Perfect
MATHEMATICS Workbook
Grade 8
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
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© Uolo EdTech Private Limited
First impression 2025
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Book Title: Perfect Mathematics Workbook 8
ISBN: 978-81-982034-4-1
Published by Uolo EdTech Private Limited
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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
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.
Worksheet 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)?
Study
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
d A is false but R is true
Rational Numbers
2 Find the additive inverse of the rational numbers.
4 Name the property illustrated through each of the operations.
c a b - 0 = a b
5 Fill in the blanks using the properties of rational numbers. Also name the property used.
6 Verify the following.
7 Simplify:
8 In the 2024-25 Union Budget of India, around 1 5 of the total budget was allocated to urban development while around 11 200 of the total budget was allocated to rural development. What was the fraction of the total budget allocated to both urban and rural development?
9 A carpenter bought a piece of wood 12 2 3 feet long. He then cut off 5 8 feet from both ends. How long is the piece of wood now?
1 Find the rational number that must be added and subtracted to take the sum of 8 9 + 5 37 6 to the nearest whole number.
2 A school prepared 25.5 litres of juice for its players. The players drank 8 2 5 litres in the first half. In the second half, the players drank 2 3 8 litres more than in the first half. What was the volume of the juice left at the end?
Worksheet 2: Aligned to NCERT Topic/s:
Properties of Rational Numbers
3 Fill in the blanks.
×= 3 2 1 8
4 If a = 5 4 , b = 3 8 and c = 7 12 then verify
5 Fill in the blanks using the properties of rational numbers. Also name the property used. a 5 9 × = 5 9
6 Use the distributive property of multiplication over addition/subtraction and solve the following.
7 Simplify and find the multiplicative inverse of the answer.
8 If the product of two rational numbers is 28 3 and one of them is −17 6 , find the other. Also find the multiplicative inverse of the result.
9 The Independence Hall is a historic civic building in Philadelphia, where both the Declaration of Independence and the Constitution of the United States were debated and adopted. Its base is square in shape. Each side of the hall is around 163 5 m in length. What is the area of the base of the Independence Hall?
10 A ribbon of length 357 8 m has been cut into 24 equal pieces. What is the length of each piece?
11 During the summer holidays, Mansi read a book. After reading 5 8 of the book, 120 pages were left. How many pages are there in the book? Do you like reading books?
1 The quotient that you get on dividing the reciprocal of the product of –2 5 and 15 18 by the product is the multiplicative identity. Is the above statement true? Solve to show your answer.
Worksheet 3: Chapter Checkup
1 Fill in the blanks.
a The sum of a rational number and its additive inverse is .
b The reciprocal of a negative rational number is
c The rational number does not have any reciprocal.
d Adding to a rational number gives the rational number itself.
2 Solve and find the multiplicative inverse of the answer. a −2 5 + 7 6
3 Find the area of a triangle with a base of 156 5 m and a height of 191 2 m.
4 If m = −3 6 , n = 1 5 and o = 8 10 then verify:
a m ÷ (n ÷ o) ≠ (m ÷ n) ÷ o b m × (n + o) = m × n + m × o
5 The sum of two rational numbers is − 8 5 . If one of the numbers is 9 17 , find the other.
6 Which rational number should be subtracted from 12 7 to get
7 Find (m + n) ÷ (m − n), where m = 5 6 and n = −8 9 .
8 Simplify.
9 One roll of ribbon is 15 2 3 m long. What is the length of 5 full and one-fourth of such rolls?
10 Nikita distributed 52 1 4 kg of rice equally among 11 families. How much rice did each family get?
11 Gross domestic product (GDP) is the total monetary or market value of all the finished goods and services produced within a country's borders in a specific time period. Japan's GDP was around 21 5 trillion dollars while India’s GDP was around 677 200 trillion dollars in 2022. Which country had a greater GDP and by how much?
12 Richa ate 1 3 4 pizza, Alex ate 5 6 more pizza than Richa and Prince ate 1 1 2 times what Richa ate. How much pizza did they eat together?
13 Shilpa had ₹750. She spent 2 5 of the money on purchasing a book and 4 9 of the remaining amount on stationery.
How much money was left with her?
14 Create a word problem on division of rational numbers.
Challenge Critical Thinking
1 Instead of multiplying a number by 3 5 , Ronita divided it by 3 5 If the difference of the wrong and the correct answer is 80, then find the number.
2 Read the statements and choose the correct option.
Assertion (A): The sum of –3 5 and –4 7 will be positive.
Reason (R): The product of two negative rational numbers is positive.
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 of A.
d Both A and R are true, but R is not the correct explanation of A.
Worksheet 4: Case Study
Mr Sharma's Grocery Initiative
Mr Sharma is opening a new grocery store. Before opening the store, he did some market research and found that the people in his locality use rice more than wheat. He also came to know that people in the locality use corn as well. He went to the wholesaler and ordered 24 bags of rice, 10 bags of wheat and 4 bags of corn. When he weighed the bags, the weight of each bag came out as shown below.
1 What is the total weight of wheat bought by Mr Sharma?
2 How much more rice (in kg) has he bought than wheat?
47 kg
48 kg
49 kg
50 kg
3 If all the four bags of corn were sold out in 10 days as each family in the locality purchased 1 2 kg of corn, how many families purchased corn?
37 families
111 families
4 Corn was sold at ₹135 per kg and the cost price of one bag was ₹1850. What was the profit earned by Mr Sharma on selling all the four bags?
5 For every kg of rice that Mr Sharma sells, he donates 100 g of rice to the orphanage in his locality. How much rice did he donate, if he sold 15 bags of rice?
Linear Equations in One Variable
1 Find the value of x using the balancing method.
2 Draw a rough diagram of a weighing scale to show the equation 3x + 5 = 9.
3 Find the value of x using the transposition method.
4 Find two consecutive even integers so that two-fifths of the smaller number exceeds two-elevenths of the larger number by 4.
5 One number is 3 times the other number. If 15 were to be added to both the numbers, then one of the new numbers becomes twice the other new number. Find the numbers.
6 The length of a rectangular field is 7 less than twice its breadth. The perimeter of the rectangle is 196 m. Find the area of the field.
7 Solve for the value of x
8 The rectangles are identical. What is the combined area of the rectangles in square units?
9 Write 3 equations that have x = 5 as the solution.
1 A two-digit number is greater than 20 but less than 30. The sum of the digits is the same as their product. What is the number?
Worksheet 2: Aligned to NCERT Topic/s:
2.3 Reducing Equations to Simpler Form
1 Write YES if the correct solutions are given for the linear equations, else write NO. a x = 2 for 5x 3x – 1 = 3 b x = 6 for 7 x + 1 = 5 x – 1
2 Find the value of x using the cross-multiplication method.
3 Do as directed.
4 The numerator of a fraction is 3 less than the denominator. If the numerator and the denominator both are decreased by 2 then the simplest form of the fraction becomes 3 4 . What is the fraction?
5 The denominator of a fraction is less than its numerator by 6. If both the numerator and the denominator are decreased by 3 then the fraction obtained is 5 3 in its simplest form. Find the original fraction.
Challenge
1 Solve the values of the variables to decode the postal code: 2abc5d.
a=1 1 7273 a a b += 26734 43 bb c -+ = 1144317 54 cc d= + 97 29 7331 d d
Which of the statements is/are true about the postal code in the above question?
Statement 1: The third digit of the postal code is one more than the second digit.
Statement 2: All the digits of the postal code are prime numbers.
Statement 3: The last digit of the postal code is twice the first digit.
Statement 4: The difference of the fourth and sixth digit is the fifth digit of the postal code.
Critical Thinking
Worksheet 3: Application of Linear Equations
1 Form the equation for the cases given.
a Thrice x added to 5 is equal to the difference of half of x and 13.
b The sum of four times y and 11 is equal to the sum of two times y and 56.
c The sum of three consecutive even numbers is 144.
d A train travels from point A to point B, a distance of 240 miles. On the return trip, the train’s speed is increased by 20 mph and takes 2 hours less.
2 The sum of four consecutive odd numbers is 352. What are the numbers?
3 The sum of three consecutive multiples of 11 is 429. What are the numbers?
4 The angles of a triangle are in the ratio 3:4:5. What is the difference between the largest angle and the smallest angle?
5 Puneet’s age is three times the age of his daughter. If the sum of their ages is 52 years, find the difference of their ages.
6 Virat scores 20 more runs than twice the number of runs scored by Rohit. Together, their total is four runs short of a triple century. What are the individual scores of Virat and Rohit, respectively?
7 Animesh left one-half of his property to his daughter, one-third of his property to his son and donated the rest of his property. If the donation was worth ₹5,00,000 then how much did he give to his daughter and son?
