, – 25, – 25y, 1, x, 12y, y

8) Classify the following expressions as a monomial, a binomial or a trinomial:

4xy, z + 6, 0, 2x – 3 y2 + 1

5 x5, 4pq + 4r + pq, 7m +5 -3

9) State with reasons, which of the following pairs of terms are of like terms and which are of unlike terms: (i) 7x, 12y (ii) 15x, –21x (iii) – 4ab, 7ba (iv) 3xy, 3x (v) 6xy2, 9x2y (vi) pq2, – 4pq2 (vii) mn2, 10mn

10) Ramu‟s father‟s present age is 3 times Ramu‟s age. Ramu‟s grandfather‟s age is 13 years more than the sum of Ramu‟s age and Ramu‟s father‟s age. How do you find Ramu‟s grandfather‟s age? (write expression)

11) A garden, roses and marigolds are planted in square plots. The length of the square plot in which marigolds are planted is 3 metres greater than the length of the square plot in which roses are planted. How much bigger in area is the marigold plot than the rose plot?

12) Collect like terms and simplify the expression: 12m2 – 9m + 5m – 4m2 – 7m + 10

13) Find the values of the following expressions for x = 2. (i) x + 4 (ii) 4x – 3 (iii) 19 – 5x2 (iv) 100 – 10x3

14) Find the value of the following expressions when n = – 2. (i) 5n – 2 (ii) 5n2 + 5n – 2 (iii) n3 + 5n2 + 5n – 2

38

15) Find the value of the following expressions for a = 3, b = - 2. (i) a + b (ii) 7a – 4b (iii) a2 + 2ab + b2 (iv) a3 – b3

16) Write -6x2y3 in expanded form.

17) Write p4 in product form.

18) Write 3 x p x p x p x q in exponential form.

19) Separate the terms of the following algebraic expression : a3 + b3 + c3 - 3abc.

20) (a) Write the coefficient of x in –x. (b) Write the coefficient of -5 in 5abc (c) Write the coefficient of x in -4ax (d) Write the coefficient of yz in -2.4 xyz.

21) Add : x2 – a2, -5x2 + 2 a2 and -4 x2 + 4 a2

22) Subtract : 3a + 4b + 2c from a +13b – 7c.

23) From the sum of 4x2 – x + 1 and 9 – 7x + 3 x2 subtract 5 x2 – 2x + 7.

24) What should be added to 4x2 – 3x + 2 to get 2 x3 – 7 x2 + 4x – 3?

25) What must be subtracted from 2x2 – xy + 5y2 to make it -5x2 -3xy -2y2?

26) By how much does -4a2b -3ab2 + b2 exceed a3 + 2a2b + 6 ab2 – b2?

27) From the sum of a + 2b – 1 and 3a – b + 6 subtract the sum of 9a + 3b – 1 and -2a - 5b -2.

28) From the sum of 2y2 + 3yz, – y2 – yz – z2 and yz + 2z2, subtract the sum of 3y2 – z2 and –y2

+ yz + z2.

29) The length of rectangle is 3x 4y 6z and the breadth is 7x 8y 17z, find the perimeter of the rectangle.

39

Race to the Top

Combine the two like terms next to each other and write the simplified expression in

the grey triangle directly above the two terms… The first two have been done for

you…

3x -2x -8x 6x -12x x 13x -9x 10x

x -10x

40

Exponents and powers

Assignment 13

1) Which is the greatest number among 82, 28, 53 and 32. (Show all working)

2) Express: (i) 729 as a power of 3 (ii) 128 as a power of 2 (iii) 343 as a power of 7

3) Express in exponential form: (i) 3125 (ii) 729

4) Express the following numbers as a product of powers of prime factors: (i) 72 (ii) 432 (iii) 1000 (iv) 16000

5) Work out (1)5, (–1)3, (–1)4, (–10)3, (–5)4.

6) Find the value of: 29 x 291 – 219 x 281

7) Find the value of: 23 + 22 + 20.

8) Simplify using laws of exponents and write in exponential form: (i) a3 × a2 × a7 (ii) (– 4)100 × (–4)20 (iii) 29 ÷ 23 (iv) 108 ÷ 104

(v) 642 (vi) (100)22

(vii) (2 × 3)5

9) Simplify the following using laws of exponents:

(i) 1255 ÷ 125 ÷ 58 (ii) −2

3

5

3

x −2

3

2

5

x −2

3

0

5

(iii)

4

7

5 x

4

9

4

4

9

2x

4

7

4 (iv) 5a X 25b

10) Write exponential form for 8 × 8 × 8 × 8 taking base as 2.

