PT_G07_MA_WB_AY25 by Uolo

Practice • Solve • Succeed

Mathematics Workbook

Perfect

MATHEMATICS Workbook

Grade 7

Acknowledgements

Academic Authors: Muskan Panjwani, Anuj Gupta, Simran Singh

Creative Directors: Bhavna Tripathi, Mangal Singh Rana, Satish

Book Production: Sanjay Kumar Goel, Tauheed Danish, Vishesh Agarwal

Project Lead: Neena Aul

VP, Learning: Abhishek Bhatnagar

All products and brand names used in this book are trademarks, registered trademarks or trade names of their respective owners.

First impression 2025

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Book Title: Perfect Mathematics Workbook 7

ISBN: 978-81-982034-2-7

Published by Uolo EdTech Private Limited

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85, Sector 44, Gurugram, Haryana 122003

CIN: U74999DL2017PTC322986

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Preface

Mathematics thrives on practice, which is crucial for mastering concepts and building confidence. A regular engagement with mathematical problems helps students apply theoretical knowledge, identify areas for improvement, and enhance their critical thinking skills. With consistent practice, students can transform abstract ideas into tangible skills, paving the way for a deeper understanding and success in the subject.

The Perfect Mathematics workbooks are a set of practice books designed for students in Grades 1 to 8. One workbook is provided per grade. Aligned with the NCERT textbooks, these workbooks provide ample practice in the concepts covered in each grade, ensuring a strong foundational understanding of mathematics.

For younger learners (Grades 1 to 5), we have included Mental Mathematics worksheets designed to enhance rapid calculation skills, and avoid relying on calculators or written methods. These exercises promote quick thinking and boost students’ confidence in their mathematical abilities.

The workbooks support learners at all levels, providing opportunities to build problem-solving skills through questions aligned with Bloom’s Taxonomy. They also feature a diverse range of question types, including Fill in the blanks, True/False, MCQs, and both short and long answer questions. To foster critical thinking and analytical skills, each chapter includes dedicated challenge questions that push students to deepen their understanding and tackle more complex problems. Additionally, we have provided a Case Study at the end of each chapter, followed by scenario-based questions that encourage students to apply their theoretical knowledge in real-life situations, bridging the gap between classroom learning and practical application.

To facilitate self-assessment, answers to all questions are provided at the end of each workbook. This enables students to check their work and learn from their mistakes, fostering a growth mindset.

In addition, each workbook is aligned to its digital component, which contains immersive gamified experiences, video solutions and additional practice worksheets. Interactive exercises on the digital platform make learning experiential and serve to make abstract mathematical concepts more concrete.

We believe that the Perfect Mathematics Workbooks will be invaluable resources for students, helping them to not only master the curriculum but also develop a love for mathematics. Happy learning!

Rational Numbers

Chapter at a Glance:

QR Code: Digital resources aligned to the key concepts covered in the book.

Worksheet 3: Chapter Checkup

Curriculum Alignment: Aligned with the topics covered in the NCERT textbooks for practice across chapters and topics.

Chapter Checkup: Chapter-end practice exercises aligned to different levels of Bloom’s Taxonomy.

4: Chapter Checkup

Picture-based Questions: Questions featuring visual stimuli to foster comprehension and interpretation.

3 Challenge

Challenge: Critical thinking questions to enhance problem-solving and analytical thinking skills. Higher-order-thinking questions, in the form of assertive reasoning, and data-sufficiency questions.

Critical Thinking

1 A book has 400 pages. Raj finishes writing 100 pages in x minutes. Raju takes twice the time taken by Raj to write the next 150 pages. Vivek takes 2 hours more than half the time taken by Raju to write the remaining pages. The total time taken to write the book was 33 hours and 20 minutes. How much time is taken by Vivek to write the remaining pages (in hours)?

Case Study: Scenario-based questions for students to apply theoretical knowledge to real-world situations.

Urban Transport Tariffs

A company that provides transportation services charges different prices in different cities based on how many people live there. They also add a fixed fee for every ride, which stays the same no matter which city you are in. The table below shows how much they charge per kilometre and the fixed fee in City A and City B.

Answer Key: Answers to all the questions in the book at the end of the book.

2 Read the statements and choose the correct option. Assertion (A) – The difference of two numbers is 25. The larger number is x. The smaller number is x – 25. Reason (R) – Numbers which follow each other in order, without gaps, from smallest to largest like 12, 13, 14 and 15 are consecutive numbers.

a Both A and R are true and R is the correct explanation of A

b Both A and R are true but R is not the correct explanation of A

c A is true but R is false

is false but R is true

Worksheet

 This chapter is not included in the new NCERT books, although it has been recommended by the National Curriculum Framework (NCF). The teachers have the discretion to decide whether to cover the chapter based on the needs of their students.

Integers

Worksheet 1: Aligned to NCERT Topic/s: 1.1 Properties of Addition and Subtraction of Integers

1 Add.

a 5 and –9 = b 15 and 14 =

c –28 and 59 = d (–23) and 12 =

e 32 and –122 = f –136 and –25 =

g –152 and 365 = h 158 and –125 =

2 Find the additive inverse of the given integers.

a 48 b –72 c 98

3 Subtract.

a 8 from –9 =

b –12 from 17 =

c 25 from –32 = d 38 from –20 =

e –36 from –98 = f 54 from 223 =

4 Determine the missing integers in the given equations.

a 12 + = 18

b – (–17) = 10

c 956 – = 422 d 215 – 136 =

e –548 + = –267 f – 192 = 564

5 Fill in the blanks.

a The sum of –5 and 8 is .

b Subtracting 15 from –20 gives .

c The absolute value of –10 is

d If you have `2000 in your bank account and you spend `3000, your account balance becomes ` .

6 Subtract 2369 from the sum of –3652 and 5864.

7 State True or False.

a The commutative property of addition holds true for integers.

b The associative property of subtraction holds true for integers.

c The commutative property of subtraction holds true for integers.

d The associative property of addition holds true for integers.

8 Fill in the blanks using the properties. Also, name the property used.

a (21) + (13) = + (21); Property used =

b + 0 = –3; Property used =

c (–35 + 13) + = –35 + ( + (–16)); Property used =

d (–23) – = –23; Property used =

9 Verify the following if p = 32, q = 29 and r = −17.

a p – (−q) = p + q b p − q ≠ q – p

10 The sum of two integers is 142. If one integer is −89, find the other.

11 Simplify.

[128 + (−78)] + [−145 − (−92)]

[−214 − (124)] + [−136 + (45)]

12 The altitude of Mount Mitchell in North Carolina, USA, is 2037 metres. A hiker climbs to an altitude of 1200 m and then descends to an altitude of 500 m. How much lower is the hiker than the altitude of Mount Mitchell?

13 A basketball team scores 80 points in the first quarter, loses 25 points in the second quarter, and then scores 15 points in the third quarter. In the final quarter, they scored 10 more points than they lost in the second quarter. What is the team’s total score?

1 Tina and Asha were asked to solve their puzzles. They need to shade the integers in a way where the sum of the integers comes up to be –3. Tina has shaded her puzzle. Help Asha shade the integers in her puzzle by shading a total 5 integers.

Worksheet 2: Aligned to NCERT Topic/s:

1.2 Multiplication of Integers

1.3 Properties of Multiplication of Integers

1 Multiply.

a 12 × 15 = b –11 × 6 =

c –21 × 13 = d –14 × (–6) =

e 25 × 0 = f 56 × (–1) =

2 What will be the sign of the product if we multiply the integers?

a 5 negative integers and 5 positive integers

3 Write the multiplicative inverse of the given integers.

b 12 negative integers and 20 positive integers

a 21 b −32 c −54

4 Solve.

a –11 × 5 × (–2) = b 56 × (–12) × 0 =

c 12 × (–1) × (–8) = d 25 × (–12) × 3 =

e –23 × 15 × (–2) × 5 = f –6 × (–12) × (–3) × (–10) =

5 Fill in the blanks using the correct property of multiplication.

a 36 × 0 = b (–123) × = –123

c (–12) × (56) = × (–12) d 56 × (–12 + 23) = × (–12) + 56 ×

e × (–1) = 2198 f (123 × 143) × (–36) = × (143 × (–36))

6 Verify the following, if m = 8; n = −3 and o = −5

7 Simplify.

8 A submarine descends 55 feet per minute from sea level. Where will the submarine be in relation to the sea level 8 minutes after it starts descending? Write your answer as an integer.

9 A shooter gets 10 points every time he hits the target and loses 6 points for missing the target. What is his overall score if he hits the target 20 times and misses 25 times?

10 Ocean trenches are the deepest places on the ocean floor. The lowest point of the Hawaiin Trench is 5500 m deep. The lowest point of the Puerto Rico Trench, in the Atlantic Ocean is around 1.5 times lower than the Hawaiin Trench. Write the approximate depth of the Puerto Rico Trench as an integer.

11 Create a word problem to multiply 2 integers 24 and −12.

1 A test has 25 questions. The test awards 5 points if the answer is correct, and takes away 2 points if the answer is incorrect. A student answered 7 questions incorrectly. How many points did the student score if he answered all the questions?

Worksheet 3: Aligned to NCERT Topic/s:

1.5 Properties of Division of Integers

1 Find the quotient.

a 72 ÷ (–4) b (–56) ÷ 7

c –176 ÷ (–11) d 192 ÷ (–12)

2 Solve.

a (–88 ÷ 4) ÷ (–1) b 125 ÷ (125 ÷ 5)

c (192 ÷ (–16)) ÷ 4 d 324 ÷ (–18 ÷ 2)

3 Find the number which when divided by (–1) gives 145.

4 Write True or False.

a (–250) ÷ 1 = –250 b 0 ÷ (–378) = –378

c (–39) ÷ (–39) = 1 d (–90) ÷ 3 = 30

5 The product of two numbers is 800. If one of the integers is −25, what is the value of the other integer?

6 Verify the following for the values of m = 12, n = 3 and o = 2.

7 Give two pairs of integers such that a ÷ b = –15.

8 A 25 storey building has its car parks on 3 levels in the basement with each floor height as 5 metres. The lift in the building descends at the rate of 2 m/sec. If Era starts from the 20th floor, how long will it take her to reach the second basement?

9 A parachute is a cloth canopy which fills with air and allows a person or heavy object attached to it to descend slowly when dropped from an aircraft. A parachute descends at the rate of 20 m/min. At a certain moment, it was at a height of 1800 m above ground level. How long will it take to reach the height of 300 m above ground level?

10 In the first level of a video game, 2 points are deducted for each time a character falls. In the second level, each fall deducts 4 points. Rahul lost 10 points in the first level and 16 points in the second level. In which level did Rahulʹs character fall more often?

11 The temperatures recorded in Leh in the last week of March 2023 were −6℃, −4℃, −5℃, −6℃, −3℃, −2℃, −2℃. What is the average temperature of Leh for the week?

Hint: Average = Total temperature across 7 days No. of days

1 The temperature recorded at 12 noon was 18℃ above zero. If it falls at the rate of 3℃ per hour until midnight, at what time will the temperature be 6℃ below zero? What will be the temperature at midnight?

Worksheet 4: Chapter Checkup

1 Add or subtract the given integers.

a (–256) + 362

c (–659) + (–1352)

2 Solve and write the additive and multiplicative inverse.

a 25 + (–63)

3 Find the product.

a 25 × (–89)

c (–36) × 48

4 Divide.

a 363 by (–11)

b 652 + (–129)

d 214 – (–126)

b –125 + 47

b (–125) × (–26)

d (245) × (–57)

b (−384) by 12

c 450 by (–25) d (–5472) by 36

5 Fill in the blanks using the appropriate property of integers.

a (–156) + 389 = 389 + b 524 + = 523

c 1885 × = (–1885) d × (–17) = ( ) × 23

e –45 × (33 + 2) = (–45 × ) + ( × 2) f 64 ÷ (–1) = ______

6 Simplify.

a 42 ÷ (–6 + 5) b –64 ÷ 4 × (2 – 6)

c (9 ÷ 3) + 7 × (4 ÷ 2) d 4(–12 + 6) ÷ 3

7 Add the sum of (135) and (–325) to the difference of 253 and (–528).

8 What should be multiplied with (–165) to get a product of 9240?

9 Add the product of 25 and (–36) to the quotient of 2380 divided by (–68).

10 What should be divided from 23,072 to get (–412)?

11 Anish and Ravi took part in a quiz. Anish scored 55, –80 and 65 points in 3 successive rounds. Ravi’s score is double of Anish’s score. What were their scores?

12 The balance in Suhani’s bank account is −₹2000 due to some penalty charges. Her mother told her that she should always maintain a balance of ₹10,000 as savings so that she can use it in case of any emergency. How much money should she deposit in her account to maintain her savings? What value do you learn from Suhani’s mother?

13 An aeroplane is flying at 12,000 feet. The plane climbs 15,000 feet to approach the cruising altitude. After a few minutes at this new altitude, the plane hits turbulence and descends 23,945 feet. Express each increase and decrease in altitude as an integer operation and determine the new altitude of the plane.

14 Mercury conducts heat well, allowing it to respond quickly to temperature changes. A mercury thermometer records a temperature of 6°F at 11 a.m. If the temperature drops by 3°F every hour, what will be the temperature by 4 p.m. of the same day?

Challenge

1 Kajal gets into the elevator on the fourth floor of a shopping mall. She goes up 10 floors to reach the food court. After an hour, she goes down 5 floors to buy books. On which floor is she now?

2 Read the statements and choose the correct option.

Assertion (A): The value of 12 × –16 × –20 –24 × 8 is −20.

Reason (R): As there are 2 negative numbers in the numerator and 1 in the denominator, the answer will be negative.

a Both A and R are correct, and R is the correct explanation for A.

b Both A and R are correct, and R is not the correct explanation for A.

c A is true, but R is false.

d A is false, but R is true.

Worksheet 5: Case Study

Temperature Transition of Elements

The melting point is the temperature at which a solid turns into a liquid or gas, while the boiling point is the temperature at which a liquid changes into vapour. Given below is a list of temperatures of different elements in degrees Celsius (℃). Read the data table and answer the questions.

1 When magnesium is heated from its melting point to its boiling point, by how many degrees celsius would the temperature increase? a 1740℃ b 440℃ c 1640℃ d 540℃

2 Which element has the highest boiling point? How much higher is it compared to the boiling point of chlorine?

3 Calculate the temperature range (difference of the melting and boiling points) for each element. Which element has the narrowest range?

4 Imagine a situation where the temperature is increased from −250℃ to 0℃. Which of the elements would have changed their state from liquid to gas?

5 The formula for converting the unit of temperature from ℃ to ℉ is ℉ = 9 5 × ℃ + 32. What is the melting point of nitrogen in ℉?

Fractions and Decimals 0 2

Worksheet 1: Addition and Subtraction of Fractions

1 Add or Subtract.

2 Simplify.

2 17 + 1 17 + 3 17

3 Aisha painted 3 5 of the wall and her sister painted 1 6 of the wall. What portion of the wall did they paint together?

4 A rectangular piece of cloth is 3 8 m long and 2 5 m wide. Find the amount of lace needed for the cloth. Challenge

1 Shade 5 fractions that add up to one whole. One fraction is shaded for you.

Worksheet 2: Aligned to NCERT Topic/s: 2�1 Multiplication of Fractions

1 Multiply.

a 9 × 6 5 = b 14 × 5 7 =

c 5 3 4 × 20 = d 2 3 × 9 3 =

2 Simplify.

a 1 2 × 3 4 × 4 5 b 1 4 9 × 3 2 × 6

3 Perform the given calculations.

4 Answer the given questions.

a 1 5 of 1000 grams = b 5 6 of a metre =

c How many days are 2 7 of 7 weeks? = d What is 7 8 of 5 dozen? =

5 Human bones make up about 1 7 of the total body weight. If a person weighs 63 kg, what would be his bone weight?

6 Ram has 2 1 5 litres of milk. He uses only 1 3 of it and gives the remaining amount to his friend.

a How much milk did he use? b How much milk did his friend get?

1 Read the statements and decide which of the given options is correct.

Assertion (A): When you multiply two fractions, the product is always less than each of the individual fractions.

Reasoning (R): Multiplying fractions involves multiplying the numerators together and the denominators together.

a Both A and R are true, and R is the correct explanation of A.

b Both A and R are true, but R is not the correct explanation of A.

c A is true, but R is false.

d A is false, but R is true.

e Both A and R are false.

Worksheet 3: Aligned to NCERT Topic/s:

2�2 Division of Fractions

1 Find the reciprocal of the given numbers.

2 Divide and simplify.

3 Answer the given questions.

a The perimeter of an equilateral triangle is 3 7 m. What is the length of each side?

b The product of two numbers is 4 5 . If one of the numbers is 2 3, find the other.

4 Akshay has a piece of cloth that is 12 cm long. He cuts it into small pieces of length 2 3 cm each. How many pieces of cloth will he have?