8 The Prelims of IBPS PO exam has 100 marks. For each correct answer, x marks are awarded and for each incorrect answer, one-fourth of a correct answer’s marks will be deducted and 0 marks are awarded for questions not attempted. Rashmi attempted 78 questions out of which 56 are correct. What is the value of x if Rashmi scored 50.5 marks?
Challenge
Critical Thinking
1 A sum of ₹870 is made up of denominations of ₹5 and ₹10. If the total number of notes is 92 then find the number of notes of each denomination.
Worksheet 4: Chapter Checkup
1 Find the value of x a b
2 Draw a rough diagram of a weighing balance to show the equation 2x + 5 = 11.
3 Solve using the transposition method.
a 5(x + 3) = 3(1.5x + 18)
b 6(2x + 11) = 8(2x – 1)
4 Find the value of x using the cross-multiplication method.
a = + 39 2(2)10 x x b ++ = +4(2)327 23(1)17 x xx
c ++ = 5114(6) 2326 xx
d ++= 4(3)4 31 58 xx
5 Place the correct mathematical operations (+, –, ×, ÷) so that the equations are true.
a 2x 3 = 7 for x = 2
b 3(x 1) 4x = 46 for x = 7
6 If you subtract 1 2 from a number and multiply the result by 1 3 then you get 1 15 . What is the number?
7 The perimeter of a rectangular swimming pool is 170 m. If the length of the pool is 4 m more than the breadth of the pool, what is the area of the pool?
8 Vikram took goats to the field. Half of the goats were grazing. Three-fourths of the remaining goats were playing nearby. The remaining 15 were drinking water from the pond. How many goats were there in total?
9 ₹x is to be divided among three friends A, B, and C. The share of A is two-fifths of the total amount, the share of B is two-thirds of the remaining amount and C’s share is ₹600. What is the value of x?
10 The ratio of the speed of a boat to the stream is 7:2. The boat takes 6 hours more travelling upstream than downstream. What is the time taken by the boat for the entire journey?
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)?
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
d A is false but R is true
Worksheet 5: Case Study
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.
1 The amount (x) paid by a customer travelling a distance of 12 km by cab in city A can be given as: a 10 + d = 12x b 10 × d + 12 = x c 10 × 12 + d = x d 10 × x + 12 = d
2 What is the fixed charge for cab services if Neha paid ₹150 for travelling a distance of 11 km in city A? a ₹30 b ₹40
3 What is the per km charge for bikes in city A if Suhani paid ₹45 for travelling a distance of 5 km? a ₹4/km b ₹5/km c ₹6/km d ₹9/km
4 Rahul and Megha wanted to reach the museum in city B. They both live 6 km far from the museum. Rahul took a bike service and paid ₹57 while Megha took an auto and paid ₹76. What is the difference in the per km charge of auto and bike services in city B?
5 Is the given statement true or false? Give your answer with reasons. (Hint: Use the fixed charges as calculated in Q2.) Shalini will pay ₹127 if she travels 7 km via cab in city B.
6 What safety measures should you take while travelling in cabs?
Understanding Quadrilaterals
Worksheet 1: Aligned to NCERT Topic/s:
3.1.1 Convex and concave polygons
3.1.2 Regular and irregular polygons
1 Fill in the blanks.
a A polygon with 7 sides is called a
b The number of diagonals in a hexagon are
c A polygon with all sides and angles equal is called a
2 Write True or False.
a A triangle is a convex polygon.
b The number of diagonals in an octagon is 7.
c A circle is an example of a 2-D geometrical shape that is not a polygon.
3 Classify the following as convex or concave polygons based on the angles of the polygons.
a 65º, 115º, 111º, 70º, 179º b 176º, 105º, 110º, 66º, 195º, 165º, 83º
4 Classify the polygons as concave or convex. a b c d
5 A polygon has 6 sides, and all the angles in the polygon measure 120°. Is this a convex or concave polygon?
6 Use the formula to find the number of diagonals in polygons with the number of sides given. Name the polygon. a 4 sides b 8 sides
7 In a regular octagon, how many diagonals can be drawn from one vertex?
8 How many non-overlapping triangles can we make in a polygon with 5 sides by joining the vertices?
9 Draw a figure made up of 4 polygons with 2 being convex and 2 being concave polygons.
Challenge
1 3 squares are joined to form an L shaped figure. Will the new polygons formed be concave or convex? How many diagonals will the new polygon have?
1 Draw quadrilaterals for each of the given conditions such that:
a Only points A, B and C are in the interior.
b Only points B, C and D are in the interior.
c Only points B, F and E are in the interior.
2 Classify the following as convex or concave quadrilaterals based on the angles of the quadrilateral.
a 190o, 60o, 30o, 80o
b 65o, 115o, 111o, 69o
c 26o, 226o, 30o, 78o
3 Find the value of x and y in the figure shown below.
133° (2y + 7)° (5x − 2)°
4 The length of a parallelogram is 15 cm longer than its breadth. If the perimeter of the parallelogram is 130 cm, find the length and breadth of the parallelogram.
5 WXYZ is a parallelogram where two adjacent angles have a ratio of 2:4. Calculate the measures of all the angles in the parallelogram. Challenge
1 PQRS is a rhombus whose diagonals intersect at Z. Draw a rough diagram and answer the questions given below.
a Name any four pairs of line segments that are equal in length.
b Name any four pairs of angles that are equal in measure.
c Identify three pairs of congruent triangles in this rhombus.
d Is ∠QRZ = ∠ZRS?
e Is ΔQPZ ≅ΔSPZ?
Worksheet 3: Aligned to NCERT Topic/s:
3.2 Sum of the Measures of the Exterior Angles of a Polygon
1 Fill in the blanks.
a The sum of the interior angles in a quadrilateral is .
b Each interior angle of a regular hexagon is .
c The polygon in which the sum of all exterior angles is equal to the sum of interior angles is called a
d The measure of each exterior angle of a regular polygon of 18 sides is .
2 Write True or False.
a The sum of all exterior angles of a polygon is always 360°.
b The number of triangles that can be formed within a polygon with n sides is n.
c The sum of the interior angles of a triangle is 270°.
d It is possible to have a regular polygon where each exterior angle is the right angle.
3 Find the measure of each exterior angle of a regular polygon with:
a 3 sides
b 8 sides
4 Find the interior angle sum of the given polygons.
c 12 sides
a b c
5 Find the value of the unknown angle in each of the following.
6 What could be the value of the unknown exterior angle in each case?
7 Find the number of sides of a regular polygon if each of its exterior angles measures:
8 The measures of the exterior angles of a hexagon are (3x – 4)°, (x + 4)°, (7x – 3)°, (8x – 1)°, (2x + 3)° and (9x + 1)°. Find the measure of each angle.
1 Rahul pins four nails to a soft wooden board. He then proceeds to tie threads between these nails so that they form a quadrilateral. The total length of thread used is 12 cm. The angles of this quadrilateral are in the ratio 1:2:3:4. Is the quadrilateral formed by the threads convex or concave? Find the measure of the largest angle?
Worksheet 4: Chapter Checkup
1 Fill in the blanks.
a A polygon with unequal sides and unequal angles is called an .
b The sum of the interior angles of a hexagon is
c The number of diagonals in a pentagon is .
d The sum of the exterior angles of any polygon is always
2 State whether the following statements are true or false.
a The diagonals of a kite bisect each other at right angles.
b The diagonals of an isosceles trapezium are equal.
c The diagonals of a rectangle are perpendicular to each other.
d All quadrilaterals are parallelograms.
3 Which of the interior angles given below would not belong to a convex quadrilateral? a 100° b 178° c 222° d 2°
4 Identify the polygons as concave or convex. a b c d
5 How many diagonals will each of these polygons have?
a Convex quadrilateral
b Nonagon
c Polygon with 17 sides
6 Which of the sets of angles given below is a set of interior angles of a quadrilateral?
a 47°, 58°, 98°, 156° b 54°, 59°, 72°, 108° c 83°, 68°, 82°, 127°
7 Find each exterior angle of the regular polygons with the given number of sides.
a 4 b 15 c 20
8 Find the value of the unknown exterior angle in each case.
9 Find the value of the unknown interior angle in each case.
10 In a parallelogram, the adjacent angles are (2z - 25)º and (3z + 10)º. Determine the measures of all four angles in the parallelogram.
11 The angles of a pentagon measure x°, (x - 5)°, (x + 15)°, (3x - 44)° and (x - 70)°. Find x
12 Find the values of wº, xº, yº and zº.
13 Sohan is designing a logo for his company which is in the shape of a regular 12-sided polygon. How many diagonals connect the interior angles of the polygon? How many triangles can be formed by connecting these interior angles?
14 In a city with several towns connected by bridges, there are 10 towns. If each town is connected to its adjacent town by a direct bridge, how many bridges are needed in total? How many diagonals does this network of bridges have?