11) Find the value of (60 – 20) x (60 + 20).

12) Find the value of (30 + 20) 50

13) Simplify 23 x 𝑎3 x 5𝑎4 .

14) Which one is greater 102 or 210.

15) Express (37 x 33) x 33 as a positive exponent.

16) Find the value of (-5)3 (-2)4 .

17) What is the value of (− 4)3 x 5−6−9

18) Find the value of (-9)3 x(-4)2

19) Find the value of (-5)3 (-2)4

41

20) Find the value of 75 73

21) Find the value of (25)10

22) Find the value of 54 x 74

23) Find x2 if x = − 9 2 ÷ − 9 − 2 0

24) Simplify: (27 x 28) ÷ 212

25) Simplify: (i) 63

23 (ii) 144

74

26) Simplify: 2 x 34 x 25

9 x 42

27) Simplify: 124 x 94 x 4

63 x 82 x 27

28) Simplify: 3 x 72 x 118

113 x 21

29) Simplify and write the answer in the exponential form.

(i) 82 ÷ 23 (ii) 23 × 22 × 55 (iii) (62 × 64) ÷ 63 (iv) [(22)3 × 36] × 56

30) Expand a3b2, a2b3, b2a3, b3a2. Are they all same?

31) Using laws of exponents, determine x so that:

(i) 3

5

3

x 3

5 𝑥+5

= 3

5

14

(ii) [(2x)6 = [(29)2

iii 2

3

2

4

= 2

3

3𝑥−1

(iv) 72x – 1 x 73 = 49

(v) 6x – 1 = 1 (vi) x3 x (-5)3 = (-10)3

32) If 4x = 256, then find the value of 62x – 8

33) Simplify using laws of exponents:

(i) 22

3 x 33 x 54

82 x 32 x 125

(ii) 7293 ÷ 729 ÷ 38

34) If 819 813 = x then find the value of x.

35) If (−5)4

x = 5 2 then find the value of x.

36) Write −64

729 in power notation form.

37) If a5 ÷ a x a x a = 196, then what is the value of a.

42

38) Find m so that 2

9

3

x 2

9

6

= 2

9

2𝑚−1

39) Expand by expressing powers of 10 in the exponential form:

(i) 172 (ii) 5,643 (iii) 56,439 (iv) 1,76,428 (v) 104278

40) The mass of the Earth = 5,976,000,000,000,000,000,000,000 kg. The mass of Uranus = 86,800,000,000,000,000,000,000,000 kg The distance between Sun and Saturn is 1,433,500,000,000 m. The distance between Sun and Earth is 149, 600,000,000 m.

Write these numbers in standard form. Can you tell which of the three distances is smallest?

41) Express the following numbers in the standard form: (i) 5985.3 (ii) 65,950 (iii) 3,430,000

42) Write in usual form :

(i) 3.15 x 105 (ii) 4.006 x 102 (iii) 9.1039 x 109

43

Symmetry

Assignment 14

1) Fill in the blanks: (a) The angle by which the object rotates is called the _______________ (b) Rotation turns an object about a fixed point. This point is the ___________________ (c) In a complete turn (of 360˚), the number of times an object looks exactly the same is called

_________ (d) A 2-D figure which has unlimited lines of symmetry and an infinite order of rotation is the

__________ (e) ______________ is a 2D shape which has no line symmetry but it has rotational symmetry.

2) How many lines of symmetry are there in: (a) Circle (b) regular hexagon (c) regular pentagon (d) rectangle (e) equilateral triangle (f) right angled isosceles triangle. (g) parallelogram

3) State true or false : (a) A square has rotational symmetry of order 4. (b) When an object rotates, its shape and size change. (c) If, after a rotation, an object looks exactly the same, we say that it has a rotational symmetry.

4) If a figure has two or more lines of symmetry, should it also have rotational symmetry of order more than 1? Give one example.

5) Name three quadrilaterals which have both line and rotational symmetry of order more than 1.

6) Find the axes of symmetry for the following:

7) Given the line of symmetry, find the other hole:

8) Find the axes of symmetry of the given figure?