5 The area of a rectangular field is 43 3 4 cm2. If its breadth is 12 1 2 cm, find its length.

6 Seema bought 5 9 kg of fruits. She packed them equally into 15 packets. a Find the weight of 1 packet of fruit in kg. b She sold 5 packets of fruit. How many kg of fruits did she sell?

7 3 7 of the people at a restaurant are males. If the number of females is 28 more than males, then how many females are there at the restaurant?

1 A cistern has two holes. One leaks at the rate of 1 4 gallons per half an hour, whereas the other leaks at the rate of 1 5 gallons every quarter of an hour. In how many hours will the cistern be empty if it contains 500 gallons of water? 1 Add.

2 Subtract.

a 322.36 from 438.2

3 Fill in the blanks.

b 132.89 from 325.566

a 236.45 + = 568.2 b 514.7 − = 241.23

4 A recipe requires 3.75 cups of flour, 2.5 cups of sugar, and 1.25 cups of butter. How much of these ingredients are needed in total for the recipe?

5 Ravi goes to buy a big box of sweets. He purchases 10.5 kg of sweets, and the weight of the empty box is 1 kg 350 g. What is the total weight of the sweets and of the box?

6 Sam ordered a coffee and a waffle. Find the change he will receive if he paid $10.

Challenge

1 The average temperature in Amsterdam for 5 months is given in the line graph. Is it correct to say that the increase in temperature from February to March is one-fourth of the increase from February to June? Give a reason for your answer.

Coffee: $1.46

Garlic bread: $3.95

Ice tea: $2.89

Waffle: $0.85

Worksheet 5: Aligned to NCERT Topic/s: 2�3 Multiplication of Decimal Numbers

2�4 Division of Decimal Numbers

1 Find the product.

a 0.12 × 15 b 112.2 × 6.5 c 32.1 × 1.33

d 5.014 × 25 e 52.25 × 5.23 f 122.56 × 5.21

2 If 365 × 124 = 45,260, then find the following without actual multiplication.

a 36.5 × 124

3 Find the quotient.

b 3.65 × 12.4 c 36.5 × 1.24

a 0.165 ÷ 1.5 b 42.7 ÷ 14 c 49.08 ÷ 0.02

d 23.85 ÷ 1.8 e 487.36 ÷ 3.2

1117.5 ÷ 12.5

4 Fill in the blanks.

a 68.527 × = 23.63 b × 1.6 = 52

c 2177.35 ÷ = 62.21 d 74.2 × 12.3 =

5 The product of two decimals is 3538.29. If one of them is 41.5, find the other.

6 Find the area and perimeter of the given square.

7 A cloth of length 2.35 m is needed to make a shirt. How many metres of cloth are needed to make 48 such shirts?

8 In July 2024, the value of 1 euro = ₹90.61 and the value of 1 dollar = ₹83.73. How much money in Indian rupees does Mrunal have if she has 8 euros and 15 dollars with her?

9 A car moving at a constant speed covers a distance of 452.8 km in 8 hours. Find the distance covered by the car in 2 4 5 hours.

124.75

10 Suhani bought 7 kg 650 g of sugar at ₹38 per kg, 2 kg 485 g of rice at ₹62 per kg and 5 kg 725 g of flour at ₹46 per kg for making a donation at a blind school. What is the total amount paid by Suhani for the donation items? Have you ever donated to needy people?

11 Rahul has a can with 25.5 litres of milk. He fills 8 bottles equally with the milk, with 1 1 2 litres of milk left. Find the volume of milk in each bottle.

Challenge

Critical Thinking

1 Saumya is making a report on the computer. She wants to place a figure which is 12.75 cm wide so that it appears centred on the page. The width of the page is 22.63 cm. How much margin should she leave at both ends so that the figure is centred?

Worksheet 6: Chapter Checkup

1 Solve the given fractions.

2 Complete the following.

a 1 9 of two hours = minutes b 2 3 of a day = hours

c 5 1 5 of a year = days d 3 4 of a metre = cm

3 Add or subtract the given decimals.

a 122.56 + 36.2

c 336.8 – 285.123

4 Multiply or divide the given decimals.

a 212.5 × 35

c 498.8 ÷ 4

b 536.3 + 311.236

d 658.412 – 247.4

b 156.52 × 12.29

d 90.15 ÷ 1.5

5 Answer the given questions.

a Which is more: The product of 3 1 5 and 2 1 4 or the quotient of 2 1 3 and 4 1 6 ?

b Which is less: The product of 25 and 4 75 or the sum of 3 1 4 and 5 4 5 ?

6 Simplify.

7 Solve to find the answer.

a A train covers a distance of 48 3 4 miles in 1 1 4 hours. How far does it go in 2 hours?

b Find the value of x, if 2 13 of x = 26.

c Find the value of x, if 22 2 9 × x = 1800

8 Miya has 3 5 of a cake. She ate 2 3 of it.

a Find out what fraction of the cake she ate.

b What fraction of the cake is left with her?

9 Aarav scored 452.65 out of 600 in the final examination. How many marks did he lose?

10 There is 0.625 kg of powdered milk in each tin. If a carton contains 12 tins, find the total mass of powdered milk in the carton.

11 The average growth rate of a hair strand is 1 cm 8 mm per month. What would be the total length of a strand of hair after 3 years of growth?

12 A tank is 4 5 full. When 65 litres of water are drawn from it, it is 7 12 full. Find out how much water is left in the tank.

13 Piyush walks at a speed of 4 1 5 km per hour for 5 hours, and then at the speed of 3 1 4 km per hour for the next 3 hours. Find the distance travelled by Piyush in 8 hours.

1 The graph shows the amount saved by Monika during 5 weeks.

a If the amount saved in Week 6 is 2.25 times what was saved in Week 2, how much was saved in Week 6?

b If Monika wants to save a total of ₹12,000 by the end of the seventh week, how much should she save in the seventh week?

2 Read the statements and decide which of the statements are necessary to answer the given question. Julia baked a batch of cookies and divided them equally into boxes. Each box contains the same number of cookies. What is the total number of cookies?

Statement 1: Julia divided the total number of cookies into 8 boxes.

Statement 2: Each box contains 5 cookies.

a Statement 1 alone is sufficient, but Statement 2 alone is not sufficient.

b Statement 2 alone is sufficient, but Statement 1 alone is not sufficient.

c Both statements together are sufficient, but neither statement alone is sufficient.

d Each statement alone is sufficient.

e Statements 1 and 2 together are not sufficient.

Worksheet 7: Case Study

A Charitable Cause

A group of students decided to organise a charity event to raise funds for their local animal shelter. They planned to sell custom-made bracelets and donate a fraction of the proceeds to the shelter. Here is how their plan unfolds: They created 3 different types of bracelets: A, B and C.

• For every 5 bracelets of type A sold, they would donate 2 5 of the proceeds to the shelter.

• For every 3 bracelets of type B sold, they would donate 3 7 of the proceeds to the shelter.

• For every 5 bracelets of type C sold, they would donate 5 8 of the proceeds to the shelter. During the event:

ο They sold 35 bracelets of type A for ₹75.5 each.

ο They sold 21 bracelets of type B for ₹90.5 each.

ο They sold 28 bracelets of type C for ₹120.5 each.

1 How much money did they get by selling type A bracelets?

2 How much money did they donate on selling type B bracelets?

3 Which type of bracelet let them donate the highest amount?

4 What is the total amount donated to the animal shelter from the proceeds of each type of bracelet sale?

5 If you need to donate or to run a charity event in your colony or community, how will you do it?

Data Handling

Worksheet 1: Aligned to NCERT Topic/s:

Find the mean of the first 10 odd numbers.

Find the mode of the given years of experience of teachers in a school: 12, 5, 7, 10, 3, 2, 1 ,7, 6, 7, 5, 10, 7, 4, 2, 1, 4, 4

The enrolment in a school during six consecutive years is given below. Find the median of the data.

An ecologist studies ecosystems, including forests, and analyses tree heights as part of understanding forests structure and health. The heights of the trees collected by an ecologist are as follows (in metres): 5, 7, 10, 12, 15, 18, 22, 30. What is the range of the given data?

The mean of 5 numbers is 26. One of the observations, which was 6, was removed. Find the new mean. Is the new mean greater or less than the original mean?

Challenge

1 The mean attendance of a class from Monday to Saturday was 33. If the mean attendance from Monday to Thursday was 32 and that from Thursday to Saturday was 34, then find the attendance on Thursday.

2 A data set has 50 different values. 47 values are between 1 and 5, whereas 3 values are more than 50. Which measure of central tendency will better represent the typical value of the data set?

b The spaces between two consecutive bars are . 1

a A bar graph consists of rectangular bars of equal .

c In a bar graph, the bars can be represented either or d The of a bar represents the frequency of the corresponding data.

The table shows the number of points scored by Rahul in 10 rounds of a game. Represent the data using a bar graph.

The table shows the favourite sport of 300 students of a school. Represent the data using a bar graph.

Calorie refers to the amount of energy that food provides when consumed. The table below displays the average intake of various nutrients (in calories) by rural and urban groups for a particular day. Using a suitable scale, draw a double bar graph to compare the data.

Challenge

Critical Thinking

The given data shows the number of toys manufactured by various manufacturing units of a company in five days of a week. Is it possible to draw two different bar graphs using the same data? If yes, then draw.

Worksheet 3: Interpreting Bar Graphs

1 cm on a scale of a bar graph represents 5 ft. Find the actual height of the building if this is represented by a bar of 5 cm height in the bar graph.

The bar graph shows the monthly expenditure of a family on fuel (in ₹) in a year. Read the bar graph and answer the questions.

a What was the family’s expenditure on fuel in March?

b In which month did the family spend the most on fuel? How much did they spend?

c What was the total expenditure of the family on fuel in the full year?

d What is the ratio of the expenditure in the first six months and the expenditure in the last 6 months on fuel?

The bar graph shows the number of cars sold by two showrooms in seven months.

a How many cars in total were sold by Showroom A in the first three months?

b How many cars in total were sold by Showroom B in the last three months?

c Which showroom sold more cars in the first 4 months?

d What is the ratio of the total number of cars sold by Showroom A and Showroom B?

1 The double bar graph shows the percentage of profits earned by two companies, A and B, over the years. Read the graph and answer the questions.

a If the income of Company A in 2011 was ₹1,42,500, what was its expenditure in that year?

b The income of company A in 2010 was equal to its expenditure in 2011, what was the total income (in lakhs) of company A in 2010 and 2011 together? Hint: Consider income as the selling price and expenditure as the cost price.

Worksheet 4: Chapter Checkup

For each set of data, find the mean, median and mode.

a 8, 12, 16, 13, 9, 10, 15, 12

Find the mean and median of:

a the first 10 natural numbers.

b the first 8 prime numbers.

The given bar graph shows the production of food grains in an Indian state for five consecutive years. Read the bar graph and answer the given questions.

a In which year was the production highest? What was the production in that year?

b What was the production in 2016?

c What is the ratio of the production in 2015 to the total production?

The data shows the total population of India based on the census conducted from 1971 to 2021, after every 10 years. Draw a bar graph for the given data.

Look at the bar graph which shows the approximate length of some national highways in India. Read the bar graph and answer the questions.

a Which national highway is the shortest?

b What is the length of the National Highway 9?

c The length of which National Highway is about three times the length of the National Highway 10?

The marks obtained by Kunal in his annual examination are shown below.

Draw a bar graph to represent the given data. Create 3 questions based on the given bar graph.

Mohan secured 75, 82, 79 and 76 marks in four tests. What is the lowest number of marks he can secure in his next test, if he needs to maintain a mean score of 80 marks in five tests?

Challenge

1 In the bar graph, the salaries of 5 employees are shown. Spot the error and explain why this bar graph is misleading. Represent the data in tabular form and redraw the correct graph.

2 The bar graph given below shows the sales of books (in thousands) from six branches of a publishing company during two consecutive years, 2010 and 2011.

Read the given statements and choose the correct option.

Assertion (A): The ratio of the total sales of Branch B2 for both years to the total sales of branch B4 for both years is 210:170.

Reason (R): Ratio is the relation between two numbers which shows how much bigger one quantity is than another.

a Both A and R are true, and R is the correct explanation of A.

b Both A and R are true, but R is not the correct explanation of A.

c A is true, but R is false.

d A is false, but R is true.

Worksheet 5: Case Study

The Geomorphology Project

Soumya, a Grade 7 student, dreams of becoming a geomorphologist. She wants to learn about the processes that shape the Earth's surface, like how mountains form and erode. Soumya has recorded the heights of various mountain peaks and put the data on a bar graph. Look at the bar graph and answer the questions.

1 The mountain peaks arranged in the decreasing order of their heights is -

a Mt Everest > Kanchenjunga > Annapurna > Nanga Parbat > Nanda Devi > Aconcagua

b Mt Everest > Kanchenjunga > Nanda Devi > Annapurna > Nanga Parbat > Aconcagua

c Mt Everest > Kanchenjunga > Nanga Parbat > Annapurna > Nanda Devi > Aconcagua

d Aconcagua > Nanda Devi > Annapurna > Nanga Parbat > Kanchenjunga > Mt Everest

2 What is the ratio of the heights of the highest and lowest peaks?

3 By how much is Mount Everest taller than the average height of the other mountains recorded by Soumya?

4 What is the median height of the mountains recorded by Soumya? If a mountain with height 8600 m is added to the list, will it affect the overall median? Justify your answer.

5 Compare the heights of these mountains with those in other parts of the world, such as the Rockies or the Alps. What differences or similarities do you notice?

Simple Equations

What Equation Is?

1 Which of the following are equations?

5x + 5 = 35

2 Tick () the linear equations in one variable and cross () the others. a x + 9 = 14

7x + 3 = 10

3 Draw balls to balance the given equation.

5x 2 + 3 2 = 18 5

4 Form equations for each of the given statements.

a A number added to half of itself is 9. b The sum of thrice a number and 5 is 17.

c Half of a number is 15. d Half of the sum of 32 times of a number and 5 is 27.

e Two more than the number of frogs is 8. f The number of students increased by 10 is 38.

5 Match each statement with its equation.

a One-tenth of a number gives 7. 10 – x = 7

b 10 subtracted from a number gives 7. x + 27 = 77

c A number subtracted from 10 gives 7. 1 10 x = 7

d The sum of a number and 27 is 77. x – 10 = 7

6 Write an equation for the given situations.

a I have m candies. Lina has 3 fewer candies than I have. We both have a total of 18 candies.

b Tina is c years old. Her 12-year-old sister is 3 years older than Tina.

c Rajat is twice as old as his brother Rakesh. The sum of their ages is 18 years.

d The length of a rectangle with a perimeter of 18 cm is 3 cm more than its breadth.

7 Check whether the value given in the brackets is the solution of the given equations.

a x – 5 = 11 (x = 7)

b 2x + 4 = 10 (x = 6)

c 4x – 3 = 17 (x = 5) d 8 – 2x = 6 (x = 2)

e 5x + 5 = 30 (x = 5)

= 3)

8 Write the given equations in statement form.

a y – 9 = 81

b 4q – 5 = 15

c 30z = 1650

d 9x + 5 = 50

1 Two different car rental companies charge different rates. Company A charges a $50 flat fee plus $2 per mile. Company B charges a $30 flat fee plus $3 per mile. If Neha wants to travel a distance of 10 miles, which company's car will cost her less?

1 Write the first step you will use to separate the variable and then solve the equation.

a x – 7 = 0

b x + 9 = 0

c x − 2 = 6

d x + 5 = 3

e y − 8 = −4

2 Solve the given equations and verify the answer.

a −x + 14 = 21

c 4z – 6 = 3

f 4a = 60

b 2x + 12 = 64

d 30p 7 = 60

3 Aakash solved the equation 12 + x = 20 and got 32. Is the answer correct? If not, find the correct answer.

4 Describe a real-world situation for each of the given equations and solve.

a x – 75 = 150

b 249 + x = 350

Challenge

1 What would you do to make equation 1 and equation 2 equivalent?

Equation 1: 

Worksheet 3: Aligned to NCERT Topic/s:

4.5 More Equations

1 Solve each equation by the transposition method.

2 Solve each of the equations. a 4y = 20

e j 8 = 6 f x 3 = −11

3 Solve the given equations. a 6x + 14 = 16

1.2x + 4.8x = 18

7 + 5x – 3x = 21

4 Give three linear equations in which x = –3 satisfies the equation.

Challenge .................................................................................................................................................................................................................

Critical Thinking

1 What is the number?

a I’m thinking of a number. If 60 is subtracted from it, the result is 4.

b The sum of 13 and an unknown number is 46.

c A certain number decreased by 21 is 81.

d The product of 7 and a number is 56.

e A number when divided by 7 gives the quotient 5.

f If 10 is subtracted from thrice a number, the answer is 35.

g A number is multiplied by 3 and then 5 is added to it to get the answer as 20.