1 Read the statements and choose the correct option.
Assertion (A): The sum of the interior angles of any polygon is given by the formula (n – 2) × 180°, where n is the number of sides.
Reason (R): A polygon can be divided into n – 2 triangles.
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 Consider a quadrilateral PQRS. If PQ is parallel to RS and PS is parallel to QR, which of the following statements is sufficient to prove that quadrilateral PQRS is a square?
Statement 1: ∠PQR = ∠SPQ = 90°
Statement 2: PQ = QR
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 Either statement alone is sufficient.
d Both statements together are sufficient, but neither statement alone is sufficient.
Worksheet 5: Case Study
Park Renovation Project
Mr Dhawan got a contract to renovate the park in his society. On analysis, he found that he had to tile the paths, build some climbing structures for the children’s play area, add some more sprinklers in the park and also build a small swimming pool at the centre of the park. Answer the questions.
1 The contractor told Mr Dhawan that each interior angle in the tile was 120°. What was the shape of the tile?
2 The park is rectangular in shape and its length and breadth are 160 m and 120 m, respectively. Mr Dhawan planted the sprinklers across the diagonals of the park. If he planted each sprinkler at a distance of 5 m then how many sprinklers did he plant across each diagonal?
3 The climbing structure was made of 4 bars forming a quadrilateral shape. The angles at the corners are measured and found to be in the ratio 2:3:4:5. Determine whether the climbing structure is a parallelogram.
4 The swimming pool that was built at the centre of the park had opposite sides parallel and equal in length. What was the shape of the swimming pool?
5 What more do you think Mr Dhawan can do to make the park useful and clean? How do you keep the park in your neighbourhood clean?
Data Handling
Worksheet 1: Aligned to NCERT Topic/s: 4.1 Looking for Information (Bar Graph)
1 Refer to the bar graph on the wheat exported by India to different countries and answer the questions.
a What percentage of the total exports was exported to Sri Lanka?
b What percentage of the total exports was exported to Afghanistan?
c What was the ratio of the wheat exported to Qatar to that exported to the Yemen Republic?
d What is the average quantity of wheat exported to these 5 nations?
2 Refer to the bar graph shown and answer the questions.
a What percentage of the total books were sold on Friday?
b What percentage of the total books were sold on Saturday?
c What is the ratio of the number of books sold on Thursday to the number of books sold on Friday? Day
d What is the ratio of the number of books that is less than the average number of books sold and the number of books that is more than the average number of books sold?
3 The data shows the export of pears in different years. Draw a bar graph for the given data and answer the questions.
a What was the total value of exports in all the years?
b What was the average export value of pears for the given period of time?
c What was the percentage increase in 2018 from 2015?
d Which two years have an average export value of ₹17.1 crores?
4 The bar graph shows the number of students who passed an examination. The total number of students in the school was 450 every year. Read the bar graph and answer the questions.
a How many students passed in 2021?
b What percentage of the students passed in 2018?
c What percentage of the students passed in 2020?
d Create a question not covered here based on the same bar graph.
5 The bar graph shows the approximate populations of different cities in the world. Read the bar graph and answer the questions.
a What is the total population of Delhi and Mumbai?
b What is the difference in the populations of Shanghai and Cairo?
c What is the average population of the six cities?
d What is the difference in the populations of Moscow and New York? Challenge
1 The teacher asked the students to collect information on the life spans of various animals. The students found the following information:
One student wants to show the results using a bar graph. Give one reason why a bar graph is not a good choice for showing this information. If we calculate the average ages of the lifespans of the animals, can we plot a bar graph? If yes, construct a bar graph for the new data.
Worksheet 2: Aligned to NCERT Topic/s: 4.1 Looking for Information (Double Bar Graph)
1 Refer to the double bar graph shown for the export of various products in the years 2021 and 2022 and answer the given questions.
a What was the percentage increase in the exports of basmati rice?
b Which product has the least exports?
c What were the total exports for the year 2021?
2 Refer to the bar graph and answer the questions.
d What were the total exports for the year 2022?
a What is the total production of tea by Company C in three years?
b What is the ratio of the tea produced by Company B in 2015 and 2016 to the total tea production by company D in three years?
c What was the percentage increase in tea production by Company D from 2016 to 2017?
d What was the percentage increase in tea production by Company B from 2015 to 2017?
3 The table below shows the test scores of two students, Ayesha and Ravi, over five subjects. Draw a double bar graph to compare their scores.
Draw a double bar graph to represent the data.
4 The double bar graph shows the runs scored by Virat Kohli and Rohit Sharma in different years. Read the bar graph and answer the questions.
x y Scale: 1 division = 200 runs
a How many runs were scored in total by Virat Kohli in the given years?
Virat Kohli Rohit Sharma
b How many runs were scored in total by Rohit Sharma in the given years?
c What is the difference in the average number of runs scored by Virat Kohli and Rohit Sharma?
d What is the ratio of the runs scored by Virat Kohli before 2017 to the runs scored by Rohit Sharma after 2015?
1 The double bar graph shows the number of film tickets sold by two different cinema halls for different genres of films. Which of the given statements is correct?
Statement 1: The ratio of sci-fi genre tickets sold by Cinema Hall 1 to Cinema Hall 2 is 8:9.
Statement 2: Cinema Hall 2 sold 25% more horror film tickets than Cinema Hall 1.
Statement 3: Cinema Hall 2 sold 60% less drama film tickets than Cinema Hall 1.
a Only Statement 2 is correct.
b Statements 1 and 3 are correct.
c Statements 2 and 3 are correct.
d All statements are correct.
Worksheet 3: Aligned to NCERT Topic/s:
4.2 Circle Graph or Pie Chart
1 There are 1200 residents in a society, of which 375 people know more than three languages. What would be the central angle representing people who know more than three languages?
2 If 45% of the total number of people like biryani, what would be the central angle representing this data?
3 Draw a pie chart for the data of workers from various states working at a garment factory. State Karnataka Tamil Nadu Andra Pradesh Kerala Others
4 Construct a pie chart to display the percentages of purchasers for different clothing brands.
5 The table shows the approximate number of lions in 5 countries. Create a pie chart to show the data.
Country Mozambique Botswana Angola Malawi Kenya
Challenge
1 A sports fest was to be organised in a school. The sports organisation was allotted a budget. The spendings on 5 different sports by the school are represented using ratios.
Football : Cricket = 2 : 3
Cricket : Badminton = 3 : 1
Football : Volleyball = 4 : 5
Volleyball : Basketball = 5 : 3
Represent the given data in a pie chart using degrees.
Worksheet 4: 4.2 Circle Graph or Pie Chart
1 The pie chart shows the number of students admitted to different college faculties. If the total number of students is 5 lakhs, find the number of students admitted to each faculty.
2 Read the pie chart on the cars sold by a showroom in a year and answer the given questions if the number of type C cars sold was 500.
a What was the total number of cars sold?
b What was the number of type D cars sold?
c How many Type A and Type B cars were sold altogether?
3 Read the pie chart showing the number of animals in a zoo and answer the questions if there are 77 elephants in the zoo.
a What is the total number of animals in the zoo?
b Which animal has the lowest number, and how much?
c What is the difference of the numbers of deer and reptiles?
4 Manya surveyed some teenagers in her city about their favourite music. 255 teenagers like classical music. Read the chart and answer the questions.
a How many teenagers were surveyed?
b What is the ratio of teenagers who like rock music to those who like hip-hop?
5 The pie chart shows the approximate percentage consumption of different energy forms in India. Read the pie chart and answer the given questions.
a Which is the most consumed form of energy?
b What is the ratio of consumption of Nuclear to the consumption of Renewable energy?
c What is the fraction of the energy consumed by Hydropower and Natural gas?
6 Create two questions on the pie chart given in Q5.
1 A company collects 60,000 tonnes of recyclable material every month. The pie charts shown below give the details of the kinds of materials collected in June and July.
a What is the difference of the central angles for glass in the two months?
b How many tonnes of paper were collected in both months together?
c In which month was more plastic collected, and by how much?
d What is the percentage change in the cardboard collection in the two months?
Worksheet 5: Aligned to NCERT Topic/s:
4.3 Chance and Probability (Theoretical)
1 Fill in the blanks.
a The probability of an event having no chance of occurring is (0/1).
b The probability of a sure event is (0/1).
c The possible outcomes when you toss a coin are and
d On rolling a dice, the event of getting a prime number has possible outcomes.
2 A glass jar contains 40 marbles in different colours such as black, green, blue and yellow. The probability of drawing a single green marble is 1 5 What does this mean?
a There are 5 green marbles in the glass jar.
b There are 8 green marbles in the glass jar.
c There are 10 green marbles in the glass jar.
d There is only one green marble in the glass jar.
3 Each letter of the alphabet is printed on an index card. What is the theoretical probability of randomly choosing any letter except Z?