44

9) In the following figure, the mirror line (ie line of symmetry) is given as a dotted line. Complete the figure performing reflection in the dotted line. Name the figure formed.

10) For the following figure identify line/lines of symmetry.

(a) (b) (c) (d)

11) Which of the following has a horizontal line of symmetry?

(a) P (b) 3 (c) M (d) W

12) In the word „MATHS‟ which letters show rotational symmetry?

13) List the numbers from 0 to 9 and show how many of them are symmetrical. Also draw their axis of symmetry.

14) What is the order of rotation and the angle of rotation of a ceiling fan with: (i) 3 blades (ii) 4 blades

15) The flag of Japan is shown below. How many lines of symmetry does the flag have?

43) Which of the figures given below have both line and rotational symmetry?

(a) (b) (c) (d)

45

1) State the order of rotation and the angle of rotation of the following figures:

(a) (b) (c) Order: _________ Order: _________ Order: _________ Angle: _________ Angle: _________ Angle: _________

(d) (e) (f) Order: _________ Order: _________ Order: _________ Angle: _________ Angle: _________ Angle: _________

(g) (h) (i) Order: _________ Order: _________ Order: _________ Angle: _________ Angle: _________ Angle: _________

(j) (k) (l) (m) Order: _________ Order: _________ Order: _________ Order: _________

Angle: _________ Angle: _________ Angle: _________ Angle: _________

46

Visualising Solid Shapes

Assignment 15

1) State true or false: (a) The circle, the square and the triangle are examples of solid shapes. (b) The cuboid, the sphere, the cylinder and the cone are examples of solid shapes. (c) Flat surfaces of solid shape are called its edges.

2) Fill in the blanks:

(a) The corners of a solid shape are called its __________ (b) The line segments of solid shape are its __________ (c) A cube has __________ diagonals. (d) The number of vertices of a cuboid is __________ (e) All the faces of a cube are__________ (f) Out of __________ faces of a triangular prism, __________are rectangles and

__________ are triangles. (g) The net of a pyramid has ____ circle/circles. (h) A circle is a ______________ figure, whereas a sphere is a __________ shape.

3) From the following nets which can be used to make cubes.

Can this be a net for a die? Explain your answer.

4) If three cubes of dimensions 2cm by 2cm are placed side by side, what would the dimension

of the resulting cuboid be?

5) The figure has ________ vertices, __________ edges and __________ faces.

6) Draw the nets that can be used to make the shapes mentioned below. (i) Cube (ii) Cylinder (iii) Cone (iv) Pyramid

7) How many triangles will a pyramid having a square as its base, have on the sides?

47

8) A die is a solid cube having dots on each face such that its opposite faces always have a

total of seven dots on them. Now look at the two dice placed side by side as shown here.

What is the total number of dots on the face opposite to 5 + 6?

9) A cube has six faces. Its four incomplete nets are given below. Complete them:

(a)

(b)

(c)

(d)

48

SAMPLE PAPER PT 1

TIME : 2hrs MATHEMATICS M.M. : 5 0

Q:1 Answers the following questions : (1 x 5 = 5 marks) (a) Express 4kg 8g into kilogram. (b) Find the product of (– 12 ) x (–11) x (–10) (c) Name a triangle with both line symmetries and rotational Symmetries of order more than one.

(d) Multiply 1

4 x 6

3

4 and express as mixed fraction

(e) The sum of two integers is zero, if one of them is −5, then other integer is_____

Questions 2 to 7 are for two marks each: (2 x 6 = 12 marks)

Q: 2 Find the product of the following using suitable property 625 x (– 35 ) + (–65 ) x 625

Q: 3 Verify a –(− b) = a + b for the following values of a and b

a = 118 , b = 125

Q: 4 Draw and Name a triangle with only one line of symmetry and has no rotational Symmetry of order more than 1. Also show the line of symmetry.

Q: 5 Sameera Purchased 3 1

2 kg apples and 4

3

4 kg oranges. What is the total

weight of fruits purchased by her ?

Q: 6 Suman reads a book for 13

4 hours every day. She reads the entire book in 6

days. How many hours in all were required her to read the book?