1 Twice the number decreased by 22 is 48. Find the number.

2 A number when added to its half gives 72. Find the number.

3 The sum of two numbers is 95. If one exceeds the other by 3, find the numbers.

4 Divide 20 into two parts so that one part is 8 more than the other. What are the two parts?

5 Find three consecutive numbers so that the sum of the second and the third exceeds the first by 24.

6 The angles of a triangle are x°, (x + 40)° and (x − 10)°. Find the angles.

7 Three sides of a triangle measure (2x + 3) units, (2x + 5) units and 3x units. Find the measure of the sides if its perimeter is 148 units.

8 The age of Olivia’s mother is 5 years more than three times Olivia’s age. Find Olivia’s age if her mother is 44 years old.

9 There are 320 books and magazines in total in a bookshop. There are three times as many books as magazines. How many books are there?

10 The cost of five books and three pens is ₹730. If a book costs ₹50 more than a pen, then find the cost of the book and the pen.

11 Create a word problem involving the application of linear equations.

Challenge

1 Savita is Tina’s older sister. The sum of the ages of Savita and Tina is 18 years, and the difference of their ages is 4 years. Find the ages of Savita and Tina.

Worksheet 5: Chapter Checkup

1 Frame equations for the given situations.

a One and a half times a number is 150. b I am thinking of a number. Five times that number is 65. ____________________________________ ____________________________________

c 3 subtracted from 5 times of p gives 22. d Double of a number added to 36 gives 48.

2 Find the value of the unknown by performing the same operation on both sides.

a x – 3 = −20

b x + 5 = 8

c x – 3 = 7 d x + 5 19 = 3 19

3 Solve the equations.

4 Find the solution of each of the equations.

a 12y = 7y – 15 b 3x – 2 = 5x – 12

c 9 2 x = 54

d −13 2 x = 26

e x 3 − 5 = 6 f 9(x + 14) = 27

5 The Sroda Treasure is the world's greatest treasure discovered in Poland in the 1980s. Nikita found an old treasure map that leads to a hidden treasure. The map contains a series of clues that involve solving equations to reveal the final code to open the treasure. The clues can be given as:

a 5m + 3 = 28 b n 2 + 3 = 7 c 2o 3 + 6 = 10

Help Nikita find the final code if it can be denoted by the word “moon”.

6 Nine added to thrice a whole number gives 45. Find the number.

7 Two-thirds of a number is greater than one-third of the number by 3. Find the number.

8 Divide 38 into two parts so that one part is 18 more than the other.

9 If one side of a square is represented by 4x – 7 and the adjacent side is represented by 3x + 5, find the value of x

10 Each of the two equal sides of an isosceles triangle is three times as large as the third side. If the perimeter of the triangle is 28 cm, find each side of the triangle.

11 A man is 30 years older than his son. In 12 years, the man will be three times as old as his son. Find their present ages.

Challenge

1 Read the statements and decide which of the given options is correct.

Assertion (A): The solution of the equation (4x − 7) = (2x − 5) is −1.

Reason (R): Adding or subtracting the same number from both sides of an equation keeps the equation balanced.

a Both A and R are true, and R is the correct explanation of A.

b Both A and R are true, but R is not the correct explanation of A.

c A is true, but R is false.

d A is false, but R is true.

2 Sushant gave an exam in which 5 marks are given for every right answer, and 2 marks are deducted for every wrong answer. How many right answers did Sushant gave?

Statement 1: Sushant scored a total of 120 marks.

Statement 2: Sushant attempted 45 questions out of the given 50 questions.

a Statement 1 alone is sufficient, but Statement 2 alone is not sufficient.

b Statement 2 alone is sufficient, but Statement 1 alone is not sufficient.

c Both statements together are sufficient.

d Both statements together are not sufficient.

Worksheet 6: Case Study

Atomic Charge Equations

The overall charge of an atom is determined by adding the charges of its electrons and protons. Negatively charged ions are referred to as anions, while positively charged ions are known as cations. For example the overall charge of the sodium cation is −10 + a. Read the table and answer the questions.

1 Which of the given expressions shows the overall charge of the chlorate anion?

b + 17

2 Which of the following equations shows the charge from the proton in the carbonate anion if the overall charge of the atom is −2.

a f – 2 = −32 b f = −32 −2 c f + 32 = −2 d f = −2 + 32

3 What is the charge from a proton in a sodium cation if the overall charge of the atom is +1?

4 What is the charge from the electron in the magnesium anion if the overall charge of the atom is +2?

5 The overall charge of the atom in the barium cation is +2. The charge from the proton in the cation is 110 more than the charge from an electron. What is the charge from the electron and proton in the cation?

Lines and Angles

1 Check whether the given angles are complementary, supplementary or neither.

a 80°, 100°

c 60°, 120°

b 45°, 135°

d 35°, 125°

e 27°, 63° f 40°, 53°

g 37°, 37°

2 Find the complement and supplement of the given angles.

h 78°, 33°

a 33° b 72°

c 41°

d 89°

3 Measure the given angles. Identify whether the pairs of angles are complementary, supplementary or neither.

4 Draw a rectangle ABCD and identify all pairs of supplementary angles.

5 Find the value of x.

X − 45)°

x � 50)°

6 If the angles (3x + 10)° and (7x – 20)° are complementary angles, find the value of x.

7 If the angles (4y + 13)° and (3y – 8)° are supplementary angles, find the measures of these angles.

8 Find the value of the unknown variables.

9 An angle exceeds its complement by 30°. Find the measure of the angle.

10 The traffic sign means ‘no stopping’. If one angle of intersection is 30°, what will be the measure of angle a? Give a reason for your answer. Challenge

1 The ratio between a complementary and supplementary angle of an angle is 4:9. Find the angle.

1 Check whether the following sets of lines are parallel or not by drawing a transversal and measuring alternate or corresponding angles.

2 Identify all the pairs of corresponding angles and pairs of alternate angles in the figure.

3 Check whether the lines are parallel in each case, based on the known angles.

4 Construct a line AB and select a point C that lies outside it. Use a ruler and compass to draw a line through C that is parallel to AB.

5 Draw a line parallel to a line p at a distance of 5.9 cm.

6 In the given figure, l ꠱ m. Also, p and q are transversals. Note that p is not parallel to q, find the values of a° and b°.

7 A line (DE) parallel to the side BC of ΔABC passes through A. The angles are ∠DAB = 90° and ∠EAC = 60°. Find the measure of all the angles of the triangle.

8 Find the value of the indicated unknown angles.

9 Find the measures of the unknown angles.

1 In the given figure, CA ꠱ FB ꠱ DE. If w = 72° and y = w 4 , find the value of z C F D E B A x y z w

Worksheet 3: Chapter Checkup

1 Check whether the given angles are supplementary, complementary or neither.

a 76°, 109° b 24°, 56°

c 44°, 46° d 14°, 166°

e 36°, 135° f 150°, 50°

2 Find the supplement of the given angles.

a 34° b 119°

c 126° d 166°

3 Find the complement of the given angles.

a 26° b 40°

c 47° d 86°

4 Find the value of x.

5 Find the values of ∠ABC, ∠ACB and ∠CAB.

6 Angled parking lets the driver park easily with minimal steering. The yellow lines in a parking space are parallel. What is the measure of ∠m?

7 Identify the figures in which the lines are parallel.

8 Find the measure of the unknown angles, as indicated in each figure.

9 PQRS is a parallelogram. Given ∠QPS = 115°, find the value of the other angles of the parallelogram.

Challenge

1 Read the statements and choose the correct option.

Assertion (A): If a transversal intersects two parallel lines, then the interior angles on the same side of the transversal are supplementary angles.

Reason (R): The sum of the measures of two supplementary angles is 180°.

a Both A and R are correct, and R is the correct explanation for the A.

b Both A and R are correct, and R is not the correct explanation for the A.

c The A is true, but R is false.

d Both A and R are false.

2 Jacob builds a shape using the magnets as shown in the figure in which A || B, C || E and F || D. Find:

Worksheet 5: Case Study

Exploring Angles

The image shows the aerial view of the buildings in a tech park. Mary and her friends decide to cover the buildings in the aerial view during a walk on a weekend. Look at the image and answer the questions that follow.

1 Find the value of x. 2 What is the angle between block A and block B?

3 What is the measure of ∠C?

4 The angle between the training centre and headquarters is 18% of 1662 3 ° . Is the training centre parallel to block B? (Used the answer that you got in Q2)

a Yes b No c Can’t say d None of these

The Triangle and Its Properties

1 Fill in the blanks.

a is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.

b is a line segment perpendicular to a side of the triangle.

c The point where the altitudes intersect is called the of the triangle.

d An may or may not lie inside the triangle.

2 Draw a triangle and the medians to its 3 sides.

3 In a DABC, BD is the median on the opposite side AC. AD = 5 cm. Find the length of AC.

4 The centre of mass of an object is the point where the total mass of the object can be considered to be concentrated. Which of the following can be considered as the centre of mass in a triangle? a centroid b

5 In a DABC, AD and CE are two medians on the opposite sides BC and AB, respectively. The two medians intersect at point G. If AG = 2 cm and BD = 4 cm, find AD and BC.

6 CF, EB and AD are the medians of a DACE. Use the given figure to answer the following questions.

a If BG = 5 cm, find GE and BE.

b If CG = 16 cm, find GF and CF.

c If AD = 30 cm, find AG and GD.

7 If PS is a median of DPQR, then find the value of ∠PSR.

d If GF = x, find GC and CF.

1 If the orthocentre and the centroid of the triangle are the same, then what kind of a triangle is it? Give a reason for your answer.

1 Find the values of x and y in the figures.

2 The angles of a triangle are in the ratio 5:6:7. Find the measures of the angles.

3 One of the exterior angles of a triangle is 130°, and the interior opposite angles are in the ratio 2:3. Find the angles of the triangle.

4 Astronomers often use the positions of three celestial bodies to form a triangular pattern for triangulation. Three celestial bodies form a triangle with interior angles a, b and c. If a = 45°, b = 60° then what is the value of c?

5 In a DABC, ∠A is 50° more than ∠B and 20° less than ∠C. What are the angles of the triangle?

6 In a DABC, ∠A – ∠B = 15°, ∠B – ∠C = 30°. Find the measure of each angle of the triangle.

7 In the adjoining figure, the side BC of a DABC is extended to form a ray BD. CE is drawn parallel to BA. Without using the angle sum property of a triangle:

a Show that ∠ACD = ∠A + ∠B; and

b ∠A + ∠B + ∠C = 180°.

Challenge

1 In which triangle is the measure of each exterior angle twice the measure of its interior angle? Explain your answer with a figure.

Worksheet 3: Aligned to NCERT Topic/s:

6.6 Two Special Triangles: Equilateral and Isosceles 6.7 Sum of the Lengths of Two Sides of a Triangle

1 State which of the following sets of lengths will form a triangle.

a 2 cm, 3 cm and 4 cm b 1 cm, 5 cm and 10 cm c 3.2 cm, 5.6 cm and 8.3 cm

2 S is any point on the side QR of triangle PQR. Fill in the blanks with the >, < or = signs.

a PS PR + SR b PS PQ – QS

3 If the following are the lengths of the two sides of a triangle, what are the possible values of the third side?

a 3 cm and 6 cm b 14 cm and 9 cm

4 In a DPQR, PS is the median. Is PQ + QR + PR > 2 PS? Give reasons for your answer.

5 Delhi, Mumbai and Chennai are metropolitan cities in India. The distance from Delhi to Mumbai is around 1450 km, from Mumbai to Chennai is around 1350 km and from Chennai to Delhi, it is 2200 km. Will these three places form a triangle on the map?

Challenge

1 O is any point in a DABC. If AB = 5 cm, BC = 6 cm and AC = 7 cm. Prove that AO + BO + CO > 9 cm.

Worksheet 4: Aligned to NCERT Topic/s:

6.8 Right-Angled Triangles and Pythagoras Property

1 Which of the following sets of lengths of a triangle belong to right-angled triangles?

a 2 cm, 3 cm and 6 cm b 6 m, 8 m and 10 m c 15 cm, 20 cm and 25 cm

2 Find the missing lengths of each of the triangles.

3 If (k, 24, 25) is a Pythagorean triplet, find the value of k

4 The sides of a rectangle are 12 cm and 16 cm. Find the length of its diagonal.

5 The hypotenuse of a right-angled triangle is 26 cm. The length of the base is 10 cm. What is the length of the altitude of the triangle?

6 Find the values of x and y in the given figure.

7 Create a word problem on the first property of the Pythagoras theorem.

Challenge

1 A right-angled triangle has a hypotenuse of length 10 units. If the difference between the lengths of the legs is 2 units, find the lengths of the legs of the triangle.

Worksheet 5: Chapter Checkup

1 Write True or False.

a There can be only two acute angles in a triangle.

b The sum of the lengths of any two sides of a triangle is greater than the third side.

c Two angles are congruent if the sum of their measures is 180°.

d Two lines are congruent if they are parallel.

2 Which of the following sets of angles will form a triangle?

a 30°, 40° and 110°

b 34°, 29° and 120°

c 50°, 120° and 10°

3 Which of the following sets of lengths of a triangle will form a right-angled triangle?

a 6 m, 8 m and 9 m

b 9 cm, 12 cm and 15 cm c 26 cm, 24 cm and 10 cm

4 Find the missing angles for the following figures.

5 DABC is an isosceles triangle with AC = BC. Will DABC be a right-angled triangle, if AB2 = 2AC2? Give reasons for your answer.

6 In a 52-inch plasma television set, the length of the screen’s diagonal is 52 inches. If the screen’s width is 48 inches, find the height of the screen.

7 A ladder 13 m long reaches a window which is 5 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. Find the width of the street.

Challenge

1 Consider the image shown. Choose which of the given options is correct.

Assertion (A): (AC)2 = (AD)2 + 2(BD)2 + (CD)2

Reason (R): According to the Pythagoras theorem, (Hypotenuse)2 = (Perpendicular)2 + (Base)2

a Both A and R are true, and R is the correct explanation of A.

b Both A and R are true, and R is not the correct explanation of A.

c A is true, but R is not true.

d R is true, but A is not true.

Critical Thinking

Comparing Quantities

1 Express the percentages as fractions in their simplest form.

2 Find out what fraction of the figure is coloured, and also write the percentage of the coloured part.

If 29% of Earth's surface is covered with land, represent the percentage of Earth's surface covered with water as a decimal.

In a class of 30 students, 20% are enrolled in the art club. What is the ratio of art club members to the total number of students?

In a jar of candies, 25% are blue and the rest are red. What is the ratio of blue to red candies?

1 In a company, every 1 out of 10 employees is a manager. Based on this information, read the assertion and the reason given and choose the correct option.

Assertion (A): 11.11% of the total people are managers.

Reason (R): The ratio of managers to employees is 1:9.

a Both A and R are true, and R is the correct explanation of A.

b Both A and R are true, but R is not the correct explanation of A.

c A is true, but R is false.

d A is false, but R is true.

c 125% of 45

Express.

a 5 cm as a percentage of 4 m 25 cm

d 14% of 4800

b 450 mL as a percentage of 3 L

c 75 seconds as a percentage of 2 minutes 30 seconds. d 800 grams as a percentage of 5 kilograms.

Find the number of which:

a 12% is 48.

c 125% is 5 hours 20 minutes.

Find the percent change.

a 320 is decreased to 272

b 2 66 3 % is 567.

d 20% is 3 m 40 cm.

b 110 is increased to 165

c 150 is increased to 195

d 400 is decreased to 360

The concentration of acetic acid in a vinegar solution is 40%. After some dilution, the concentration increases to 50% acetic acid. What is the percent change in the concentration of acetic acid?

Yash scored 360 marks out of 500, and Jaya scored 450 marks out of 600. Who has the better percentage?

At a community gathering focused on promoting environmentally friendly practices, such as using bicycles instead of smoke-emitting vehicles, there are 1440 people in total. If 40% of the people at the gathering are women, how many women are attending the event? How does using bicycles help the environment?

Challenge

1 Is the percentage increase from 80 to 100 the same as the percentage decrease from 100 to 80? Why or why not?

Worksheet 3: Aligned to NCERT Topic/s:

7.3 Prices Related to an Item or Buying and Selling

Find the gain or loss.

a CP = ₹620 and SP = ₹745 b CP = ₹5230 and SP = ₹6000

Select the correct answer.

a CP = ₹405 and SP = ₹510 then gain = ?

Find the missing term. a SP = ₹500, CP = ₹450 then profit = ?

CP = ₹2364, loss = ₹364 then SP = ?

The marked price of a toy car is ₹540. If the discount given by the shopkeeper is 20%, what is the selling price of this toy?

Mia sold a ring which she had bought from an exhibition for ₹9000, to her friend for ₹7600. What is the cost price of the ring for Mia’s friend?

Alex’s father bought a scooter for ₹49,000. He spent ₹6000 on transportation and ₹5000 on repairs. If he sells the scooter for ₹58,000, what is the total profit/loss?

A man sold two watches at the same price, one at a 10% profit and the other at a 10% loss. Find his overall percentage of gain or loss.