4 Neeta is playing a game using a fair coin. Contestants win the game if the coin lands tails up.
a What is the theoretical probability that the coin will land tails up?
b If 250 contestants play the game, about how many of them are expected to win?
5 Amit rolls a six-sided dice labelled 1 to 6.
a Find the probability of rolling a 4.
b Find the probability of rolling an odd number.
6 A game board has a spinner with 10 equal-sized sections, of which 4 are green, 3 are blue, 2 are yellow and 1 is black. What is the sum of the probabilities of the pointer landing in the green, blue, yellow and black sections?
7 A 12-sided solid has equal-sized faces numbered 1 to 12.
a Find the probability of getting a number greater than 10.
b Find the probability of getting a number less than 5.
8 Write 2 events based on the situation given in Q7. Write their theoretical probability.
Challenge
Critical Thinking
1 Navin is getting dressed. He considers two different shirts, three pairs of pants and three pairs of shoes. He chooses one of each of the articles at random.
Shirts
Collared shirt
T-shirt
a How many different outfits are possible?
Pants
Khakis
Jeans
Capris
b What is the probability that he will wear his jeans but not his sneakers?
Shoes
Sneakers
Flip-flops
Sandals
Worksheet 6: Aligned to NCERT Topic/s:
4.3 Chance and Probability (Experimental Probability)
1 Which of the following are examples of a random experiment?
a Tossing a coin
b Drawing a black card from a deck of playing cards
c Throwing a ball
d Rolling two dice together
2 To play a game, you spin the spinner shown. You win if the arrow lands in one of the areas marked ‘WIN’. Leena played this game many times and recorded her results. She won 8 times and lost 40 times. Use Leena’s data to find the experimental probability of winning this game.
3 During a 24-hour period, the ratio of pop songs to rap songs played on a radio station is 60:75.
a What is the experimental probability that the next song played will be a rap song?
b Out of the next 90 songs, how many would you expect to be pop songs?
4 A board game uses a bag of 105 lettered tiles. You randomly choose a tile and then return it to the bag. The table shows the number of vowels and the number of consonants after 50 draws.Predict the number of vowels in the bag.
Vowel Consonant 30 times 20 times
5 The Venn diagram shows two sports played by 90 Grade 8 students. What is the probability that a randomly chosen student plays:
a both tennis and squash?
c tennis?
b neither tennis nor squash?
d tennis or squash, but not both?
6 We held a survey of all the students in our school to find out how many own a mobile phone. The results are shown in the two-way table.
Owns a mobile phone Does not own a mobile phone
If we choose a student at random, what is the probability that the student:
a owns a mobile phone?
c is a boy who owns a mobile phone?
b does not own a mobile phone?
d is a girl who does not own a mobile phone?
Challenge Critical Thinking
1 The table shows the result of flipping two coins. Read the statements and choose the correct option.
Assertion (A): The experimental probability of getting two tails is 11 50 .
Reason (R): Experimental probability of an event = Number of times the event occurs Total number of trials
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 false.
d A is false, but R is true.
Worksheet 7: Chapter Checkup
1
The graph shows the percentage break up of sales of units of different products in 2020. Read the bar graph and answer the questions. The total number of units sold by the company was 5,20,000.
a How many units of Product A were sold?
b How many units of Product C were sold?
c What is the difference in the number of units of Product B and units of Product D sold?
d What is the ratio of the units of Product A and units of product C sold?
2 The data shows the number of students of two different schools who participated in different activities at a function. Draw a bar graph to represent the given information.
3 The bar graph shows the cars sold by two different dealers Read the bar graph and answer the questions.
a How many cars were sold by Dealer A in total?
b How many cars were sold by Dealer B in total?
c What is the ratio of the cars sold in 2019 to those sold in 2022?
d What percent of the total number of cars sold by Dealer A were sold in 2018?
4 Mark the central angles in the pie charts shown below.
Items Sold
Others, 36 Rice, 158 Pulses, 67 Spices, 45 Bread, 54
Items Sold
Sandwiches, 80 Burgers, 72
French fries, 54 Ice creams, 64 Shakes, 90
5 Draw a pie chart for the given data showing the types of pets owned by the families in a locality.
6 Draw a pie chart for the given data showing the types of books read by people in a town.
7 The pie chart shows the sales at a stationery shop in a month.
a Which is the most popular item in the store?
b What is the fraction of the notebooks sold in the month?
c What is the percentage of the party supplies sold at the shop?
8 The pie chart shows the percentages of ice creams sold by a vendor in 5 days. If the vendor sold 198 ice creams on Wednesday, then find the total number of ice creams sold in 5 days.
9 Fill in the blanks.
a The probability of an event that is sure to happen is .
b If an event cannot occur, then its probability is
c The probability of selecting P from the word ‘SPECIAL’ is .
d The probability of an event can’t be more than .
e If a dice is rolled once, the probability of getting an even prime number is
10 Sneha draws a card at random from the cards given. What is the probability of drawing a card that shows a shape with: triangle circle rhombus Square rectangle hexagon pentagon octagon
a only three sides?
c more than four sides?
b only four sides?
d no sides?
11 200 apples are packed in a carton out of which 30 apples are rotten. If one apple is taken out from the carton at random, find the probability of getting a:
a good apple.
b rotten apple.
1 Read the statements and choose the correct option.
Assertion (A): The given pie chart shows the spending of a country on various sports during a particular year. If the total amount spent on sports during the year is ₹3,60,00,000, the amount spent on Basketball exceeds the amount spent on Tennis by ₹5,00,000.
Reason (R): The amount spent on each sport is given as
Central angle of sector 360° × Total amount spent
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 A is not true but R is true.
2 Statement: 300 marbles are placed in a jar, of which 50 are blue. One marble is drawn from the jar at random.
Conclusion I: The probability of drawing a blue marble is one-sixth.
Conclusion II: The probability of drawing a non-blue marble is 80%.
Which of the following conclusions follow?
a Only conclusion I follows b Only conclusion II follows
c Either I or II follows
d Neither I nor II follows
Worksheet 8: Case Study
COVID-19: Health Metrics and Pandemic Response
You are a health analyst reviewing data from a health department about the COVID-19 pandemic. The data shown in the pie chart represents the age distribution aspect and case severity aspect of the pandemic in India. The case severity of the patients was proportionate for all ages.
Under 18 years
18 years – 40 years
40 years – 60 years
60+ years
Answer the following questions based on the data. (The data is collected for 2,00,000 people)
1 How many patients were aged between 18 years and 60 years? a 80,000 b 60,000 c 1,40,000 d 1,80,000
2 How many patients above 60 years had moderate symptoms?
3 Find the number of patients who had severe symptoms and were aged less than 18 years.
4 Calculate the number of COVID-19 patients between 18 years and 60 years with mid symptoms?
Squares and Square Ro ts
1 Look at the digits in the units place of each of the given numbers. Answer the given questions.
i What will be the units digits of the squares of the numbers?
ii Which of the numbers will have odd or even squares?
2 Show the square of the numbers 5 and 7 using a square grid.
3 Find the square of the numbers.
4 Find the squares of the given numbers using the distributive property.
5 Express the numbers as the sum of odd numbers.
676
6 List all the triangular numbers between 20 and 50. Express them as square numbers.
7 Find the difference of the squares of the consecutive numbers. How many non-perfect squares are there between the squares? a 12, 13 b 20, 21
17, 18
8 Express the squares of the given odd numbers as the sum of two consecutive numbers.
57
9 Evaluate.
752
10 Find using the (a + b) (a − b) rule.
75 × 77
63
77
512 – 502
952
64 × 68
11 Find a Pythagorean triplet whose smallest member is given below.
50 × 52
12 Observe the pattern.
Write the missing numbers.
42 = 16
342 = 1156
3342 = 111556
33342 = 1 5 6
333342 = 2 = 111111555556
14 Without adding, find the sum.
13
15
13 Observe the pattern. Fill in the missing digits. 92 = 81
992 = 9801
9992 = 998001
99992 = 99980001
999992 = 9 _ _ _ 8 _ _ _ _ 1
9999992 =
1
15 Shreya made the pattern using stickers of circles. Look at the pattern and answer the questions.
a How would you express each square pattern as a square of a number? Write the rule.
b Find the rule of the pattern up to the 6th term.
c Use the rule to find the value of 562
1 Create a list of four different Pythagorean triplets.
Worksheet 2: Aligned to NCERT Topic/s: 5.5 Square Roots
1 What could be the units digit of the square root of the numbers? a 1369
3136 c 5184 d 8281 e 9604
2 Draw a square with an area of 16 square units. What is the length of each side?
3 Find the square root of the numbers using successive subtraction.
144
36
441
4 Check if the given numbers are perfect squares using prime factorisation. Also, find the number whose square is the number given.