Q: 7 Find [ (– 20 ) + 5 ] ÷ [ ( – 4) + 1 ]

Questions 8 to 14 are for three marks each : (3 x 7 = 21 marks)

Q: 8 In a quiz competition, Team ‘A’ score in five successive rounds was 10, −15, 20, −5, 25 and Team ‘B’ Score in five successive rounds was 10 , 0 , −20 , 30 , 40 respectively. What was the total score of both teams at the end of quiz and which team scored more ? Q: 9 Use the sign < ,> or = in the following, after solving each side: [

(−2) + (−5)] x 2 [ (−2) x (−5)] + 2

49

Q: 10 Find (a) 2.7 ÷ 100 (b) 0.08 x 100 (c) 0.5 x 0.05

Q: 11 Fill in the blanks:

Shape Order of Rotation Angle of Rotation

Square

Rhombus

Semi – circle

Q: 12 Simplify: 54 – [ 26 + {20 – (4 of 6 ÷ 2) } ]

Q: 13 Identify the order of rotational symmetry for the given figures:

(a) (b) (c)

Q: 14 Find (i) 76.5 ÷ 0.15 (ii) 3 1

5 ÷ 1

2

3

,

Questions 15 to 17 are for four marks each: ( 4 x 3 = 12 marks)

Q: 15 A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 5 per bag of grey cement sold. (a) The company sells 3000 bags of white cement and 5000 bags of grey cement in a month. What is its profit or loss? (b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey cement sold is 6400 bags.

Q: 16 Solve : (a) 2 2

3 + 3

1

2 (b) 8

1

2 – 3

5

8

Q: 17 Simplify the following 43 – [ 5 – 3{ 8 – ( 32 ÷ 4 of 2 ) } ]

50

Sample Paper – PT 2

SECTION A (Question numbers 1 to 6 carry one mark each)

1) In the figure, if BC = CD, then AC is called the ___________ of the triangle.

1

2) Name the triangle having exactly one line of symmetry.

1

3) Solve : 3 x 5

6.

1

4) What is the range of the following data : 13, 14, 15, 17, 15, 13, 14, 25, 24, 15

1

5) What is the supplement of 135°?

1

6) Name a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry

1

SECTION B (Question numbers 7 to 12 carry two marks each)

7) Simplify : 31

5 ÷ 1

2

3.

2

8) Solve: (a) 16.7 ÷ 1000 (b) 0.03 x 0.2

2

9) Write down a pair of integers whose : (a) Sum is -4 (b) Difference is – 3

2

10) (a) What is the value of 80 x 40

80+ 40

(b) Express 432 as a product of powers of prime factors.

2

11) Express : (a) 3 x 104 + 7 x 102 + 5 x 101 in the usual form. (b) 95 830 000 000 as standard form.

2

12) A box consists of 2 rectangles, 2 squares, 1 rhombus and 1 parallelogram. What is the probability of getting :

(a) A square (b) A triangle

2

D

A B

A

C

A B

A

B

A B

A

A

51

SECTION C (Question numbers 13 to 22 carry three marks each)

13) Find the mean, median and mode of the following data: 4, 6, 7, 6, 3, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8

3

14) The length of a rope is 131

5 m and 9

1

2 m of that rope is used for tying a bundle.

Find the length of the remaining rope.

3

15) (a) Using laws of exponents, simplify and express in exponential form 52 3 𝑥 54 ÷ 57

(b) Simplify : (–3) × (–2)3

3

16) Simplify and find the value of : 28 x 42 x 125

16 x 43 x 52

3

17) (a) Solve : (-72) ÷ [(-36) ÷ (-2)] (b) Solve (using property) : (-59) x 27 + 59 x (-73)

3

18) (a) What is the order of rotational symmetry and the angle of rotational symmetry of an equilateral triangle.

(b) What other name can you give to the line of symmetry of a circle?

3

19) For the given figure find: (a) One pair of vertically opposite angles (b) One linear pair (c) One pair of adjacent angles

3

20) Solve using BODMAS : 4.5 + 3.706 – 0.36 ÷ 1.2

3

21) Find the measure of x and y if p is parallel to q.

3

22) PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.

3

e

c

a b d

x

y

42° p

q

52

SECTION D (Question numbers 23 to 30 carry four marks each)

23)

Find angles x and y shown in the figure

4

24) AM is the median of a triangle ABC. Prove that AB + BC + CA > 2AM?