1 Read the statements and choose the correct option.

Assertion (A): The vendor buys oranges at ₹26 per dozen and sells them at 5 for ₹13. The vendor’s gain percent is 20%.

Reason (R): Gain percent = Gain Cost Price × 100%

Which of the following options is correct?

a Both A and R are true, and R is the correct explanation of A.

b Both A and R are true, but R is not the correct explanation of A.

c A is true, but R is false.

d A is false, but R is true.

7.4 Charge Given on Borrowed Money or Simple Interest

Find the simple interest and amount.

a P = ₹5000, R = 5% per annum and T = 3 years b P = ₹6000, R = 12% per annum and T = 5 years

c P = ₹2000, R = 10% per annum and T = 3 years d P = ₹2250, R = 2% per annum and T = 4 years

Find the time taken. a P = ₹7500, R = 3% per annum and SI = ₹2250 b P = ₹2000, R = 4% per annum and SI = 1 4 of P

Find the principal amount.

a R = 6% per annum, T = 8 years and SI = ₹23,520 b R = 5% per annum, T = 1 9 3 years and SI = ₹2800

Find the rate of interest. a P = ₹9500, T = 7 years and SI = ₹1995

P = ₹20,000, T = 12 years and SI = ₹18,000

A principal of ₹40,000 is deposited in a bank which offers simple interest at a rate of 10% per annum. What is the total amount at the end of 2 years?

Akila needed some urgent funds, and her friend decided to help her. She borrowed a sum of money from her friend and paid an interest of ₹450 after a year at an interest rate of 4.5% per annum. How much money did Akila borrow? Do you help a friend in need?

Preeti, a small-scale entrepreneur, took out a loan of ₹2,50,000 from a bank under the Prime Minister's Employment Generation Programme (PMEGP), a scheme by the Government of India to promote entrepreneurship and create selfemployment opportunities. The loan was offered at an interest rate of 8% per annum. Calculate the simple interest she has to pay after 4 years.

Challenge

1 A certain sum of money lent out at a certain rate of interest per annum triples itself in 15 years. In how many years will it quadruple itself?

Evaluate.

a 25% of ₹460 b 1 12 2 % of 20 L c 1 50 2 % of 1000

Find the profit or loss for the given cases. Fill in the blank.

a CP = ₹150, SP = ₹200, Profit =

c CP = ₹5100, SP = ₹5235, Profit =

What percent of:

a 6 L is 20 mL?

Find the percentage when:

a 12 is increased to 18

b CP = ₹1580, SP = ₹1235, Loss =

d CP = ₹458, SP = ₹369, Loss =

b 20 km is 1000 m? c ₹15 is ₹2 and 10 p?

b 15 is increased by 15

Find the profit% or loss%.

a CP = ₹50, SP = ₹65

Find the discount%.

a Discount = ₹80, MP = ₹640

Find the missing terms in the questions.

a P = ₹500, R = 2% p.a., T = 3 years, A = ?

b CP = ₹150, SP = ₹125

b Discount = ₹289, MP = ₹1156

b P = ₹5500, R = 14

A person buys a pen for ₹100 and sells it for ₹125. What is the gain or loss? What is the gain % or loss %?

Green energy, such as solar and wind power, is crucial for reducing carbon emissions and combating climate change. Following the announcement of new increased subsidies, the price of an energy company's stock increases from ₹54 per share to ₹72 per share in a week. By what percentage has the stock's price increased?

In a school of 480 students, the ratio of boys to girls is 7:8. a What percentage of the total students are boys? b What percentage of the total students are girls?

Sonu sells a watch at a 5% discount. If he sold the watch at a 6% discount, then he would have earned ₹27 less. What is the marked price of the watch?

1 Seats for Mathematics, Physics and Biology in a school are in the ratio 6:8:12. There is a proposal to increase these numbers by 40%, 50% and 75% respectively. What will be the ratio of the increased seats?

2 Read the statements and choose the correct option.

Assertion (A): A sum of ₹1000 was lent to two people, equally one at the rate of 5% and the other at the rate of 8%. The simple interest earned after one year is ₹65.

Reason (R): SI = PRT 100

Options:

a Both A and R are true, and R is the correct explanation of A.

b Both A and R are true, but R is not the correct explanation of A.

c A is true, but R is false.

d A is false, but R is true.

Worksheet 6: Case Study

The Greenhouse Project

A school decided to build a greenhouse to educate students about sustainable farming. They planned to grow organic vegetables and fruits, which they would sell to the local community. The project was also part of a larger initiative to raise awareness about climate change and sustainable living practices.

The school invested ₹50,000 in building the greenhouse. This included the cost of materials, labour, and initial seeds. In the first year, the greenhouse generated ₹70,000 in revenue from selling produce. The yearly maintenance costs, including water, fertilisers, and electricity, were ₹20,000. To cover the initial costs, the school took out a loan of ₹30,000 at an annual simple interest rate of 8%. The loan is to be repaid in 3 years.

To attract more customers, the school decided to mark the price of their products higher and then offer a discount. The total marked price of the products was ₹80,000, and they offered a 10% discount on the marked price.

Answer the following questions:

1 What was the total profit made by the greenhouse in the first year?

a ₹0 b ₹20,000 c ₹30,000 d ₹50,000

2 What was the selling price of the products after the discount?

a ₹68,000 b ₹70,000 c ₹80,000 d ₹72,000

3 The percentage profit made by the greenhouse in the first year was %.

4 The total amount of the loan repaid after 3 years, including interest, was ₹36,000. (True/False)

5 How does sustainable living help the environment?

Rational Numbers 08

Worksheet 1: Aligned to NCERT Topic/s: 8.2 Need

Rational Numbers in

Form

Write three equivalent fractions for the given rational numbers.

Rayan shared his pudding with a friend. He ate 1 3 of the cup and his friend ate 0.5 of the cup. Did they eat the same amount of pudding? Do you share things with your friends?

1 Statement: Maya, Riya and Sia shared a pizza. The pizza was cut into equal parts. They each ate one part. No pizza was left. Which of the following conclusions do not follow for the given statement?

Conclusion 1: The pizza was cut into 3 equal parts.

Conclusion 2: Maya got more pizza than Riya.

Conclusion 3: If Tia joins them, each of them will get 1 5 th of pizza.

Worksheet

The points P, Q, R, S, T, U, V and W on a number line are such that: VT = TU = UW and PR = RS = SQ. Name the rational numbers represented by R, S, T and U.

List 5 rational numbers between the following.

a –1 and 0

b –4 5 and –2 3

c 1 6 and 2 6

Which of the given rational numbers is the greatest? a 8 3 , –4 3 , 1, –2 5 b 1 2 , –3 5 , 4 9 , 9 10 c 1

, 3 9 , 5 –15

Arrange the given rational numbers in ascending order.

Arrange the temperatures (given in °C) in order from warmest to coldest.

9 3 , 44 15 , – 3 8 , – 14 7 b 3 4 , – 3 4 , 7 8 , 9 10

Raman and Farhan were talking about whose bottle can hold more water. They poured the water from their bottles into glasses. Raman filled 11 5 glasses, while Farhan filled 13 7 glasses. Whose bottle can hold more water? How do you use water responsibly in times of need?

1 Which rational number is greater?

a The rational number whose numerator is the largest two-digit number and denominator is the smallest three-digit number. OR

b The rational number whose numerator is the smallest three-digit number and denominator is the largest three-digit number.

Worksheet 3: Aligned to NCERT Topic/s:

8.9 Operations on Rational Numbers

8.9.1

8.9.2 Subtraction Add

Subtract the first rational number from the second rational number.

a 3 6 and 1 2

b 7 9 and 2 5

c 5 7 and 3 8 d –1 8 and 7 8

Evaluate.

a 5 + 8 9 + –3 9 b (–7) 8 + (–5) 12 + 9 16

Express each of the given rational numbers as the sum of an integer and a rational number. a 54 17

– 0.6 c –17 7

The sum of two rational numbers is –2. If one of the numbers is –14 5 , find the other number.

What number should be added to –5 7 to get –1?

A carpenter bought a piece of wood 17 4 metres long. He then cut off 3.4 metres of the wood. How long is the piece of wood now?

The distance from Ghaziabad to Delhi is 57 2 kilometres, and the distance from Delhi to Gurgaon is 32.7 kilometres. What is the total distance from Ghaziabad to Gurgaon via Delhi? (Write your answer as a fraction.)

Challenge

How much did the taxi driver save if he earned ₹800?

Critical Thinking

Statement 1: He spent ₹ 630 9 on tea and snacks, ₹ 508 2 on food, ₹44 on repairs of the taxi and saved the rest.

Statement 2: The taxi driver spent 46% of his earnings.

Which of the statements are sufficient to answer the question?

a Statement 1 alone is sufficient.

b Statement 2 alone is sufficient.

c Both Statement 1 and Statement 2 together are sufficient.

d Either Statement 1 and Statement 2 alone are sufficient.

Find the product. a 3 5 and 2 4

3 8 and 4 7 c 6 11 and 11 7

– 3 20 and 8 9

Divide the given rational numbers. a –6 5 by –2 3 b –4 5 by –3

c –1 8 by 3 4

Simplify.

–16 21 by 4 3

Multiply the sum of 6 7 and 5 9 by the product of 4 –9 and 15.

Sambhav is training for a race. He ran 11 1 4 km in total in 5 days. How far did he run each day? Write one benefit of physical exercise.

Rima has a piece of ribbon of length is 153 60 m, She would need 20 such pieces for an art work she is making. What is the length of ribbon required?

Challenge

Critical Thinking

1 Rama builds a garden in her backyard that is 41 3 metres in length and 1.75 metres in width. Which of the following statements is true?

Statement 1: The area of the garden is more than 7 m2.

Statement 2: The perimeter of the garden is 12.16 m.

Worksheet 5: Chapter Checkup

1 Find the rational number whose numerator is (65 – 32) and denominator is (3 × 9).

2 Represent 3 2 and –3 4 on a number line.

3 Reduce the rational numbers to the standard form.

8 72 b – 12 60 c 3 –45 d 36 54

4 Find the additive inverse of the following.

a 4 5 + 6 7 b 4 7 + 13 14

5 Find three rational numbers equivalent to the following.

6 Find the value of x

7 List five rational numbers between the following.

a 3 5 and 4 5 b 2 9 and 3 9

Evaluate. a 7 10 + 9 15 b 2 5 –1 2

c 15 42 × 42 50 d 4 14 ÷ 28 80 e (8 9 × 5 4) – (1 5 × 5 9) f (1 2 × 1 4) + (1 2 × 6)

9 Find the multiplicative inverse of (–5 × 12 15) – (–3 × 2 9 )

10 Do – 4 9 and – 16 36 represent the same number? Why or why not?

11 Divide the sum of 65 12 and 8 3 by their difference.

12 A library has a collection of 18,000 books, each belonging to a specific genre, which is a category of literature characterised by similarities in form, style or subject matter. If 1 6 of the books are mystery novels, 2 6 are science fiction and the rest are historical fiction, how many historical fiction books are there?

13 Sakshi was playing in a park. She noticed an insect that crawled 31 6 inches in one minute. The next minute, the insect crawled 2.75 inches. How far did the insect crawl in total? Write one way by which we can be kind towards smaller organisms such as insects.

14 Tanmay is buying a computer on sale. The original price was ₹12,000. If the sale price is 5 6 of the original price, how much did he pay for the computer?

15 Create a word problem on dividing two rational numbers.

Challenge

1 I simplified a rational number to − 1 7 by removing the common factor 7. What was the original rational number?

2 Read the statements and choose the correct option.

Assertion (A): The price marked on an Air conditioner is ₹30,000. If its sale price is 5 6 of the marked price then it is bought for ₹25,000.

Reason (R): There was a sale of ₹5000 on the AC.

a Both A and R are true, and R is the correct explanation of A.

b Both A and R are true, but R is not the correct explanation of A.

c A is true, but R is false.

d A is false, but R is true.

Worksheet 6: Case Study

Carbon Emissions

Carbon emissions contribute significantly to global warming, and various sectors of the economy contribute differently to total emissions. The total global carbon emissions in a given year are estimated to be around 40 billion metric tonnes. Below is the distribution of these emissions across different sectors:

Energy Production: 7 20 of total emissions.

Transportation: 30% of total emissions.

Agriculture: 6.8 billion metric tonnes.

Answer the following questions:

Industry: 0.25 of total emissions.

Residential: 8:100 of total emissions.

1 What is the combined fraction of total carbon emissions from the energy production and industry sectors?

2 How many metric tonnes of carbon emissions are produced by the transportation sector? a 10 billion metric tonnes

12 billion metric tonnes c 8 billion metric tonnes

6 billion metric tonnes

3 The industry sector contributes 25% of the total emissions. Express this percentage as a decimal and a fraction.

4 What decimal of the total emissions do the agriculture emissions represent?

5 Discuss the importance of reducing emissions across all sectors to slow down climate change.

Perimeter and Area

Worksheet 1: Aligned to NCERT Topic/s:

9.1 Area of a Parallelogram

Find the area of the parallelograms.

Given below are measures of some parallelograms. Find the missing measures. a b = 11 cm, h = ?, A= 88 sq. cm

Parallelogram-shaped tiles are preferred in the footpaths to decrease the gaps and have a seamless finish. The base of a parallelogram is twice its height. If its area is 648 sq. cm, find the base and the height of the parallelogram.

The difference in the lengths of two adjacent sides of a parallelogram is 8 cm. The perimeter of the parallelogram is 64 cm. If the perpendicular on the longer side of the parallelogram is the same as the difference in the lengths of the adjacent sides, what is its area?

The adjacent sides of a parallelogram are in the ratio 4 : 3. If the longer side is 8.5 cm, find the perimeter of the parallelogram.

1 The length of one side of a parallelogram is three-fourths of the other side. 2 perpendiculars are dropped from adjacent corners. The length of the perpendicular on the larger side is 18 m. What is the length of the perpendicular on the smaller side?

Worksheet 2: Aligned to NCERT Topic/s: 9.2 Area of a Triangle

Find the area of the triangle in the given figures.

Find the missing measure in the triangle where b is the base, h is the height and A is the area.

Find the area of a right-angled triangle of which the base is 16 cm and altitude is 10 cm.

ΔSTU is a right-angled triangle with S = 90°, ST = 6 cm, TU = 10 cm, and SU = 8 cm. OS is perpendicular to TU. Find OS.

Find the missing measure in the triangle where b is the base, h is the height and A is the area.

a b = 11 cm, h = 8 cm, A = ? b b = 15.8 cm, h = ?, A = 49.77 sq. cm

c b = ?, h = 7.6 cm, A = 39.90 sq. cm

ΔSTU is a right-angled triangle with S = 90°, ST = 6 cm, TU = 10 cm, and SU = 8 cm. OS is perpendicular to TU. Find OS.

In ΔABC (see figure), AB = 15 cm, BC= 8 cm and AD = 7.5 cm. Find: a area of ΔABC b altitude CE

In ΔABC (see figure), AB = 15 cm, BC= 8 cm and AD = 7.5 cm. Find:

a area of ΔABC b altitude CE

The base and height of a triangle are in the ratio 3 : 4. If the area of the triangle is 96 sq. cm, find its base and height.

ABCD is a rectangle with dimensions 30 m by 25 m. AOB is a triangle so that O is the point of intersection of the diagonals. Find the area of the shaded region.

The base and height of a triangle are in the ratio 3 : 4. If the area of the triangle is 96 sq. cm, find its base and height.

Find the area of the shaded region.

ABCD is a rectangle with dimensions 30 m by 25 m. AOB is a triangle so that O is the point of intersection of the diagonals. Find the area of the shaded region.

EFGH is a rectangle in which EF = 28 cm and EH = 22 cm. P, Q, R, and S are midpoints of the sides of the rectangle EFGH. Find the area of the shaded region.

Challenge

1 The figure shows a square ABCD of side 14 cm, and a triangle CEF. The ratio of lengths DF to FC is 1: 4 and DF = BG = BE. Find the difference between the 2 shaded areas.

Chapter 12 • Perimeter and Area

Worksheet 3: Aligned to NCERT Topic/s:

9.3 Circles

9.3.1 Circumference of a Circle

Find the circumference of the circle for the radii. (Take π = 22 7 )

Find the diameter of the circle for the given circumference.

Find the perimeter of a semicircle in which the diameter is 50 cm. (Take π = 3.14)

Find the ratio of the circumferences of two circles whose radii are in the ratio 5:6.

The diameter of the wheel of a truck is 57.15 cm, How many revolutions will it make to cover 1 km 30 m?

A wire is bent into the shape of a square of side 88 cm. If the same wire is looped in the form of a circle, what will the radius of the circle be?