6545
9054
7396
5 Find the square root of the numbers using prime factorisation. a 6561 b 8836 c 20,164
6 For each of the numbers, find the smallest number by which it should be multiplied to get a perfect square. Also, find the square root of the square number.
7 Find the smallest square number that is divisible by 6, 9, 12, 16 and 18.
8 The students of a class collected ₹1296 for a COVID relief fund. Each student contributed an amount equal to the number of students in that class. How many students were in the class?
Challenge
1 Five friends—Sheetal, Shyna, Hitesh, Rohit and Hetal, play a number game. Sheetal thinks of a positive integer, which Shyna then doubles. Hitesh triples Shyna’s number, and finally, Hetal multiplies Hitesh’s number by 6. Rohit notices that the sum of these four numbers is a perfect square. What is the smallest number that Sheetal could have thought of?
Worksheet
5.5.4 Finding square root by division method
5.6 Square Roots of Decimals
1 How many digits would be there in the square roots of the numbers (without any calculation)?
2 Find the square root using the long-division method.
3 Find the least number which must be subtracted from each of the numbers to get a perfect square. Also, find the square roots of the perfect squares so obtained.
1456
5243
8912
4 Find the lowest number which must be added to each of the numbers to get a perfect square. Also, find the square roots of the perfect squares so obtained.
5 Find the square roots of the decimal numbers.
6 Simplify. a 256 × 361 b 92.16 + 0.9216
7 Find the longest side of a right angled triangular field with the other two sides of 15 m and 20 m.
1 There are (2217 – x) students in a school. During the assembly meeting, the number of students in each row is equal to the total number of rows. What is the least value of x?
Worksheet 4: Chapter Checkup
1 Find the squares of the given numbers.
2 Find the value of:
452 – 162
3 Express 324 as the sum of odd numbers.
4 Find the Pythagorean triplets whose smallest members are 96 and 24.
5 Which of the numbers are perfect squares? Find their square roots. Verify your answer. a 265 b 2116
6 Find the square roots correct to two decimal places. a 7.8961
b 33.64 × 67.24
7 Find the lowest number, which must be added to 6,57,700 to get a perfect square. Also, find the square root of the perfect square so obtained.
8 The length and breadth of a rectangular room are 26 m and 18 m, respectively. What is the length of the longest straight line that can be drawn on the floor of the room?
1 Is the square root of x greater than 10?
Select the statements which are sufficient to answer the question.
Statement 1: x is greater than 100.
Statement 2: x is smaller than 150.
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 either statement alone is not sufficient.
d Both statements together are not sufficient to answer the question.
2 Read the assertion and the reason to decide which of the following options is correct.
Assertion (A): The square of any positive integer is always greater than the integer itself.
Reason (R): When a number greater than 1 is multiplied by itself, the product is always greater than the original number.
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
Let’s Renovate the Park
A committee decided to renovate the rectangular park in their society. The area of the rectangular park is 9600 sq. m. The length of the park is 160 m. A square recreational zone that will include a children's playground, seating areas, and exercise stations is to be constructed inside the park. The square recreational zone is approximately one-fourth of the total area of the park. The park should have space for a garden that is at least 1200 sq. m.
1 What is the side length of the square recreational zone? a 45
2 A path is built inside the park across the diagonals. What will be the length of the path from one corner to the other? a 20 m
170.88 m c 190.93 m
220 m
3 How much approximate area is left inside the rectangular park after making the square recreational zone?
4 A circular fountain is to be built at the centre of the park. The radius of the fountain is 5.6 m. The fountain is to be tiled from inside. The cost of tiling is ₹9856 per sq. m. What is the total cost of tiling?
5 Do you visit your city parks? What do you do to keep them clean?
Cubes and Cube Ro ts
Worksheet 1: Aligned to NCERT Topic/s: 6.2
Cubes
1 Which of these show the cube of the number 4 and 3? Colour the cubes.
2 Find the cubes of the numbers.
a 15 b 26
3 Look at the digits in the units place of each of the numbers. Answer the questions.
i What will be the digit in the ones place of the cube of each number?
ii Which of the numbers will have odd or even cubes?
iii Which of the numbers are not perfect cubes?
a 1331
b 5800
c 24,387
d 1,25,000
4 Find the cube of the rational numbers.
a 4 7 b − 8 9
5 Find the cube of the decimal numbers. a 2.8
1.2
6 Check if the numbers are perfect cubes using prime factorisation. Also, find the number whose cube is the number. a 2195 b 13,824
7 Find the smallest number by which the number should be multiplied to get the perfect cube. In each case, find the number whose cube is the new number. a 432 b 128
8 What is the least number by which the number should be divided to get the perfect cube? In each case, find the number whose cube is the new number. a 576 b 5145
9 Use the pattern given below to find the values of 113 and 203
• 1 = 1 = 13
• 3 + 5 = 8 = 23
• 7 + 9 + 11 = 27 = 33
• 13 + 15 + 17 + 19 = 64 = 43
10 Use the pattern given below to evaluate the given expressions.
• 13 + 23 = 1 + 8 = 9 and (1 + 2)2 = 32 = 9
• 13 + 23 + 33 = 1 + 8 + 27 = 36 and (1 + 2 + 3)2 = 62 = 36
• 13 + 23 + 33 + 43= 1 + 8 + 27 + 64 = 100 and (1 + 2 + 3 + 4)2 = 102 = 100 a 13 + 23 + 33 + 43 + 53 + 63 + 73 + 83 + 93 b 13
1 Mitali forms a solid, as shown. It is made up of 2 cm cubes. What is the volume of this solid? Can we rearrange the cubes to form a perfect cube? If not, how many more 2 cm cubes will be needed to form a perfect cube?
Worksheet 2: Aligned to NCERT Topic/s:
Cube Roots
1 Shade the side to show the cube root of 216.
2 Find the cube root using prime factorisation.
3 Find the cube root of the numbers using successive subtraction.
4 Find the value of:
5 Find the length of each edge of each given cube if its volume is: a 5,92,704 cu. cm b 85,184 cu. cm
6 Find the smallest number that must be subtracted from each number to make it a perfect cube. Also, find the cube root of the perfect cube obtained. a 408 b 2215
7 Inspired by the Orca statue made from cubes at Canada Place, a sculptor decided to create a structure using cubes for his next project. If the structure has a volume of 74,088 cu. cm, then what is the length of each side?
1 1*28 is a 4-digit number. If the number is a perfect cube, find the missing digit and the cube root of the number.
1 Find the cube of each of the numbers. a 41 b 16 7
2 Shade the figure that shows the cube of a number. Write the number.
3 Which of the following are perfect cubes? Find the number whose cube is the given number. a 8,30,584 b 2,10,000
4 Using patterns, find the value of:
5 Evaluate:
6 Find the length of the edge of the cube if its volume is 2,26,981 cu. m.
7 Find the smallest number that must be subtracted from 2789 to make it a perfect cube. Also, find the cube root of the perfect cube obtained.
8 Find the smallest number that must be added to 4900 to make it a perfect cube. Also, find the cube root of the perfect cube obtained.
9 Look at the solid. The shaded portion of the solid has an area of 147 sq. cm. What is its volume?
1 In a competition, a school decides to award prizes for three values: punctuality, respect and discipline. The numbers of students getting prizes are in the ratio of 2:3:5. If the product of the numbers is 2,05,770, find the number of students getting the prize for each value.
2 A city wants to construct a large water tank in the shape of a cube to store rainwater during drought periods. If they estimate the tank needs to hold 8000 cubic metres of water,
a What should be the dimensions of the cube?
b If they want to install eight such tanks adjacent to each other, what should be the length of the side of the shape thus formed?
Worksheet 4: Case Study
Cubes in Urban Planning
In the city, urban planners are faced with the challenge of designing efficient and aesthetically pleasing public spaces. There's a plan to make a new gathering spot downtown. They want it to be a place where people can gather, sit, and enjoy some greenery.
The design team proposes using concrete to make large cubes. These cubes will serve multiple functions, including seating, planters, and artistic displays. Each cube will have a different edge length.
Answer these questions.
1 How many cubic metres of concrete are needed to construct a cube with an edge length of 1.5 metres?
a 1.875 cubic metres
c 3 cubic metres
b 2.25 cubic metres
d 3.375 cubic metres
2 If a cube proposed as a planter has a volume of 64 cubic metres, what is its edge length?
a 4 metres
c 8 metres
b 6 metres
d 16 metres
3 The volume of a cube with an edge length of 2.5 metres, designed for artistic purposes is cubic metres.
4 A cubical design can accommodate 4 smaller cubes of length 1.8 m each with a volume of cubic metres.
Comparing Quantities
1 Convert the decimals into percentages and the percentages into decimals.
2 Express each of the percentages as a fraction.
4 Answer the questions. a What percentage of 30 is 60?
What percentage of 3 L is 900 mL?