4

25) Find the value of x and y in the figures, and give proper reasons for your answers :

(a) (b)

4

26) Solve : (a) 0 = 18 + 9(m – 2)

(b) 7b

8 - 15 = -1

4

27) (a) Age of Muskan‟s father is 4 years more than 5 times Muskan‟s age. What is the present age of Muskan, if her father is 34 years old?

(b) Write the following statement in the form of an equation: “If you subtract 5 from 6 times a number „p‟, you get 7.”

4

M

A

C

A B

A

A

125° x

80° 3y

y 2y

53

28) (a) In the given figure, check whether p is parallel to q or not.

(b) Find the angle which is equal to its complement.

4

29) (a) In a class test containing 15 questions, 4 marks are given for every correct answer and -2 marks are given for every incorrect answer. Nishant attempts all questions but only 9 of his answers are correct. What is his total score?

(b) A kite is flying at a height of 10 m above the ground level. At a particular point it is exactly above the fish moving in a pond 3 m below the ground level. What is the vertical distance between these two points?

4

30) The number of boys and girls in various clubs of a school are given below :

Clubs Debating Hindi Maths Music Theatre

Number of Girls

35 20 50 40 45

Number of Boys

25 15 70 35 35

(a) Draw a double bar graph to represent the above data. (b) In which club are there more boys than girls?

4

146°

34° p

q

- 54 -

Sample Paper – PT 3

General Instructions: 1. All questions are compulsory. 2. This question paper consists of 20 questions divided into four sections - A, B, C & D 3. Section A contains 5 questions of 1 mark each, Section B contains 5 questions of 2 marks each Section C contains 5 questions of 3 marks each and Section D contains 5 questions of 4 marks each.

SECTION A ( 1 mark each)

Q: 1 Which angle is included between the sides DE and EF of ΔDEF ?

Q: 2 Find the product of 9

2 X (

–4

5 )

Q: 3 Write 44

− 72 in standard form

Q: 4 Find the ratio of 9m to 27cm. Q: 5 It is given that DE = PR and DF = PQ .What additional information is needed

to establish ΔDEF ΔPRQ using SAS congruence rule ? SECTION B ( 2 marks each)

Q: 6 A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?

Q:7 Fill in the boxes with appropriate Sign: ( ‘<’ , ‘>’ or ‘=’ )

(a) −8

5 □

−7

4 (b)

− 7

8 □

14

−16

Q: 8 Draw the number line and represent − 5

8 on it.

Q: 9 If ΔRPQ ΔFED ,Write the parts of ΔRPQ that corresponds to

(i) R (ii) RP (iii) Q (iv) RQ Q: 10 Find (a) 15% of 250 (b) 75% of 120

SECTION C ( 3 marks each) Q: 11 The cost of flower vase is Rs 1240. If the shopkeeper sells is at loss of 15%

Find the price at which it is sold Q: 12 What rate gives Rs 450 as interest on a sum of Rs 3,000 in 3 years ?

Q: 13 Write four rational numbers between −4

5 and

−2

3

Q: 14 In given figure AB and CD bisect each other at O.

- 55 -

(i) State the three pairs of equal parts in ΔAOC and ΔBOD

(ii) Is ΔAOC ΔBOD ? Give reasons (iii) Is AC = BD ? Give reasons.

Q:15 In given ΔABC AB = AC and D is mid-point of side BC.

(i) State the three pairs of equal parts in ΔADB and ΔADC

(ii) Is ΔADB ΔADC ? Give reasons.

(iii) Is B = C ? Give reasons.

SECTION D ( 4 marks each)

Q: 16 Find (i) 5

63 – (

− 6

21 ) (ii)

− 3

8 –

7

11

Q: 17 In given figure BD and CE are altitudes of ΔABC such that BD = CE.

(i) State the three pairs of equal parts in ΔCBD and ΔBCE

(ii) Is ΔCBD ΔBCE ? Give reasons.

(iii) Is DCB = EBC ? Give reasons. (iv) Is BE = CD ? Give reasons.

Q: 18 Juhi sells a washing machine for Rs 13,500. She loses 20% in the bargain. What was the price at which she bought it?

Q: 19 Rs 6,050 is borrowed at 6% rate of interest p.a. Find the interest and amount to be paid at the end of 3 years.

Q: 20 Find the value of

(i) 3

13 ÷ (

− 4

65 ) (ii)

−7

12 ÷ (

−21

8 )

- 56 -

NOTES