1 The diameter of a circular field is 96 metres. An adult man starts walking around the field at a speed of 8 metres per minute. However, after completing one round, he decides to take a 5-minute break. After the break, he resumes walking, but his speed decreases by 20% due to fatigue. Moreover, instead of walking directly along the circumference for the second round, he decides to take a path that deviates slightly inward, reducing the total distance by 10%. What is the total time taken by the man to walk around the field twice, including the break? (Take π = 3.14)

Worksheet 4: Aligned to NCERT Topic/s:

9.3.2 Area of Circle

Find the area of the circle for the radii. (Take π = 22 7 )

Find the diameter of the circle for the areas.

Find the area of the figures. (Take π = 22

Find the ratio of the areas of two circles whose radii are in the ratio 4:7.

The ratio of the areas of circle P and circle Q is 25:36. If the radius of circle Q is 36 cm, what is the area of circle P?

Metal washers are circular discs with a hole in the centre through which a fastener like a screw fits. They are used to evenly distribute the load of the fastener across the material it connects to. A small metallic washer of radius 8 mm has a hole of 2.5 mm radius. What is the area of the washer?

1 Sonal was making a party hat using a sheet of golden paper as shown in the figure. Find the area of the sheet of paper used to make 20 party hats. 24 cm

Worksheet 5: Area of Combined Shapes

Find the area of the shaded region.

From a circular sheet of metal of radius 8 cm, a quarter circle of radius 5 cm is removed. Find the area of the remaining sheet. (Take π = 3.14)

1 Two circles are drawn inside a big circle of diameter 28 cm. The diameters of the two circles are 1 4 and 3 4 of the diameter of the big circle as shown in the given figure. Find the ratio of the areas of the unshaded part and the shaded part of the circle.

Worksheet 6: Word Problems on Perimeter and Area

The Lincoln Memorial is a monument dedicated to Abraham Lincoln, featuring a large rectangular structure with a colonnade of Doric columns. Its floor has a length of 57.8 metres and a width of 36.1 metres. What is its floor area?

In a circular garden of diameter 160 m, a pond is constructed in the centre in the form of a circle of radius 28 m. Find the area of the remaining garden. (Take π = 3.14)

A rectangular field of dimensions 100 m × 50 m has crossroads running parallel to the two sides and cutting at right angles through the centre of the field. If both roads are 2 m wide, find: a the area covered by the roads. b the cost of grassing the remaining area at the rate of ₹110 per 10 sq. m.

A circular track has to be covered with grass. The inner circumference of the circular track is 176 m. The track is 8 m wide. Calculate the total area of the track that will be covered with grass.

A swimming pool of length 12 m and breadth 5 m is to be built with a coping 1.5 m wide all around it. Find the area of the coping. Also, find the cost of the coping if the rate is ₹50 per sq. m.

1 A dining tent is being set up in a camping area. The radius of the tent is 25.5 m. Holes are being dug to fix wooden sticks. These wooden sticks will be used to tie the ropes that will hold the tent in place. The sticks are to be placed at a distance of 3.5 m from the edge of the tent.

a How many wooden sticks are needed, if they are to be placed 7 m apart along the curved path?

b The circular stage at the centre where the food will be placed is 8.5 m in radius. Find the area left for the people to sit in.

Worksheet 7: Chapter Checkup

Find the area of the figures given below.

The area of a square is 81 sq. cm. Find the area of the square formed by joining the midpoints of the square.

If the length of a rectangle is doubled and its breadth is one-third of the original, then find the ratio of the area of the new rectangle to the area of the original rectangle.

A man wants to acquire a rectangular plot 160 m long and of the same area as that of a square plot of side 108 m. Find the width of the rectangular plot.

A floor 6.68 m long and 8.2 m wide is covered with rectangular tiles of size 64 cm by 32 cm. Find the total cost of the tiles at the rate of 20.50 per tile.

ABCD is a parallelogram of area 1520 sq. m. DP and BQ are the heights on the sides AB and DA, respectively. AB = 28 cm, AD = 32 cm. Find the length of DP and BQ.

Support structures in 3D printing are designed as scalene right angled triangles to make the structure strong and easy to remove after the print. Find the area of a scalene right-angled triangle whose base is 15 cm and altitude is 8 cm.

The sum of the circumference and the radius of a circle is 153 cm. Find the diameter and the circumference of the circle. Also, find the area of the circle.

Challenge

Critical Thinking

1 The perimeter of a rectangle is 80 m. What is the maximum area this figure can have if the sides are natural numbers in metres?

2 Read the statements and choose the correct option.

Assertion (A): If the radius of a circle is 14 m then the area of the circle is 88 sq. cm and its circumference is 616 m.

Reason (R): The area of a circle is given by the formula A = πr2, while the circumference is given by C = 2πr, where r is the radius.

a Both A and R are correct, and the R is the correct explanation for the Assertion.

b Both A and R are correct, but the R is not the correct explanation for the Assertion.

c The A is correct, but the R is incorrect.

d The A is incorrect, but the R is correct.

e Both A and R are incorrect.

Area

Worksheet 8: Case Study

Designing a Living Space

Before the construction of any building, first a plan is made to understand the area and the appearance of the space inside a building. Tia makes a plan for a 1 BHK home with the little knowledge she has about the area and perimeter. Look at the plan and answer the questions.

1 The length and breath of the garden area is:

2 The area of the bathroom is:

3 The perimeter of the living area is

4 What is the perimeter of the kitchen and dining area together?

5 Tiles have to be fitted in the bathroom. The area of one tile is 4 sq. m. How many tiles will this area require?

Algebraic Expressions

1 If 89 is the successor of a natural number n, then what is the value of n?

2 If an even number is denoted by n; the next even number can be given as .

3 The height of a triangle is 20 cm. If its area is 175 cm2, find the length of its base.

4 The perimeter of a square is 62 cm. Find its area.

5 Find the rule for the given pattern: 1, 3, 5, 7, 9,…. Also, find the 100th term of the pattern.

6 A wire is in the shape of a regular pentagon of perimeter 30 cm. If the same wire is bent in the form of a regular hexagon, what would be the length of each side of the hexagon?

1 Kunal has a square plot of an area double that of Nikhil’s rectangular plot. If the length of Nikhil’s plot is 25 m and its perimeter is 75 m, find the perimeter of Kunal’s plot.

1 Using constants, variables and mathematical operations, form algebraic expressions for the given statements.

a Addition of x and y

c 3 less than z added to the product of x and y.

b One-fourth of a number a added to thrice the number b.

d The product of m and n subtracted from twice the product of p and q.

2 List the coefficients of a and b in the expressions.

a 6a2b + 12bc

3 List the terms in the following expressions.

c 0.5xy + 1.2x2y − 3.3y

4 Find the odd one out.

a 8mn, 6mn2, 5nm, nm

d 2 5 yz + 5 6 x2y + 0.6xy

b 3p2q2, 5p2q, 8q2p2 , q2p2

c 0.2xy, 2yx, 0.5zx, 0.8xy d ab2, 5a2b, 7ba2 , a2b

5 Group the like and unlike terms.

Questions Like Terms Unlike Terms

a m2n, 3mn, 5m2n, 6nm, 8nm2, 5m, 7n

b 2a2c, 3ac2, 3ca2, 5b2a, c2a, 8b2c

c pqr, pq2, 9qrp, 5pr, 6rpq, 8rp

d 2klm, 5mln, k2lm, 5lmn, 6lk2m

6 Draw a factor tree for the given expressions.

a 5xy + 8yz

b 3pq2 − 5pr + 2

c 1.2x2y − 3xyz

d m + mn2 − 6l + 8nl

7 Maria has made twice as many paintings as John. If John has made x paintings, write an algebraic expression for the total number of paintings they have made together.

8 A rectangle has a length that is 5 cm longer than its width. If the width is w cm, write an algebraic expression for the perimeter of the rectangle.

9 Create a situation for the expression 3x + y.

Challenge

1 Which of the following statements are true?

i 6mn + 2mn2 + 3 is a binomial.

ii 3 × m is a monomial.

iii 9pq + 2qr + 5s has 9, 2, 5 as constant terms.

iv 4a2 + 5ab + 3c + 8 is a trinomial with no constant term.

a Statements i, ii, iii are true.

c Statements i, iii, iv are true.

b Only statements i, ii are true.

d Only statement ii is true.

Worksheet 3: Addition of Algebraic Expressions

1 Add the monomials.

a 5xy and x =

c 4ab and −3ab =

2 Add the expressions.

a 2x + 3y and x + y

3p2 and 5p2 =

10x2y and 7x2y =

2x + 3y + z and 2x + y − z c

3 Kunal wants to help his friend who is going through a tough time. He bought a shirt for his friend for ₹(3x2 + 2xy + 9y2) and spent on a meal worth ₹(5x2 − xy + 3y2). How much money did he spend in total to show his support and friendship?

Challenge

1 Read the statements and choose the correct option.

Assertion (A): The perimeter of the given triangle is 6a + 3.

Reason (R): The area of a triangle is 1 2 × base × height.

a Both A and R are true, and R is the correct explanation of A.

b Both A and R are true, but R is not the correct explanation of A.

c A is true, but R is false.

d A is false, but R is true.

Worksheet 4: Subtraction of Algebraic Expressions

1 Subtract.

3 What should be subtracted from 5xz2 + 2xy − 7yz to obtain 7xy − 4x2z + 12yz + 3? Challenge

1 Read the statement and the conclusions. Choose the correct option.

Statement: P = 6a2 + 12ab + 3ab2; Q = 5ab – 8ab2; R = 15ab – 4a2 + 9

Conclusion I: 3Q = 15ab – 24ab2

Conclusion II : The value of P – R + 3Q = 10a2 + 12ab – 21ab2 – 9

a Only Conclusion I follows.

c Both conclusions follow.

b Only Conclusion II follows.

d Neither conclusion follows.

Worksheet 5: Aligned to NCERT Topic/s: 10.6

Finding the Value of an Expression

1 If a = 5, find:

a (a + 6) b (2a − 3)

2 Simplify the expressions.

a 5x − (y − 2x + 8y) b (10m − 3mn + 4m) + 5mn

3 Simplify and find the value for m = −2.

a (5m − 3m2 − 6m) − 2m2 b 2(m2 − m) + 3(m2 + m)

4 Find the value of the expressions, when x = 1, y = −1.

a x2 + y2 b 5x2 + 2y2 − 1

5 Add the expressions and find their value for x = −2 and y = 1.

a 4x 3y and 5y + 2x b x2y + 2xy and 3xy 4

Challenge

1 Read the given statement and the conclusions. Choose the correct option.

Statement: Manisha has a triangular plot with sides (3x2 + 3y + 15) m, (2x2 – y + 30) m and (7x2 + 2x – 10) m.

Conclusion I: The perimeter of her plot is (12x2 + 2y + 2x + 35) m

Conclusion II: If x = 2 and y = 1, the perimeter of her plot is between 90 m and 100 m.

a Only Conclusion I follows.

c Both conclusions follow.

Worksheet 6: Chapter Checkup

b Only Conclusion II follows.

d Neither conclusion follows.

1 Classify the expressions as monomial, binomial, trinomial and quadrinomial. ab + 4a − 5ac, 3yx2 + 5xy − 3yx − 8, m × n, 2x2 + y

2 State whether the pair of terms is like or unlike.

a 5m2n, 6n2m b 2ab, −3ba

c x2y, −5yx d 2p2q2, 8q2p2

e 3mn, −5m f 6ab2, −2ab2

3 Draw a factor tree for the expressions.

a x2y + yx b 2cb2 + 6ab + 8c

4 Add the following.

a 5a2b, −3ab2, −7ab2 and 14a2b b (10x + 12y – 12xy – 12), (18 – 5x – 10y + 5xy) and 9xy

5 Find the perimeter of the rectangle. The dimensions are given in metres.

6 What will be the value of y3 + 4y2 – 7y – 2 if y = –3?

7 Find the value of the expression 4x3 – 5y2 + 7 if x = 2, y = 3.

8 Find the value of the expression m3 3 + 5m – 3 – 5n if m = –5, n = 3.

9 Simplify and find the value for m = −1, n = −1.

10 Sunil has a rope which is (5x − 2y + 2) metres long and is attached to another rope of length (3x − xy + 5) metres. Find the total length of the rope, if x = 5 and y = 2.

11 Kunal has an equilateral triangular-shaped wooden frame with a perimeter of 96 cm. He wants a square frame with the length of each side equal to that of the triangular frame. What will be the perimeter of the square frame?

Challenge

1 What value of a and b will make the statement true? (3x2 + 14xy – ay2) – (bx2 – 12xy + 3y2) = 8x2 + 26xy –12y2

Critical Thinking

2 Is 3x – 2y = 0?

Statement 1: x = 2 3 y

Statement 2: y = 6

a Statement 1 alone is sufficient, but statement 2 alone is not sufficient.

b Statement 2 alone is sufficient, but statement 1 alone is not sufficient.

c Both statements together are sufficient, but neither statement alone is sufficient.

d Each statement alone is sufficient.

e Statements 1 and 2 together are not sufficient.

Worksheet 7: Case Study

Planning a Beautiful Garden

An architect is a person who designs buildings and other structures. They plan how buildings will look and how they will be built, considering things like safety, functionality, and aesthetics. Samira and her family have recently purchased a plot of land for their new home. The plot has a total area of (4x2 + 3x − 2) m2. They are very excited to build their dream house on it and plan to utilise the remaining space for a beautiful garden.

After consulting with an architect, they decided to construct a house that occupies an area of (x2 + 2x + 1) m2 on the plot, and the rest was reserved for constructing the garden.

Answer the following questions:

1 What is the expression for the area of the garden?

2 If x = 2, what is the area of the garden?

3 For x =2, if the cost of landscaping the garden is ₹500/m2. How much did the family spend on landscaping?

4 If Samira’s neighbour’s garden is (x2 + 4) m2 in area, what is the total garden area altogether?

Exponents and Powers

Worksheet 1: Aligned to NCERT Topic/s: 11.2 Exponents

1 Write the base and power of the following:

911

(–17)9

2 Write the following in the exponential form.

5 × 5 × 5 × 5

c 7 × 7 × 7 × 8 × 8 × 8 × 8 × 8

3 Find the square and cube of the numbers.

4 Evaluate:

5 Express the numbers as products of powers of prime factors. a 64 b 105

c 480 d 1038

6 Find the reciprocal of each of the following.

(–3)4 c 1 4

7 Which is greater?

a 34 or 43

8 Simplify.

(–5)4 or 54

a 113 × 122 b 103 × 151 c 73 × (–3)4

9 Find the value of x.

11x = 1,331

1 Ramu scored 3125 points in a game. Ramu expressed his points as 5x+1. What is the value of x?

Worksheet 2: Aligned to NCERT Topic/s:

11�3 Laws of Exponents

11�4 Miscellaneous Examples Using the Laws of Exponents

1 Simplify using the laws of multiplication of exponents and express the answer in exponential form. a (–9)3 × (–1)3

(–5)2 × (–5)4 × (–5)6

2 Solve using the laws of division of exponents and fill in the blanks. a 57 ÷ 37 = b 1315 ÷ 139 = c (–11)4 ÷ (–11)1 = d (–15)8 ÷ (5)8 =

3 Simplify and express in exponential form.

4 Evaluate:

5 Find the value of (20 + 30) × (60 + 71).

6 Find the value of p for which 6p × 63 = 362.

7 The weight of an adult dolphin is 23 × 5 × 11 kg and weight of an adult shark is 24 × 53 kg. Find the product of the weights. Challenge

1 Read the statements and choose the correct option.

Assertion (A): 46 × 56 = 206

Reason (R): a m × bm = (ab)m

a A is true but R is false.

b A is false but R is true.

c Both A and R are true and R is the correct explanation for A.

d Both A and R are true but R is not the correct explanation for A.

Worksheet 3: Aligned to NCERT Topic/s:

11.6 Expressing Large Numbers in the Standard Form

1 Express the number in standard form.

a 864000

c 4152000000

2 Write the number in the usual form.

a 3 × 104

c 7.11 × 107

b 5500000

d 614000000000

b 4.55 × 105

d 9.8 × 109

3 Find the number from the following expanded form. Write it in exponential form.

7 × 106 + 5 × 105 + 4 × 103 + 6 × 102 + 8 × 101 + 2 × 100

4 Express the numbers in the statements in the standard form.

a The distance between India and the United States is 13568000 m. =

b The population of India was around 1410000000 in 2021. =

c The distance between Venus and Uranus is around 2760000000 km. =

d The diameter of Jupiter is around 140000000 m. =

Challenge

1 Raj was solving a problem as shown below.

5–4 × 7–3

35–5 = 5–4 × 7–3 5–5 × 7–5 = 5 49

Identify the error and rectify it.