6 Solve the given questions.
a Increase ₹190 by 20%
b Decrease 150 kg by 30%
7 The price of olive oil has increased by 10%. If the original price was ₹250 per litre, find the new price.
8 A number is increased by 30% and then reduced by 20%. Find the net increase or decrease in the number.
Challenge
Critical Thinking
1 A company manufactures smartphones. During quality testing, it is found that 15% of the smartphones are defective. Out of the defective phones, 40% can be repaired and sold at a lower price, whereas the remaining 60% are beyond repair and are scrapped. The company manufactures 10,000 smartphones. Answer the questions.
a How many smartphones are defective?
b How many defective smartphones can be repaired?
1 The marked price of a radio is ₹4000. Find the discount and the selling price if the rate of discount is given.
2 If ₹175 is the discount offered on an article whose marked price is ₹900, then find its selling price.
3 The marked price of a washing machine is ₹14,500 and its selling price is ₹13,775. Find the discount allowed and the discount percentage.
4 The selling price of a dining table is ₹16,000. Find the marked price if a 20% discount is allowed.
5 A pair of trousers was sold for ₹7500 after a discount of ₹500 was offered on it. What was the percentage of the discount?
6 Two successive discounts of 25% and 12% on an article are equivalent to a single discount of x %. What is x?
1 The tickets for a circus are sold at half their regular price. Amit, being an early bird, gets an additional discount of 10% on the reduced price. What is the total discount percentage that Amit gets on the regular price?
Worksheet 3: Aligned to NCERT Topic/s:
7.3 Sales Tax/Value Added Tax/Goods and Services Tax
1 Manohar wants to buy a vacuum cleaner to clean his house that costs ₹8000. What amount should he give to the shopkeeper if the GST on the vacuum cleaner is 18%? Do you help your parents in keeping the house clean? How?
2 Akash bought a computer for ₹38,000 and a printer for ₹8000. If the rate of tax is 7% for these items, find the price he must pay to buy these two items.
3 Renu bought a mobile phone for ₹16,240 that included GST of 12%. Find the price of the mobile phone before the GST was added.
4 The tax charged on a refrigerator is 9%. If the tax amount is ₹1170, find the actual selling price.
5 Ajay sells a harmonium for ₹17,280 including the tax. What is the selling price he will get after depositing the tax to the government at the rate of 8%?
1 During the festive season, a store puts all the shirts at a discount of 20%. Daniel was offered an additional 5% discount on a shirt that had a marked price of ₹2500. He paid a total of ₹2128 including the tax. Find the tax percentage.
Worksheet 4: Aligned to NCERT Topic/s:
7.4 Compound
Interest
1 Find the missing figures in the table.
2 You are considering opening a high-yield savings account at Ally Bank. As of July 2024, Ally Bank offers a simple interest rate of 4.25% per annum. You plan to deposit $20,000. Calculate the interest earned and the total amount after 3 years.
3 A certain amount of money amounts to ₹4400 in two years and ₹4600 in three years. Find the principal and rate of interest.
4 Find the interest on a deposit of ₹3650 from January 3, 2016 at the rate of 10% p.a. up to March 17, 2016.
5 Create a word problem on finding simple interest.
1 A person deposited ₹600 for 3 years, ₹900 for 2 years and ₹1500 for 4 years. He received the total simple interest of ₹360. Find the rate of simple interest per annum.
Worksheet 5: Aligned to NCERT Topic/s:
1 Find the amount and the compound interest on ₹1600 for 5 years at 6% per annum, compounded annually.
2 What sum of money will amount to ₹4410 in 2 years at 5% per annum, compounded annually?
3 In how much time will ₹60,000 amount to ₹69,457.50 at 5% per annum compounded yearly?
4 Suhani invested ₹50,000 at 12% p.a. compounded annually. Find the amount she will get: a at the end of the second year. b at the end of the third year.
5 Find the compound interest on ₹2,00,000 for 18 months at 8% per annum, compounded half yearly.
6 Find the simple interest on ₹2500 for 2 years at 10% per annum. If the bank pays compound interest, compounded annually, what is the difference in the interest earned in both cases?
7 The simple interest on a sum of money for 2 years at 6% per annum is ₹9000. Find the compound interest on that sum at the same rate, compounded yearly, and for the same period.
Challenge Critical Thinking
1 A sum compounded annually becomes 216 125 times of itself in 3 years. Find the rate of interest per annum.
1 Savita deposited ₹8000 in a bank at a rate of 12% per annum. She withdrew the money after 9 months. What is the interest she received? What was the amount she collected from the bank?
2 Kanchan borrowed a sum of money from Sonali at 8% interest per annum. After 4 years, Kanchan had to give Sonali ₹9900 to clear the debt. What was the amount Kanchan borrowed originally?
3 Narendra lent a sum of ₹3200 to Suresh at a rate of 6% interest per annum. Suresh paid Narendra ₹3680 to clear the debt. How long did Suresh use Narendra’s money?
4 Aditya paid ₹6720 to clear a debt of ₹6000 to the bank after 1 year and 6 months. What is the rate of interest charged by the bank?
5 Rahul took out a loan of ₹25,000 from the bank to renovate his house. If the rate of interest is 8.5% per annum compounded annually, what amount will he have to pay to the bank after 3 years to discharge his debt?
Challenge
1 Choose the correct option.
Assertion (A): Raj borrows ₹80,000 for 4 years at 10% per annum, compounded annually. Then she has to pay ₹1,17,128 after 4 years.
Reason (R): Interest is the ratio of amount to principal.
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 7: Chapter Checkup
1 Convert into percentages.
2 Convert as directed. a 46% into ratio b 0.008% into fraction c 33 2 3 % as fraction
3 Find the value. a 5 4 % of ₹5000 b 1 8 % of 1600 L
4 Find the unknown in each case.
a MP = ₹625, SP = ₹500, % Discount =?
b MP = ₹1780, % Discount = 15%, SP =?
5 If 65% of the students in a school are boys and the number of girls is 700, find the total number of students in the school.
6 Find the bill amount of a refrigerator which costs ₹27,500 and the GST is charged at 18%.
7 Tulsi got her first salary. She bought a watch for her mother for ₹1980 including tax at 10%. Find the original price of the watch.
8 A man spends 20% of his salary on house rent. After spending 40% of the remainder, he is left with ₹9600. Find his monthly salary.
9 Rohit buys a book at a discount of 20%. He manages to get an additional 10% discount on the book since it was slightly torn. What is the marked price of the book if it was sold for ₹1008?
10 Amit buys a television set whose marked price was ₹45,000. He then gets a discount of 15% and pays a tax of 12%. How much does he pay for the television set?
11 Find the missing values in the table.
12 Find the amount and compound interest if the interest is compounded annually.
13 A sum of money amounts to ₹780 in two years and ₹1230 in seven years. Find the principal and rate of simple interest.
14 A local government organises blood donations every year in the city. In the initial year, 10,000 people donated blood. Each year, there was an increase of 15% in the number of people who donated blood. How many people donated blood after 2 years?
Challenge
Critical Thinking
1 In a school election, there are two candidates running for the position of student body president: Sarah and Alex. What percentage of the total number of students voted for Alex if there are 600 students in the school who are eligible to vote.
Statement 1: 70% of the eligible students cast their votes.
Statement 2: 60% of the eligible votes were received by Sarah
a Statement 1 alone is sufficient to answer.
b Statement 2 alone is sufficient to answer.
c Statement 1 and 2 together are sufficient to answer.
d Statement 1 and 2 together are not sufficient to answer.
2 The difference between simple interest and compound interest at the rate of 10% for two years is ₹1. What is the principal if the interest is compounded annually?
Vaccination Rates and Public
Health
Impact during the COVID-19 Pandemic
COVID-19 had a great impact on our lives. The COVID-19 pandemic, caused by the SARS-CoV-2 virus, led to a global health crisis starting in late 2019. Vaccination emerged as a key strategy to control the spread of the virus and mitigate its impact on public health. The total COVID cases reported until 20 June, 2024 were 800,000,000.
Read the questions and answer them. (The data is taken from the WHO website and has approximate values)
1 The number of people who had COVID in China was 100 million. What percentage of all the people in the world who were affected by COVID were Chinese?
a 10%
b 12.5%
c 15% d 20%
2 25% of the people who were diagnosed with COVID were American. How many Americans were diagnosed with COVID?
a 150,000,000
c 200,000,000
b 175,000,000
d 250,000,000
3 45 million Covid cases were reported in India. The total cases in the South-East Asia region were 60,000,000. What percentage of the people in the South-East Asia region who had COVID were Indians?
4 There are 1,40,00,00,000 people in India. 70% of the total population was vaccinated with a complete primary series of the COVID-19 vaccine. 25% of the people who took the vaccination were also vaccinated with at least one booster dose. How many people took booster doses?