Worksheet

4: Chapter Checkup

1 Write the following in exponential form.

a 8 × 8 × 8 × 8 × 8 × 8

b (–15) × (–15) × (–15) × (–15) × (–15) × (–15) × (–15) × (–15)

Critical Thinking

2 Consider: p = 3 & q = 4 and find: a (p + q)4 b (p − q)2

3 Write the value of the following: a (7 × 2)4 b (–1)9

c 103 × 103

4 Express the numbers as the product of prime factors in exponential form. a 256 b 582

5 Simplify:

a 153 × (−2)4 20 b n 23 × (−1)221 100 × n 20

c (170 – 230) × (170 + 230)

6 Compare and write the correct sign.

7 If

8 Match the numbers with their other forms.

a 9.1 × 106 9.1 × 107

b 90100 91100000000

c 9.11 × 1010 9100000

d 91000000 9.01 × 104

9 Find the distance in centimetres for the aircraft moving at the speed of 690 km/hr and covering the distance in 3 hours 20 minutes.

10 According to the census, the male population of a country in 2011 was 623700000. Express this in standard form.

Challenge Critical Thinking

1 There are 1000 bacteria in a colony. The colony of bacteria increases exponentially by 4 times each hour.

Statement 1: The population of bacteria between hour 2 and hour 3 can be around 4.80 × 105.

Statement 2: The population of bacteria between hour 4 and hour 5 can be around 7.68 × 105

a Only Statement 1 is true.

b Only Statement 2 is true.

c Both statement 1 and statement 2 are false.

d Both statement 1 and statement 2 are true.

2 What is the value of b in (−48)−1 ÷ b? Which of the given statements is sufficient to answer the given question?

Statement 1: (−48)−1 when divided by an even number leaves an even remainder.

Statement 2: (−48 )−1 when divided by b results in (−6)−1

a Only Statement 1 is sufficient, but Statement 2 is not sufficient.

b Only Statement 2 is sufficient, but Statement 1 is not sufficient.

c Both Statements are sufficient.

d Both Statements are not sufficient.

Worksheet 5: Case Study

Exponents in Computers

Computers and storage devices are widely used today. Bytes are the units used to measure the capacity of storage devices. An electronic store sells storage devices like hard disks, CDs, DVDs, flash drives and RAM for computers. 1 GB = 1000 MB

1 The capacity of a CD is 700 MB. The capacity of a CD in exponential form is

a 21 × 51 × 72 MB b 23 × 55 × 71 MB

c 22 × 52 × 71 MB d 22 × 5 × 72 MB

2 The capacity of a hard disk is 512GB. The capacity of a hard disk in MB is

a 5.12 × 102 MB b 5.12 × 105 MB

c 51.2 × 105 MB d 5.12 × 103 MB

3 The maximum capacity of the hard disk that the store sells is a 32TB hard disk. What is the capacity of the hard disk in MB? Write the answer in the standard form.

(Hint: 1 TB = 1000 GB)

4 Radha bought 2 flash drives, each with a capacity of 64MB and 8GB respectively. Write the difference in capacity in exponential form in MB.

Symmetry

1 Tick ( ) the figures that show reflection symmetry.

2 Is the given dotted line in the figures a line of symmetry? If not, then draw the figure with the correct line of symmetry.

3 Identify and draw the lines of symmetry in the given figures.

4 The word ‘DICTIONARY’ was invented by John of Garland in 1220. Which letters of the word ‘DICTIONARY’ have no line of symmetry?

5 Complete the given figures such that they are symmetrical about the given mirror line of symmetry. a b c

6 Shade the squares such that the given figures are symmetrical about the given dotted line of symmetry.

7 On the given grid, draw a quadrilateral with an area of 13 square units which has exactly one line of symmetry.

1 In a park, there is a flowerbed in the shape of a regular hexagon. There is a semi-circular flowerbed on the outside of each edge of the hexagon.

a Draw a rough sketch of the flowerbed. b Is the figure symmetrical? If so, draw the lines of symmetry.

Worksheet 2: Aligned to NCERT Topic/s:

1 Classify the given figures as rotationally symmetrical with order more than 1 or not showing rotational symmetry.

a b c d

e f g h

2 Given the angle of rotation, find the order of rotational symmetry.

3 What letters of the English alphabet have. Explain your answer by drawing lines of symmetry and rotational symmetry for at least 1 of the letters.

a both lines of symmetry and rotational symmetry?

c reflection symmetry but no rotational symmetry?

b rotational symmetry but no reflection symmetry?

d neither reflection symmetry nor rotational symmetry?

4 Look at the given figures. Answer the questions. a b c d

i Mark the centre of rotation in each of the given figures.

ii If each figure is turned up to 360° about the centre point, then how many times will the figure match the original?

iii Find the angle of rotation of the given figures.

5 Esha rotated the given shape as shown.

a Did she rotate it clockwise or anticlockwise?

b What degree of rotation did she make?

c Did the figures look identical after rotation? If yes, find the angle of rotation.

d What is the order of rotation of the shape?

6 Anu wants to make rangoli on Diwali. She doesn’t know how to make them, but she knows about rotational symmetry. She uses her knowledge and the help of her friends to draw the following rangoli designs. Look at these designs and answer the following questions.

a Find the lines of symmetry in each of the given designs.

b Write the order of rotational symmetry for each of these designs. Use it to find the angle of rotation as well.

c Make a card for your neighbour with Diwali wishes using a design with 4 lines of symmetry.

centre of rotation

image

1 Colour the parts of the given figure in such a way that the figure has the given order of rotational symmetry. a Order: 2 b Order: 3 c Order: 4

Worksheet 3: Chapter Checkup

1 Is the given dotted line in the given figures a line of symmetry? Draw the correct line of symmetry, wherever required.

2 Identify and draw lines of symmetry in the given figures.

3 Satya has drawn an incorrect mirror image of the object. Identify the error and correct it.

4 Look at each letter of the English alphabet. Some letters have one line of symmetry, and some letters have more than one line of symmetry. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Find: a at least 5 letters that have a horizontal line b at least 5 letters that have a vertical line of symmetry. of symmetry.

Object Mirror image

5 Complete the given table. Use the table to find the order of rotation and angle of rotation for each of the given figures.

S. No. Figure Rotation by 90° Rotation by 180° Rotation by 270° Rotation by 360° Number of times a shape looks the same

6 Complete the given figures such that they are symmetrical about the given lines of symmetry (mirror line).

7 Name and draw.

a A triangle that has no rotational symmetry.

b A quadrilateral that has no reflection symmetry.

c A triangle that has only 2 lines of symmetry.

8 This clock has been reflected in a mirror. What time is it?

d A polygon that has both reflection symmetry and rotational symmetry of order 9.

9 If the given shape is turned 270° clockwise and then 45° anticlockwise, find the new position of point C.

10 Shade the squares such that the given figures are symmetrical about the lines of symmetry and are also rotationally symmetrical. a b

11 Shade the squares such that the given figures have rotational symmetry of the order stated below.

Order 2 b Order 4

12 What section of these circular grids should be shaded such that the overall shape in the first grid has one line of symmetry, and the second grid has a rotational symmetry of order two? Make sure you mark your line of symmetry.

Reflective symmetry

Rotational symmetry of order 2

13 What is the minimum number of squares that can be added to the given shape such that the final shape has a rotational symmetry of order 4?

1 The figure shows the London Eye in London. Mounted on the wheel are 32 ovoid capsules that carry about 25 passengers each. The wheel moves very slowly, two revolutions per hour.

a What is the order of rotational symmetry of this wheel?

b How many lines of symmetry does the London Eye have?

2 Read the statements and choose the correct option.

Assertion (A): The number of lines of symmetry for two regular figures of different sizes but the same number of sides is the same.

Reason (R): For two regular figures, if the number of lines of symmetry is the same, the figures need not be identical.

a Both A and R are correct, but the R is not the correct explanation for the A.

b A is correct, but the R is false.

c Both A and R are correct, and the R is the correct explanation for the A.

d Both A and R are false.

Worksheet 4: Case Study

The instrument that measures wind speed is called an anemometer. Look at the figure given alongside. In an anemometer, three or four cups are mounted symmetrically at right angles to a vertical axis. As the wind blows, the cup rotates, making the rod spin. The stronger the wind blows, the faster the rod spins.

1 The order of rotation in a 4-cup anemometer is .

a 4

c 2

2 Write True or False.

b 6

d 3

a The angle of rotation in a 3-cup anemometer is 180°.

b The angle of rotation in a 4-cup anemometer is 90°.

3 The figure shows the aerial view of the cups along with the rod. Draw the 3 cups of the anemometer, when it is rotated anticlockwise by 270°.

4 The 3-cup anemometer rotates 90° when the wind speed is 1.2 mph. What will be the degree of rotation, when the wind speed is 4.8 mph?

(Given: The cups rotate at a uniform interval)

Visualising Solid Shapes 3 1

1 How many dimensions does a solid have?

2 Fill in the blanks.

a The solid that has only one vertex is a .

b If three cubes are joined side by side, the shape obtained is a .

c The number of edges in a football is

3 The pillar of the Ashoka Pillar has one curved surface and two flat faces. Name the 3-D shape.

4 Identify the prisms or pyramids. a b c d

5 Write down the number of edges and vertices in the 3-D shapes. a Sphere b Cone c Tetrahedron d Triangular prism

6 If a certain number of ₹2 coins are placed one on top of another, what shape will be obtained? Challenge

1 The figure shows a glass greenhouse. Look at the figure and choose the correct answer.

a The figure is made only of triangular prisms.

b The figure is made of a rectangular prism and square pyramid.

c The figure is made of a rectangular prism and triangular prism.

d The figure is made of 2 rectangular pyramids.

Worksheet 2: Aligned to NCERT Topic/s:

Nets for Building 3-D Shapes

1 List the number of faces and the type of faces for each of these 3-D shapes.

a Octagonal prism

2 Match the solids with their correct nets.

b Nonagonal pyramid

3 Draw the nets of the shapes.

a Pentagonal prism b Hexagonal pyramid

4 This is the net of a triangular prism. Label the base.

1 Dice are cubes with dots on each face. Opposite faces of a dice always have a total of seven dots on them.

Here are two nets to make dice (cubes); the dots are drawn on some of the faces. Complete the net by drawing the dots in each.

Worksheet 3: Aligned to NCERT Topic/s: 13�4 Drawing Solids on a Flat Surface

1 Make an oblique sketch of the isometric sketch.

2 Make an isometric sketch of the oblique sketch.

3 Draw an oblique sketch of a cube that has a side of 5 units.

4 Write the dimensions of the given oblique sketches.

5 Write the dimensions of the isometric sketches.

1 Draw the oblique and isometric sketches of the given shape.

1 What shapes do you get when you give a vertical and a horizontal cross section to the following?

A party hat

2 Match the shapes with their horizontal cross sections.

3 Draw the shadow of the objects.

4 Draw the front, top and side views of the following cube structures.

5 Draw the front, side and top views of each object.

6 Can a cube cast a shadow in the shape of a rectangle? Give a reason for your answer.

1 Kush has a 3-metre-long cylindrical pipe that has a radius of 7 cm. If he slices the pipe along the base horizontally, what will its cross-sectional area be?

Worksheet 5: Chapter Checkup

1 Name the 3-D shapes.

2 Name the 3-D shapes of the objects.

3 Name the solids that have:

a 8 triangular faces

b c d

b 6 triangular and 2 hexagonal faces

4 Name the solids that can be formed by the nets. a b c d

5 Draw a net of the solids.

a Cube

b Pentagonal pyramid

6 Draw the net of a cuboid that has the same breadth and height but a length that is double the breadth.

7 Draw (i) an oblique sketch and (ii) an isometric sketch for a cuboid of dimensions 5 cm, 1 cm and 1 cm.

8 What shadow will be formed by the objects when light falls on them from the front?

9 What will the horizontal and vertical cross sections of the objects in question 8 be?

Challenge

1 Vansh cuts a cuboid cake of dimensions 20 cm × 10 cm × 4 cm exactly in half. What two possible cross sections does he get, and what is the cross-sectional area of both sections?

2 Ram placed 5 cubes of 2 cm each, edge to edge. He then placed 4 cubes of the same measurement on top of them and then three, two and one. How many cubes did he place in total? Draw the front, top and side views of the structure formed.

Worksheet 6: Case Study

3-D Shapes in Space

Our solar system comprises of many planets, stars, natural and artificial satellites, asteroids and many more. All these appear in 3-D shapes.

Sanjay decides to make a 3-D model of an artificial satellite and an asteroid as shown below.

1 The figure shown is the artificial satellite that Sanjay wants to make. The 3-D shape he will use to make it is a .

2 Look at the octahedron asteroid shown and answer.

Number of vertices =

Number of faces =

Number of edges =

3 The vertical and horizontal cross sections of the octahedron are a:

a hexagon and hexagon

c hexagon and circle

4 Draw any 2 views of the artificial satellite.

b Quadrilateral and hexagon

d square and triangle

Introduction to Probability 1

Worksheet 1: Chance

Write the chance of the given events happening, using words like sure, impossible, likely, unlikely and equally likely.

a Getting a number greater than 5 on rolling a dice.

b Getting heads on tossing a coin.

c A lion flying in the sky.

d A child going to school on Monday.

e Picking a pencil from a box of pencils.

Ramesh spins the spinner as shown. What is the chance of the following events?

a Getting an even number.

b Getting a number from 1 to 10.

c Getting the number 5 or 6.

d Getting the number 20.

Ajay spins the spinner. What is the chance of the spinner stopping at:

yellow?

Challenge

1 Name one event for each.

Worksheet 2: Theoretical Probability

red?

Sameer spins the number spinner shown. Answer the questions.

a How many possible outcomes are there?

b What are the favourable outcomes of spinning a number greater than 3?

c How many times can the arrow land on an even number?

d How many times can the arrow land on a prime number?

Each letter of the alphabet is printed on an index card. What is the theoretical probability of randomly choosing any letter except Z?

Anand plays a word board game. He places 98 lettered tiles and 2 blank tiles in a bag. Players will draw tiles from the bag one at a time without looking. What is the probability that the first tile drawn will be?

a A blank tile

b Labelled with a letter

Use the spinner to find the theoretical probability of the event for the given events.

a Spinning red

c Spinning an odd number

e Spinning a number less than 7

Challenge

b Spinning a 1

d Spinning a multiple of 2

f Spinning a 9

Critical Thinking

1 Amit calculates the probability of getting a number less than 3 when randomly choosing an integer from 1 to 10.

Favourable outcomes

Total outcomes = 3 10

Describe Amit’s error and give the correct probability.

Worksheet 3: Experimental Probability

A spinner has four sections marked A, B, C and D. The table shows the results of several spins. Find the experimental probability of spinning each letter as a fraction in its simplest form.

Malati has a bag of marbles. She removes one marble at random, records the colour and then places it back in the bag. She repeats this process several times and records her results in the table. Find the experimental probability of drawing each colour.

Use the bar graph to find the experimental probability of the event.

a Spinning a 6 =

b Spinning an even number =

c Spinning an odd number =

d Spinning a number less than 3 =

e Spinning a 7 =

f Not spinning a 1 =

Challenge

1 There are 700 students at a high school. You survey 75 randomly selected students and find that 60 plan to go to college after completing high school. How many students are likely to go to college after completing high school?

Worksheet 4: Chapter Checkup

Write the chance of the given events happening, using words like sure or impossible.

a Kitten with wings b Child wearing woollens in winter

What is the chance of the events happening? Fill in the blanks with words like sure, impossible, likely, unlikely or equally likely.

a January coming before February is a/an event.

b The sun setting in the East is a/an event.

c A child going to school on a Wednesday is a/an event.

Use the labels on the right to describe the chance that a dice when rolled will show:

a An odd number:

b 6: c A number greater than 6:

d Zero: e A number less than 10:

Fiction books have stories that come from the author’s imagination, whereas non-fiction books are based on real facts and true events. A library has 3000 fiction books, and 4000 non-fiction books. What is the probability that a book selected at random is fiction?

Use the spinner to find the theoretical probability of the events.

a Spinning blue =

b Spinning a 1 =

c Spinning an even number =

d Spinning a 4 =

10 coloured discs are placed in a hat. 5 are red, 3 are yellow and 2 are black. If one disc is drawn from the hat, what is the probability that the disc will be:

a Red?

c Red or black?

e Blue?

b Black?

d Not black?

f Red, yellow or black?

Each student in a class planted a tree on different days of the week. The number of students who planted a tree on a particular day is shown using the circle graph. What is the probability that a randomly picked student planted a tree on Wednesday?

Monday, 8 Tuesday, 10 Wednesday, 6 Other, 6 Number of Students Planting Trees

If the probability of an event is 1 5, how many times, on average, would you expect it to occur in 20 trials?

Challenge

1 Read the statements and choose the correct option.

Assertion (A): If a dice is thrown, the probability of getting a number greater than 4 and less than 5 is zero.

Reason (R): Probability of an impossible event is zero.

a Both A and R are true, and R is the correct explanation of the A.

b Both A and R are true, and R is not the correct explanation of the A.

c A is true, but R is false.

d A is false, but R is true.

2 In a class of 30 students, each student is given a coloured card randomly. The cards are either red, blue or green. What is the probability that a randomly selected student has a blue card? Choose the correct option.

Statement 1: There are 8 red cards.