5 The pandemic made people prioritise personal and public health through practices like handwashing and wearing masks. What else do you think people learnt during the pandemic?
Algebraic Expressions and Identities
Worksheet 1: Aligned to NCERT Topic/s: 8.1 Addition and Subtraction of Algebraic Expressions
1 Look at the given algebraic tiles. Write algebraic expressions for the tiles. Also, identify the terms containing variables.
Expression:
Expression:
Expression:
Term with variable:
Expression:
Term with variable:
2 Circle the pairs of like terms and cross out the pairs of unlike terms.
3 Simha bought a few blue straws of length x cm each and a few green straws of length y cm each. Use the pictures to write the algebraic expressions.
4 Draw algebra tiles to show the expressions. Solve the expressions.
5 Add the expressions horizontally. Verify your answer by solving them vertically.
a 3x + y + 1 and 2x – 5y – 4
b 3xy2 + 5xy – 6 and 7y2x – 2xy + 3
c −5p2 − 4 5 p + 2 and 3p2 + 5p − 3 4
6 Find the difference of the expressions horizontally. Verify your answer by solving them vertically.
a 5x2 – 3x – 1 and 3x2 – 4x + 7
7 Simplify the expressions.
a 3(5x – 4) – 2(7x + 3) + 4(8x – 2)
b 8mn + n3 − 4 5 and 2mn –1 2 n3 + 1 5
8 Find the missing expression. a (6a4 – 4 + 8a) + = (a4 + 5 + 8a + 8a3) b − (6x2 + 6x + 11) = (10x2 + 4x – 1)
9 Subtract (40 – 13p2) from the sum of (−18p2 + p – 32) and (13p + 20p2 – 12).
10 What should be subtracted from (7h – 3ht + 7h3) to get (−6h + 3ht – 9h3)?
11 Harsh has a rope of length (m2 + 13m – 18) metres, and Rohan has a rope of length (8m + 30m2 – 4) metres. What is the difference of the lengths of their ropes?
12 A field is in the shape of a quadrilateral whose sides are (9s2 + 17) metres, (34s + 7 – 18s2) metres, (9s + 2s2) metres and (17s2 – 25) metres. If it needs fencing on all sides, find the length of fencing required for the field.
13 Write a word problem for adding two expressions.
Critical Thinking
1 Find the errors. Also, find the correct solution. ( 2 3 1
8.2 Multiplication of Algebraic Expressions: Introduction
8.3 Multiplying a Monomial by a Monomial
8.4 Multiplying a Monomial by a Polynomial
8.5 Multiplying a Polynomial by a Polynomial
1 Look at the algebraic tiles. Identify the expressions. Draw and complete the multiplication chart of expressions. Write the product you get.
2 Draw algebraic tiles to find the product of the given polynomials.
3 Find the products.
4 Multiply and verify the result for the values of the variables.
5 Simplify. Find the value of each of the results for a = −1, b = 2, c = 10.
6 Find the area of the rectangles using the lengths and breadths.
7 Find the volume of the cuboids using the lengths, breadths and heights (all measures are in centimetres).
8 Find the volume of the cubes using the edges (all measures are in centimetres).
9 Find the coefficient of the x4 term in the product of (5x3 − 4x2 + 2x − 1) and (x2 − 3x + 5).
10 Draw a rectangle and write statements to form expressions for the sides of the rectangle. Find the area of the rectangles for given values.
11 Sara wants to build a rectangular garden of length (3x + 2)m and breadth (4x – 1) m. What is the cost of planting the grass in the garden if the cost of planting the grass is �(2x – 3) per sq. m?
Challenge
1 Read the statements and choose the correct option.
Assertion (A): The product of (2x + 3)(x – 1) is 2x2 + x – 3.
Reason (R): The distributive property states that a(b + c) = ab + ac, which applies to polynomial multiplication.
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 3: Chapter Checkup
1 Match the following.
a 4x + y, 2x – 1 quadrinomial
b 8a2b, 9pq, −6x trinomial
c 3xy + x – 1, 8z2 − 3z + 5 monomial
d −6x2y + 2xy – 6x + 4, p2 – 7pq + 4q – 1 binomial
2 Circle the like terms and cross out the unlike terms.
a 2a, − 3 5 a b 6pq, −4x2y
c −7a2b3c, 8ab2c3 d − 5 6 abc, − 1 2 cba
3 Draw algebra tiles to solve.
a (3x2 + 2x – 6) + (–x2 – 2x + 1) b (–x2 + 4x + 2) – (3x2 – 2x – 3)
4 Add the expressions.
a −3m2 + m – 2 and 4m2 + 6m + 7 b 7z3 + 4z2 + z – 1 and 2z3 – 6z2 – 2z + 2
5 Subtract the expressions. a 8z5 – 9z2 + 1 2 z + z6 + 17z3 from
6 Simplify the expressions.
a (7s2 – 4s4 + 3s) + (5s2 + 6s4) − (9s2 – 8s3 + 2s4) b (8t4 – 3t2 + 2t) – (4t2 – 5t) + (7t – 9t2 + 6t4)
7 Add (3x2 − 2x + 1) to the difference of (−2x3 + x) and (7x – 3 + 7x3).
8 Find the products.
a 6xy2z4 , -11x2yz2,3y3z
c (-2p3+8p2+10p -5)(p2+3p +9)
b (4y +7)(2z2+5z – 6)
d st(-5stu +3u – 9)
9 Multiply and verify the result for the values of the variables.
a (9h + 4)(2h – 11), forh = 2
b (2a2 − 5a − 8)(4a2 − a + 3), fora = −5
10 Simplify. Find the value of each of the results for a = −1, b = 2, c = 10.
a –1 5 a(8a + 5b – 11c) − 5 6 a(3a – 5b + 12c)
11 Find the area of the rectangles using the lengths and breadths.
12 Find the volume of the cuboids using the lengths, breadths and heights (all measures are in cm).
13 Find the volume of the cubes using the edges (all measures are in cm).
5s (stu + 2)
14 This is a rectangular field. The shaded region is the footpath all around it. Find the difference in the perimeter of the field with and without the footpath. (All measures are in cm.)
15 A construction company is working on a project. They need to find the total cost of materials for building a rectangular structure with a length of (5x + 3) m and a width of (2x − 1) m. If each square metre of material costs ₹100, what is the total cost?
16 Hetal’s mother went to the market to buy some fruit. She bought bananas for ₹(15x + 6), grapes for ₹(13x2 – 9x + 2) and apples for ₹(−8x2 + 4x – 18) less than the cost of the grapes. Find the total amount she spent to buy the fruit.
17 Create a word problem to multiply a trinomial by a trinomial.
Challenge
Critical Thinking
1 Ananya has a sheet of chart paper whose sides are (4x + 5) metres and (3x2 – 5 + 6x) metres. If she cuts squares from all the corners of the chart paper of side x metres, find the perimeter of the remaining chart paper.
2 Read the question and identify which statement(s) are sufficient to answer the given question. What is the area of the rectangle?
Statement 1: The length of the rectangle is (x + 2).
Statement 2: The breadth of the rectangle is (3x – 4) and the value of x is 7 cm.
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.
Shopping Complex Blueprint
Mr Aneja gets a contract to design a shopping complex as given in the figure. He created a basic layout plan for the shopping complex. The layout is a regular hexagon. It has a circular fountain at the centre. The radius of the circular fountain is 7(x – 13) m.
Answer the following questions.
1 Mr Aneja wanted to calculate the complete area of the shopping complex. What is the area of the shopping complex?
a 6(3x2 + 13x – 56) m2 b (18x2 + 65x – 300) m2
c 18(x2 + 4x – 20) m2
(6x2 + 26x – 112) m2
2 The water sprinklers are to be purchased by Mr Aneja. He wanted to find out how much area the fountain covers. What is the area of the circular fountain?
a (154x2 – 4000x + 26000) m2 b 154(x2 – 26x + 169) m2
c (49x2 – 182x + 828) m2
49(x2 – 91x + 441) m2
3 The tiling of the shopping complex is to be done. What will be the area of the floor that has to be tiled if the area of the fountain is not to be tiled? What will be the total cost of tiling the shopping complex if the cost of tiling is ₹80 per sq. m? The fountain region is not to be tiled.
4 If 4 rectangular shops, each with a length of (x – 3) m and a breadth of (x – 9) m are made on the layout, then what is the remaining area on the hexagonal layout?
5 Suggest some ways in which Mr Aneja can make the shopping complex more environmentally friendly.
Mensuration
Worksheet 1: Aligned to NCERT Topic/s: 9.2 Area of a Polygon (Area of Figures Made with Parallelograms, Triangles and Circles)
1 The Place Charles de Gaulle in Paris is a circular plaza with the Arc de Triomphe at its centre. If the radius of this circular track is approximately 120 metres, what is the area of the circular plaza? (Use π = 3.14)
2 A rectangle of length 14 cm has an area of 84 sq. cm. The perimeter of a square is the same as the perimeter of the rectangle. What is the length of side of the square?