Statement 2: The probability that a randomly selected student has a green card is 2 5 .

a Statement 1 alone is sufficient to answer the question.

b Statement 2 alone is sufficient to answer the question.

c Statements 1 and 2 together are sufficient to answer the question.

d Statements 1 and 2 together are not sufficient to answer the question.

Worksheet 5: Case Study

Suhani’s Creative Challenge

The beads jewellery market in Jaipur is a thriving segment of the city’s renowned jewellery industry, known for its rich tradition, skilled craftsmanship, and diverse range of products. Suhani creates handcrafted necklaces using colourful beads in Jaipur. She keeps all her beads in a small cloth bag. She usually makes 25 necklaces a day. When she started making her last necklace of the day, she saw that she had run out of blue beads. She counted the remaining beads in the bag. She found 5 black beads, 7 green beads, 8 red beads and 7 yellow beads. Suhani decided that these beads were enough to make a bracelet. So, she put them back in the bag and started picking beads at random to make the bracelet.

1 What is the probability that the first drawn bead is red? a 7 27 b 8 28 c 8 27 d 8 25

2 Which of the following is an impossible event?

a The bead drawn is not red.

c The bead drawn is blue.

b The bead drawn is either green or yellow.

d The bead drawn is neither red nor black.

3 What is the probability that the bead is either red or black?

4 What is the probability that the drawn bead is neither green nor black?

Answers

Chapter 1

Worksheet 1

1. a. −4 b. 29 c. 31 d. −11 e. −90 f. −161 g. 213 h. 33

2. a. −48 b. 72 c. −98 d. 124 3. a. −17 b. 29 c. −57 d. −58 e. −62 f. 169 4. a. 6 b. −7 c. 534 d. 79 e. 281 f. 756 5. a. 3 b. −35 c. 10 d. −₹1000 6. −157

7. a. True b. False c. False d. True

8. a. 13, Commutative property b. −3, Existence of additive identity c. −16, 13, Associative property d. 0, Subtraction property of zero 9. Students will verify by placing the values.

10. 231 11. a. −3 b. −429 c. 142 d. 155 12. 1537 m 13. 105 points

Challenge 1. Answers may vary. Sample answer: Students can shade: –11, 5, –5, 2

Worksheet 2

1. a. 180 b. −66 c. −273 d. 84 e. 0 f. −56

2. a. negative sign b. positive sign

3. a. 1 21 b. − 1 32 c. − 1 54

4. a. 110 b. 0 c. 96 d. −900 e. 3450 f. 2160

5. a. 0 b. 1 c. 56 d. 56, 23 e. −2198 f. 123

6. Students will verify by placing the values.

7. a. 345 b. −1190

8. 440 feet below sea level, –440. 9. 50 points

10. 8250 m below sea level or –8250.

11. Answer may vary. Sample answer: The temperature of a deep freezer decreases by −12℃ every hour. What will be the temperature after 1 day?

Challenge 1. 76 points

Worksheet 3

1. a. −18 b. −8 c. 16 d. −16 2. a. 22 b. 5 c. –3 d. −36

3. −145 4. a. True b. False c. True d. False

5. −32 6. Students will verify by placing the values.

7. Answers may vary. Sample answers: First pair: a = −270, b = 18

Second pair: a = 30, b = –2 8. 55 seconds 9. 75 minutes

10. First level 11. −4℃

Challenge 1. 8 p.m., –18℃

Worksheet 4: Chapter Checkup

1. a. 106 b. 523 c. −2011 d. 340 2. a. −38; 38; 1 −38

b. −78; 78; 1 −78 3. a. −2225 b. 3250 c. −1728 d. −13,965

4. a. −33 b. –32 c. –18 d. −152 5. a. –156 b. –1

c. –1 d. 23, –17 e. 33, –45 f. –64 6. a. −42 b. 64

c. 17 d. −8 7 591 8. −56 9. −935

10. −56 11. 40, 80

12. ₹12,000. The value that we learn from Suhani’s mother is managing personal finances.

13. +12,000 feet; +15,000 feet; −23,945 feet; New altitude = +3055 feet

14. –9℉

Challange 1. 9th floor 2. Option a

Worksheet 5: Case Study

1. b. 440 ℃ 2. Magnesium, 1124 ℃ 3. Nitrogen 4. oxygen, chlorine and nitrogen 5. −346 ℉

Chapter 2

Worksheet 1

1. a. 11 9 b. 13 22 c. 1 6

3. 23 30 of the wall 4. 1 11 20 m

Challenge 1. 1 6 , 1 4, 1 12, 3 8, 1 8

Worksheet 2

1. a. 104 5 b. 10 c. 115 d. 2 2. a. 3 10 b. 13 3. a. 3

Challenge 1. Option d

Worksheet 3

Worksheet 4

1. a. 236.15 b. 533.594 2. a. 115.84 b.

Worksheet 5

6. 15,562.5625 cm2; 499 cm 7. 112.8 m 8. ₹1980.83

9. 158.48 km 10. ₹708.12 11. 3 litres

Challenge 1. 4.94 cm

Worksheet 6: Chapter Checkup

1. a. 17 39 b. 103 12 c. 16 9 d. 82 15 2. a. 131 3 b. 16 c. 1898 d. 75 3. a. 158.76 b. 847.536 c. 51.677 d. 411.012

4. a. 7437.5 b. 1923.6308 c. 124.7 d. 60.1

5. a. Product of 31 5 and 21 4

b. Product of 25 and 4 75 6. a. 929 30 b. 314 17 c. 100 147 d. 207 280

7. a. 78 miles b. 169 c. 81 8. a. 2 5 b. 1 5 9. 147.35 marks

10. 7.5 kg 11. 64.8 cm 12. 175 litres 13. 303 4 km

Challenge 1. a. ₹2821.5 b. ₹2910.07 2. Option c

Worksheet 7: Case Study

1. c 2. b 3. Type C 4. ₹3980.25 5. Answer may vary.

Chapter 3

Worksheet 1

1. 10 2. 7 3. 4.17 4. 88.6 5. 1725 6. Range = 25 metres 7. 31, greater

Worksheet 2

1. a. width b. equal c. horizontally, vertically d. height 2.

Challenge 1. Yes, it is possible to draw two different bar graphs. We can do so by taking different scales. Answer may vary. One can be drawn using 1 division = 5000 toys and other can be drawn using 1 division = 10,000 toys as shown below.

Worksheet 3

1. 25 ft. 2 a. ₹2200 b. January and August, ₹2400 in each

c. ₹24,200 d. 60:61 3. a. 210 cars b. 210 cars c. Showroom A d. 17:16

Challenge 1. a. ₹1,05,555.56 b. ₹2,48,055.56

Worksheet 4: Chapter Checkup

1. a. 11.875; 12; 12 b. −11.875; −15; −15

2. a. 5.5; 5.5 b. 9.625; 9

3. a. 2018, 90 million tonnes b. 70 million tonnes c. 60:350

Questions may vary. Sample questions.

1. What is the total of the marks obtained by Kunal in all the subjects?

2. In which Subject did Kunal score the highest marks?

3. What are the average marks obtained by Kunal?

7. 88 marks

Challenge 1. The graph is misleading; the numbers on the y-axis start at 19. It should always start at 0. The tabular form and correct graph would be:

Name of employees Raj Sahil Nivira Yuvan Kabir

Answer may vary

Chapter 4

Worksheet

x + 2 =

balls on RHS of the balance.

c. 10 – x = 7 d. x + 27 = 77 6. a. m + m – 3 = 18 OR 2m – 3 = 18

b. c + 3 = 12 c. x + 2x = 18 OR 3x = 18 d. 2(2x + 3) = 18

7. a. No b. No c. Yes d. No e. Yes f. No

8. Statements may vary. Sample statements a. 9 subtracted from y gives 81. b. 5 subtracted from 4 times q gives 15. c. 30 times z equals 1650. d. The sum of 9 times x and 5 gives 50.

Challenge 1. Company B

Worksheet 2

1. a. Add 7 to both sides; x = 7 b. Subtract 9 from both sides; x = −9 c. Add 2 to both sides; x = 8 d. Subtract 5 from both sides; x = −2 e. Add 8 to both sides; y = 4 f. Divide by 4 from both sides; a = 15

2. a. x = –7 b. x = 26 c. z = 9 4 d. p = 14 3. Incorrect; 8

4. Answers may vary. Sample answers: a. Veena had saved some money in her money bank. She spent ₹75 on buying stationery items. If she is now left with ₹150, how much money did she have to begin with? ₹225 b. Ankur has 249 postcards. He added new postcards to his collection. If he has 350 postcards in all, how many new postcards did he add to his collection? 101 postcards

Challenge 1. We shall either multiply both sides of equation 1 by 6 or divide both sides of equation 2 by 6.

Worksheet 3

1. a. x = 6 b. a = 4 c. x = 3 7 d. n = 1.4 e. x =

2. a. y = 5 b. y = 6 c. a = –12 d. m = 3 e. j = 48

3. a. x = 1 3 b. x = 7 c. x = 3 d. x = 4 3 OR x = 1 1 3

4. Answer may vary. Sample answer. x + 6 = 9; x −2 = −5; 2x = −6

Challenge 1. a. 64 b. 33 c. 102 d. 8 e. 35 f. 15 g. 5

Worksheet 4

1. 35 2. 48 3. 46 and 49 4. 6; 14 5. 21, 22, and 23

6. 50°, 90°, and 40° 7. 43 units, 45 units, and 60 units

8. 13 years 9. 240 books 10. Book = ₹110; Pen = ₹60

11. Answers may vary. Sample answer. A bicycle rental shop charges a flat fee of ₹100 to rent a bike plus ₹30 per hour for the duration of the rental. Write a linear equation for the total cost of renting a bike for x hours. Find the total cost given by a person to rent the bicycle for 4 hours.

Challenge 1. 11 years; 7 years

Worksheet 5: Chapter Checkup

1. a. 11 2 x = 150 b. 5x = 65 c. 5p − 3 = 22 d. 2x + 36 = 48

2. a. −17 b. 3 c. 10 d. –2 19 3. a. x = 2 b. a = 3 c. y = 9

d. x = 3 4. a. y = −3 b. x = 5 c. x = 12 d. x = –4 e. x =

33 f. x = –11 5. 5668 6. 12 7. 9 8. 10; 28

9 12 10 4 cm; 12 cm; 12cm 11. 3 years; 33 years

Challenge 1. Option d 2. Option c

Worksheet 6: Case Study

1. Option a 2. Option d 3. Option c 4. −10

5. Charge from the electron = −54; Change from the proton = 56

Chapter 5

Worksheet 1

1. a. Supplementary b. Supplementary c. Supplementary d. Neither e. Complementary f. Neither g. Neither

h. Neither 2. a. Complement = 57°; Supplement = 147°

b. Complement = 18°; Supplement = 108°

c. Complement = 49°; Supplement = 139°

d. Complement = 1°; Supplement = 91°

3. a. Neither b. Complementary

4. a.

5. a. 25° b. 216° 6. 10° 7. 113°, 67°

8. a. 45° b. m = 120°, n = 60° 9. 60°

10. 30°. The angles in vertically opposite sides are equal

Challenge 1. 18

Worksheet 2

1. a. Not parallel b. Not parallel c. Not parallel d. Parallel

2. Pairs of corresponding angles: 2 and 6, 2 and 10, 6 and 10, 1 and 5, 1 and 9, 5 and 9, 3 and 7, 7 and 11, 3 and 11, 4 and 8, 8 and 12, 12 and 4. Pairs of alternate angles: 2 and 8, 1 and 7, 3 and 5, 4 and 6, 1 and 11, 2 and 12, 3 and 9, 4 and 10, 6 and 12, 5 and 11, 7 and 9, 8 and 10.

3. a. Not parallel b. Not parallel c. Not parallel d. Parallel

4. D A B P Q R C S l

5. P q B A

5.9 cm 5.9 cm E F

6. a° = 118°, b° = 108° 7. ∠ACB = 60°, ∠ABC = 90°, ∠BAC = 30°

8. a. x° = 80°, y° = 32° b. m° = n° = 70° c. p° = 60°, q° = 105° d. h° = 45°, g° = 72° 9. a. y° = 35°, x° = 50° b. 108°

Challenge 1. 126°

Worksheet 3: Chapter Checkup

1. a. Neither b. Neither c. Complementary d. Supplementary e. Neither f. Neither

2. a. 146° b. 61° c. 54° d. 14° 3. a. 64° b. 50° c. 43°

d. 4° 4. a. 20° b. 29° c. 28° d. 22.5° 5. ∠ABC = 75°, ∠ACB =67°, ∠CAB = 38° 6. 115° 7. a. Not parallel b. Parallel 8. a. 115° b. 130°

9. ∠PQR = 65°, ∠RSP = 65°, ∠QRS = 115°

Challenge 1. Option b 2. 40° b. 96° c. 84° d. 84°

Worksheet 4: Case Study

1. 33.3° 2. 23.34° 3. Option d 4. Option c

Chapter 6

Worksheet 1

1. a. Median b. Altitude c. orthocentre d. altitude

2. A C B 3. 10 cm

4. Option a 5. AD = 3 cm, BC = 8 cm

6. a. GE = 10 cm, BE = 15 cm b. GF = 8 cm, CF = 24 cm

c. AG = 20 cm, GD = 10 cm d. GC = 2x, CF = 3x 7. 72°

Challenge 1. Equilateral triangle since in an equilateral triangle, the median is the the same as the altitude.

Worksheet 2

1. a. 105° b. 165° 6 or 27.5° c. x = 70°, y = 55°

d. x = 30°, y = 30° 2. 50°, 60°and 70° 3. 52°, 78°, 50°

4. 75° 5. 70°, 20° and 90° 6. 80°, 65°, and 35°

7. Prove using the linear pair of angles and the exterior angle property.

Challenge 1. Equilateral triangle

Worksheet 3

1. a, c 2. a. < b. > 3. a. 3 cm < x < 9 cm

b. 5 cm < x < 23 cm 4. Yes. As we have shown, the triangle inequality property holds true for this statement, hence, PQ + QR + PR > 2 PS. 5. Yes

Challenge 1. Solve using the Triangle Inequality Theorem.

Worksheet 4

1. b, c 2. a. 16 m b. 24 cm 3. 7

4. 20 cm 5. 24 cm 6. x = 5 cm; y = 12 cm

7. Answers may vary. Sample answer: A ladder 13 m long is placed on the ground in such a way that it touches the top of a vertical wall 12 m high. Find the distance of the foot of the ladder from the bottom of the wall.

Challenge 1. 8 m and 6 m

Worksheet 5: Chapter Checkup

1. a. False b. True c. False d. False 2. a, c

3. b and c 4. a. ∠P = 16; ∠Q = 94° b. ∠x = 50°

c. ∠y = 63° 5. Prove using the Pythagoras Theorem.

6. 20 inches 7. 17 m

Challenge 1. Option a

Chapter 7

Worksheet 1

1. a. 11 20 b. 9 2500 c. 9 400

2. a. 1 2; 62% b. 5 8; 62.5% c. 62 100; 62%

3. a. 0.48 b. 0.0125 c. 0.00005 d. 0.112

4. a. 20% b. 120% c. 234% d. 1210%

5 0.71 6. 1:5 7. 1:3

Challenge 1. Option d

Worksheet 2

1. a. 62.5 b. 225 c. 56.25 d. 672 2. a. 1 3 17 % b. 15%

c. 50% d. 16% 3. a. 400 b. 850.5 c. 4 hours 16 minutes

d. 17 m 4. a. 15% decrease b. 50% increase

c. 30% increase d. 10% decrease 5. 25% increase

6. Jaya 7. 576 women

Challenge 1. No, because the base values for the calculations are different. The percentage increase is calculated relative to the smaller number (80), and the percentage decrease is calculated relative to the larger number (100).

Worksheet 3

1. a. Gain of ₹125 b. Gain of ₹770

2. a. (ii) b. (ii) 3. a. ₹50 b. ₹2000

c. 23 9 117 % d. 16 2 3 % 4. ₹432 5. ₹7600

6. Loss = ₹2000 7. 1% loss

Challenge 1. Option a

Worksheet 4

1. a. ₹750; ₹5750 b. ₹3600; ₹9600 c. ₹600; ₹2600

d. ₹180; ₹2430 2. a. 6.25 years b. 10 years

3. a. ₹6000 b. ₹49000 4. a. 3% b. 7.5%

5. ₹48,000 6. ₹10,000 7. ₹80,000

Challenge 1. 22.5 years

Worksheet 5: Chapter Checkup

1. a. 80% b. 3 16 c. 11 500 2. a. ₹115 b. 2.5 L c. 505

3. a. ₹50 b. ₹345 c. ₹135 d. ₹89

4. a. 1 3 % b. 5% c. 14% 5. a. 50% b. 100%

6. a. 30% profit b. 162 3 %

8. a. ₹530 b. ₹10,683.75 9. Gain = ₹25, 25% 10. 33 1 3 % 11. a. 46 2 3 % b. 53 1 3 % 12. ₹2700

Challenge 1. 14:20:35 2. Option a

Worksheet 6: Case Study

1. a. ₹0 2. Option d 3. 0% 4. False

Chapter

Worksheet 1

9. No

Challenge 1. Conclusion 2 and conclusion 3 do not follow.

Worksheet 2

3. Answers may vary. Sample answers: a. –1 6 , –2 6 , –3 6 , –4 6 , –5 6 ,

, c. 7 36, 8 36, 9 36, 10 36, 11 36 4. a. 8 3 b. 9 10 c. 4 11 d. 3 9 5. a.

Worksheet 3

9. 306 5 km 10. Answers may vary. Sample answer.

Raj bought 14 9 m of cloth. He again bought 13 8 m of cloth. How much cloth does he have in total?

Challenge 1. (d) Either Statement 1 and Statement 2 alone are sufficient.

Worksheet 4

1. a.

Challenge 1. Both statements are true.

Worksheet 5: Chapter Checkup

1. 33

5. Answers may vary. Sample answers: a. 2 12; 3 18; 4 24

b. – 18 24; – 27 36

6. a. 56 b. 80

7. Answer may vary. Sample answer: a. 19 30, 20 30, 21 30, 22 30, 23 30

b. 13 54, 14 54, 15 54, 16 54, 17 54 8. a. 13 10 b. –1 10 c. 3 10 d. 40 49 e. 1 f. 25 8

9. – 3 10 10. Yes, as both are equivalent rational numbers.

11. 97 33 12. 9000 books 13. 71 12 inches 14. ₹10,000

15. Answers may vary. Sample answer.

A gardener has 7 8 litres of liquid fertilizer. He needs to divide it equally among 1 2 litres of water to dilute it properly for his plants. How many litres of water can he mix with the fertilizer?

Challenge 1. –7 49 2. a

Worksheet 6: Case Study

1. Option b 2. Option b 3. 0.25; 1 4

4. 0.17 5. Answers may vary.

Chapter 9

Worksheet 1

1. a. 63 sq. cm b. 48 sq. cm 2. a. 8 cm b. 16.56

4. 160 sq. cm 5. 29.75 cm 6. 16.7 cm (approx.)

Challenge 1. 24 m

Worksheet 2

1. a. 104 sq. cm b. 40 sq. in 2. a. 44 sq. cm b. 6.3 cm

3. 4.8 cm 4. a. 30 sq. cm b. 4 cm

5. Base = 12 cm, height = 16 cm 6. 562.5 sq. cm

Challenge 1. 117.6 sq. cm

Worksheet 3

1. a. 88 cm b. 176 cm c. 268.4 cm 2 a. 24 cm b. 112 cm c. 160 cm 3. 128.5 cm 4. 5:6

5. 574 revolutions 6. 56 cm

Challenge 1. 85.07 minutes

Worksheet 4

1. a. 154 sq. cm b. 1386 sq. cm c. 38.5 sq. cm

d. 346.5 sq. cm 2 a. 14 cm b. 28 cm c. 7 cm d. 21 cm

3. a. 77 sq. cm b. 346.5 sq. mm c. 346.5 sq. mm

d. 18.865 sq. cm 4. 16:49 5. 2828.57 sq. cm 6. 181.5 sq. mm

Challenge 1. 27,154.2 sq. cm

Worksheet 5

1. a. 1148 sq. cm b. 33.6 sq. cm 2. a. 42 sq. cm b. 11.43 sq. cm 3. 181.335 sq. cm

Challenge 1. 3:5

Worksheet 6 1. 2086.58 sq. m 2. 17,634.24 sq. m 3. a. 296 sq. cm b. ₹51,744 4. 1609.15 sq. m 5. 42 sq. m, ₹2100

6. Answer may vary. Sample answer: The length of the side of a square picnic mat is 62 cm. Find the area and the perimeter of the square picnic mat.

Challenge 1. a. 26 sticks b. 1814.92 sq. m

Worksheet 7: Chapter Checkup

1. a. 18 sq. cm b. 24 sq. cm 2. 40.5 sq. cm 3. 2:3 4. 72.9 m 5. ₹5483 (approx) 6. DP = 54.29 m, BQ = 47.5 m

7. 60 sq. cm 8. 42 cm, 132 cm, 1386 sq. cm

Challenge 1. For length = 20 m and breadth = 20 m, the area is the maximum. 2. Option d

Worksheet 8: Case Study

1. Option c 2. Option d 3. Option c 4. 72 m

5. 12 tiles

Chapter 10

Worksheet 1

1. 88 2. n + 2 3. 17.5 cm 4. 240.25 cm2

5. (2n − 1), 199 6. 5 cm

Challenge 1. 100 m

Worksheet 2

1. a. x + y b. a 4 + 3b c. z – 3 + xy d. 2pq − mn

2. a. 6ab; 6a2, 12c b. 3c, –10b; –10a c. 15ba, 12c; 15a2, 7bc

d. 5ac, 3b, –6c; 3a 3. a. 5m2 , mn b. 6ab, 8a2bc, –2bc2 , –ca

c. 0.5xy, 1.2x2y, –3.3y d. 2 5 yz, 5 6 x2y, 0.6xy

4. a. 6mn2 b. 5p2q c. 0.5zx d. ab2

5. Like terms Unlike terms

a. (m2n, 5m2n, 8nm2), (3mn, 6nm) 5m, 7n

b. (2a2c, 3ca2), (3ac2 , c2a) 5b2a, 8b2c

c. (pqr, 9qrp, 6rpq), (8rp, 5pr) pq2

d. (5mln, 5lmn), (6lk2m, k2lm) 2klm

6 a. Expression 5xy + 8yz 5xy 8yz

5 x y 8 y z Terms Factors b. Expression 3

–5

c. Expression 1.2x2y – 3xyz 1.2x2y –3xyz 1.2 x x y –3 x y z Terms Factors d. Expression

7. 3x 8. (4w + 10) cm 9. Answer may vary. Sample answer: An eraser costs ₹3 each and a pencil costs ₹1 each. Write an expression to show the total cost of the eraser and the pencil.

Challenge 1. Option d

Worksheet 3

Challenge 1. Option b

Worksheet 4

–2

a +

Challenge 1. Option c

Worksheet 5

1. a. 11 b. 7 2. a. 7x – 9y b. 14m + 2mn 3.

4. a. 2 b. 6 5. a. −10 b. −10

Challenge 1. Option a

Worksheet 6: Chapter Checkup

1. Trinomial, quadrinomial, monomial, binomial 2. a. Unlike b. Like c. Unlike d. Like e. Unlike f. Like

3. a. Expression x2y + yx x2y yz x x y y z Terms Factors b. Expression 2cb2 + 6ab + 8c 2cb2 6ab 8c 2 c b b 6 a b 8 c Terms Factors

4. a. 19a2b – 10ab2 b. 5x + 2y + 2xy + 6 5. (18a – 10) metres 6. 28 7. –6 8 −84.67 9. a. −2 b. −18 10. 33 metres 11. 128 cm

Challenge 1. a = 9; b = –5 2. Option a

Worksheet 7: Case Study

1. Option c 2. Option c 3. ₹5500 4. (4x2 + x + 1) m2

Chapter 11

Worksheet 1

1. a. 9; 11 b. −17; 9 c. n; 10 d. 3 8; 5 e. –7 11; 8

2. a. 54 b. (–9)7 c. 73 × 85 d. n 5 × p 5 e.

3. a. 64; 512 b. 121; 1331 c. 324; 5832 d. 441; 9261 4. a. 4913 b. –3125 c. 5184 d. 8 729 e.

Worksheet 2

Challenge 1. Option c

Worksheet 3

1. a. 8.64 × 105 b. 5.5 × 106 c. 4.152 × 109 d. 6.14 × 1011

2. a. 30000 b. 455000 c. 71100000 d. 9800000000

3. 7504682; 7.504682 × 106 4. a. 1.3568 × 107 b. 1.41 × 109 c. 2.76 × 109 d. 1.4 × 108

Challenge 1. The powers of the numbers in the numerator and denominator is negative. So, the final answer will be 245.

Worksheet 4: Chapter Checkup

1. a. 86 b. (−15)8 c.    3 7    9 2. a. 2401 b. 1 3. a. 38,416

b. −1 c. 10,00,000 d. 1 4. a. 28 b. 2 × 3 × 97 5. a. 2700 b. – n 3 102 c. 0 d. 16 6. a. < b. < c. <

8 a. 9100000 b. 9.01 × 104 c. 91100000000 d. 9.1 × 107

9. 2.3 × 108 centimeters 10. 6.237 × 108

Challenge 1. Option b 2. Option b

Worksheet 5: Case Study

1. Option c 2. Option b 3. 3.2 × 107 MB 4. 7.936 × 103 MB

Chapter 12

Worksheet 1

Challenge 1. Colours may vary. Sample figures.

a. b. c.

1. c. d. 2. a. Yes b. No, c. Yes d. Yes

e. No, f. No, Line of symmetry not possible

Worksheet 3: Chapter Checkup

1. a. Yes b. Yes c. No, d. Yes e. No,

e. f. No line of symmetry.

3. a. b. c. d.

5. a. b. c.

6. a. b.

c. d.

7. Answers may vary. Sample answer.

Challenge 1. a. b. Yes, It has 6 lines of symmetry.

Worksheet 2

1 a. more than 1 b. No rotational symmetry c. more than 1

d. No rotational symmetry e. more than 1 f. more than 1

g. No rotational symmetry h. No rotational symmetry

f. No, Lines of symmetry may vary. Sample answer:

4. N, R 1

2. a. 5 b. 3 c. 4 d. 2 3. a. Letter H, I, O, X b. Letter N, S, Z

c. Letter A, B, C, D, E, K, M, T, U, V, W, Y d. Letter F, G, J, L, P, Q, R

2. a. 1, b. 0, c. 4,

d. 2, e. 1, f. 4,

3. Error: The marked portion of the mirror image should be flipped on the opposite side.

Correct image:

Object Mirror image

4. a. B, C, D, E, K b. A, T, U, V, W

Object Mirror image

5. S. No. Figure Rotation by 90° Rotation by 180° Rotation by 270° Rotation by

6. a. b. c.

7. a. Scalene triangle b. Parallelogram c. None

4. i. a ii. a. 4 b. 4 c. 4 d. 6

iii. a. 90° b. 90° c. 90° d. 60°

5. a. Anticlockwise b. 90° c. No d. 1

6. a. 4 lines of symmetry in each figure.

b. For both the figures, order = 4, angle of rotation = 90°

c. Answer may vary. Sample answer: Happy Diwali

d. Nonagon, 140° 40° 8. 7:15

9. The new position of C will replace H in the original A F G D H C B E

10. Answer may vary. Sample answers: a. b.

11. Answer may vary. Sample answers: a. b.

12. Figure may vary. Sample figures:

13. Minimum of 6 squares should be added to get a rotational symmetry of order 4.

Worksheet 3

1. 2. 3.

Challenge 1. a. 32 b. 32 2. Option c

Worksheet 4: Case Study

1. Option a 2. a. false b. true

4. Angle of rotation when the wind is 1.2 mph = 90°

Angle of rotation when the wind speed is 4.8 mph

= 90° × 4.8 mph 1.2 mph = 360°

Chapter 13

Worksheet 1

1. 3 dimensions 2. a. cone b. cuboid c. 0

3. Cylinder 4. a. Pentagonal pyramid

b. Square prism or cuboid c. Rectangular pyramid

d. Hexagonal prism

5. a. E = 0; V = 0 b. E = 1; V = 1 c. E = 6; V = 4 d. E = 9; V = 6

6. Cylinder

Challenge 1. Option c

Worksheet 2

1. a. 10; 2 octagonal identical faces and 8 rectangular faces b. 10; 1 nonagonal base and 9 triangular lateral faces

2. a. b. c. d.

3 a. b.

4. The triangles are the bases.

Challenge 1.

4. a. 5 units × 4 units × 1 unit b. 3 units × 5 units × 2 units

c. 6 units × 3 units × 3 units 5. a. 4 units × 4 units × 4 units

b. 3 units × 5 units × 2 units c. 5 units × 2 units × 2 units

Challenge 1.

Worksheet 4

1. a. Vertical: triangle, Horizontal: circle b. Horizontal: square, Vertical: square c. Horizontal: rectangle, Vertical: rectangle

d. Horizontal: circle, Vertical: circle

2. a. b. c. d. e.

3. Figures may vary. Sample figures:

a. b. c. d.

4. a. Front , Top , Side

b. Front , Top , Side

5. a. Front , Side , Top

b. Front , Side , Top

6. Yes, if the light source creating the shadow falls at an angle on the cube.

Challenge 1. 154 cm2

Worksheet 5: Chapter Checkup

1. a. Cone b. Cube c. Cylinder d. Triangular prism

2. a. Cuboid b. Square pyramid c. Cube d. Cylinder

3. a. Octahedron b. Hexagonal prism 4. a. Cylinder

b. Square pyramid c. Cube d. Triangular pyramid

5. a. b.

6. Figures may vary. Sample figure: 7. i. ii.

8. a. Rectangle b. Rectangle c. Rectangle

9. a. Horizontal: Vertical:

b. Horizontal: Vertical:

c. Horizontal: Vertical:

Challenge 1. Two possible cross section areas can be 40 cm2 and 200 cm2

2. Figures may vary. Sample figures: 15; Front Top Side

Worksheet 6: Case Study

1. cuboid

2. 6, 8, 12

3. b

4. Top view Front view

Chapter 14

Worksheet 1

1. a. Unlikely b. Equally likely c. Impossible d. Likely e. Sure 2. a. Equally likely b. Sure c. Unlikely d. Impossible 3. a. Impossible b. Equally likely

Challenge 1. Answers may vary. Sample answers: a. Wearing a mask due to increasing pollution b. Travelling to the moon

c. Christmas falls in the month of January. d. Sun sets in the west.

Worksheet 2

1. a. 8 b. 4, 5, 6, 7, 8 c. 4 d. 4 2. 25 26 3. a. 1 50 b. 49 50 4. a. 1 3 b. 1 6 c. 1 2 d. 1 2 e. 1 f. 0

Challenge 1. Error: He included the number 3 also whereas the numbers are 1 and 2 only; 1 5

Worksheet 3

1. 7 20, 7 40, 11 40, 1 5 2. 6 25, 1 5, 3 10, 13 50

3. a. 7 50 b. 12 25 c. 13 25 d. 7 25 e. 0 f. 21 25

4. Answer may vary. Sample answer: A coin was tossed 20 times. Heads turned up 10 times on the coin. What is the theoretical and experimental probability of the coin turning up heads?

Challenge 1. 560 students

Worksheet 4: Chapter Checkup

1. a. Impossible b. Sure 2. a. Sure b. Impossible

c. Likely 3. a. Equally likely b. Unlikely c. Impossible d. Impossible 4. 3 7 5. a. 1 4 b. 3 8 c. 5 8 d. 1 8

6. a. 1 2 b. 1 5 c. 7 10 d. 4 5 e. 0 f. 1 7. 6 30 or 1 5 8. 4 times

Challenge 1. a 2. c

Worksheet 5: Case Study

1. c 2. c 3. 13 27 4. 5 9

About the Book

Perfect Mathematics workbooks are aligned with the latest NCERT textbooks and are NCF 2023 compliant. Aligned with NEP 2020, this workbook bridges abstract concepts to real-world applications by offering questions that enhance a child's mathematical skills. The workbook has hundreds of practice questions, ample writing space for clear responses and a variety of question types. Perfect Mathematics workbooks also provides a mental maths worksheet for each chapter for Grades 1 to 5. This book supports learners at all levels, providing opportunities to build critical thinking skills through questions and activities aligned with Bloom’s Taxonomy. For those seeking a greater challenge, the workbook includes thought-provoking higher order questions that push learners to apply, analyse and evaluate their concept knowledge.

Key Features

• Curriculum Alignment: Aligned with the lates NCERT textbooks and educational standards such as the NCF 2023.

• Mental Maths: In-built mental maths worksheets for Grades 1 to 5 to help students improve their ability to perform calculations rapidly without relying on calculators or written methods.

• Practice Questions: A wide variety of practice questions to reinforce concepts.

• Question Types: Includes a variety of question types like Fill in the Blanks, True or False, MCQs, and Short and Long answer questions.

• Challenge: Critical thinking questions to enhance problem-solving and analytical thinking skills. Higher order thinking questions in the form of assertive reasoning and data sufficiency questions.

• Case Study: Scenario-based questions to apply theory to real-life situations.

• Answer Key: Answers to all the questions at the end of the book.

• QR Codes: Digital integration through the Uolo app to promote self-learning and practice.

About Uolo

Uolo partners with K-12 schools to provide technology-enabled learning programs. We believe that pedagogy and technology must come together to deliver scalable learning experiences that generate measurable outcomes. Uolo is trusted by over 15,000+ schools across India, Southeast Asia and the Middle East.

ISBN 978-81-982034-2-7