3 Find the number of square-shaped tiles of side 100 cm required to tile a 1.5 m wide path around a rectangular park of length 40 m by 32 m.
4 The figure comprises a right-angled triangle and a quarter circle. Find the area of the quarter circle.
5 Every circle in the given figures has a diameter of 28 cm. Find the area of the shaded regions in these squares.
6 John and David are calculating the area of the parallelogram. John multiplies the length of the side CD by the length of line Y. David multiplies the length of side BC by the length of line Z. Who is correct: John, David or both of them? Explain your answer.
7 A park near Aana’s home is in the shape of a rectangle. The park is 8 m long. If Aana walks diagonally across the park, it is a 10 m walk. How much farther would Aana walk if she walked along the length and breadth of the park instead of diagonally across it? Do you go for regular walks? How does it improve your health?
8 The ratio of the two sides of a parallelogram is 4:3. If its perimeter is 56 cm, and the height of the parallelogram is one-eighth of the longer side which is also the base of the parallelogram, then find its area.
9 Fertiliser is a substance added to soil or plants to provide essential nutrients that help them grow better. Raghav wants to spread fertiliser in his entire lawn as shown in the figure. At the market, the fertiliser is sold only in 10 kg bags, costing ₹16 each. If he spreads the fertiliser at a rate of 20 g per sq. m, then find the cost of the fertiliser which he uses for his lawn.
1 Suppose you have a sheet of paper in the shape of a parallelogram. You fold the paper from the top right-hand corner, as shown in the figure. The shaded area you get is three-eighths of the original area. If you fold the bottom left-hand corner of the sheet, what is the fraction of the shaded area left compared to the original parallelogram?
Worksheet
2: Aligned to NCERT Topic/s: 9.2 Area of a Polygon (Area of Quadrilaterals)
1 Find the area of the figures.
2 A rope of length 80 cm is cut into two pieces. One piece is used to form a rectangle of length 14 cm and width 8 cm. The other piece is bent into a rhombus. Draw the rhombus so formed and label the length of its each side.
3 The Louvre Pyramid in Paris was designed by architect I. M. Pei. It is made up of 673 glass segments, arranged in a pattern that includes triangular and rhombus shapes. If each diagonal in the rhombus shaped glass is around 2.69 metres then what is the area of each glass panel?
4 The diagonal of a quadrilateral is 32 cm, and the perpendiculars dropped on it from the opposite vertices are 12 cm and 15 cm. Find the area of the quadrilateral.
5 A quadrilateral whose area is 170 sq. cm and diagonal measures 17 cm has a perpendicular on the diagonal of length 15 cm. What is the length of the other perpendicular?
6 Two parallel sides of a trapezium are in the ratio 4:6 and the distance between them is 15 cm. If the area of the trapezium is 450 sq. cm, find the lengths of its parallel sides.
Challenge
1 Read the statements and choose the correct option.
Critical Thinking
Assertion (A): The area of a trapezium is equal to the area of a rectangle if the non-parallel sides are equal and its height is equal to the width of the rectangle.
Reason (R): The height of the trapezium is the perpendicular distance between the parallel sides.
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.
9.2 Area of a Polygon (Area of Combined Shapes)
1 Find the area of the figures.
2 Find the area of the polygons.
3 Find the area of the shaded regions.
4 The Parthenon, located on the Acropolis of Athens, is a quintessential example of classical Greek architecture. The layout of the Parthenon is shown. The length of the Parthenon is around 69.5 m and the width is around 30.9 m. What is the total area of the Parthenon?
5 Find the area of a regular hexagon of side 15 cm each. Is there more than one way of finding its area? Draw the figure and find out.
6 Two tiles are fitted together as shown.
If the length of one tile is 10 cm, then find the area of the tiling pattern obtained by fitting five such tiles together.
7 A chimney works by allowing smoke and hot gases from a fireplace, stove, or furnace to escape safely out of a building. The measurements of a chimney are given. Find its area.
1 Gaurav has some right-angled triangular tiles whose sides are 13 cm, 12 cm and 5 cm. He makes the shape using four of these tiles and some square tiles. Find the area of the shape.
Solid Shapes 9.4 Surface Area of Cube, Cuboid and Cylinder (Surface Area)
1 Find the lateral surface area and total surface area of the cube for the side given. a ɑ = 17 mm b ɑ = 21 m
4 Find the lateral surface area and total surface area of a hollow cylinder with the given dimensions. (Use π = 22 7 ) a R = 14 cm, r = 8 cm and h = 1 m b R = 11 dm, r = 1 m and h = 40 cm Worksheet 4: Aligned to NCERT
2 Find the lateral surface area and total surface area of a cuboid of the given length, breadth and height.
a l = 12 cm, b = 8 cm and h = 15 cm b l = 60 cm, b = 7 cm and h = 18 cm
3 Find the lateral surface area and total surface area of the cylinder for the given height and radius.
a r = 12 cm and h = 14 cm b r = 7 2 m and h = 22 m
5 Identify and find the missing dimensions of the solid shapes.
LSA = 225 cm² TSA = 1800 m²
6 The perimeter of each face of a cube is 32 cm. What is the total surface area of the cube?
7 The curved surface area of a cylinder is 1200 sq. cm. If the radius of the base of the cylinder is 10 cm, what is its height?
8 A hollow cylindrical tube is open at both ends and is made of iron of 2 cm thickness. The external diameter of the tube is 50 cm and the length of the tube is 140 cm. What is the lateral surface area of the tube?
9 Three similar cubes are placed adjacent to each other. What will be the ratio of the total surface area of the new shape to the sum of the surface areas of the cubes?
Challenge
1 Read the statements and choose the correct option.
Assertion (A): The total surface area of the cylinder with a radius of the base 14 cm and height of 30 cm is 3872 cm².
Reason (R): If r is the radius and h is the height of the cylinder, then the total surface area = (2πrh+ 2πr²)
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: Aligned to NCERT Topic/s:
9.6 Volume and Capacity
1 Find the volume of the given solids.
a Cube:
i a = 16 cm
b Cuboid:
c Cylinder:
ii a = 24 mm
2 Find the volume of a hollow cylinder with the dimensions given.
a R = 15 m, r = 8 m and h = 3.5 m
b R = 18 cm, r = 7 cm and h = 21 5 cm
3 Identify and find the missing dimension for the given volume of the solid shapes.
= 5.5 mm
= 11m
= 17 cm
= 3060 cm3
h = ?
= ?
= 3993 mm3
= 21 m
= 352 m3
= ?
= ?
= 1331 dm3
4 The area of the base of a rectangular tank is 1300 cm2. The volume of the tank is 5.2 m3. What is the depth of the tank?
5 The diagonal of a cube is 8 3 cm. What is the volume of the cube?
6 A warehouse measures 50 m × 35 m × 20 m. How many cubical wooden crates of length 50 cm can fit inside the warehouse?
7 A container can hold 60 L of water. How many 10 cm ice cubes can be formed from the water in the container?
8 If each edge of a cube is increased by 50%, what is the percentage increase in the volume of the cube?
9 If the volumes of two cubes are in the ratio 1:64 then what is the ratio of their total surface areas?
10 A rectangular block measures 15 cm × 12 cm × 18 cm. What is the volume of the largest cube that can be cut from this cuboid?
11 How many aluminum rods of length 3.5 m and diameter 4 cm each can be made from 1.76 m3 of aluminum?
12 Create a word problem on finding the volume of a cylindrical shape.
Challenge
1 Read the statements and choose the correct option.
Assertion (A): The surface area of a cylinder is always greater than its volume.
Reason (R): The surface area of a cylinder depends on both the radius and height, while the volume depends only on the 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 6: Chapter Checkup
1 Find the area of the shaded rhombus if the length of the rectangle is 9.2 cm and the breadth is 6.4 cm.
2 Identify how many unit cubes can fit inside the cube or cuboid of the dimensions given.
a l = 12 m, b = 10 m, h = 5 m b a = 3 m
3 Find the capacity (in litres) of the containers of the dimensions given.
a Cube (a = 150 cm)
b Cuboid (l = 2 m, b = 15 dm, h = 50 cm)
c Cylinder (r = 8 m, h = 3 m) d Hollow cylinder (R = 3 m, r = 120 cm, h = 1.4 dm)
4 In a rhombus, one diagonal is five times the other. If the area of the rhombus is 1000 sq. cm, find the length of the diagonals.
5 What is the height of a cylinder of radius 5 m and a total surface area of 660 m2? Draw the cylinder and mark the dimensions.
6 The radius of the base of the cylinder is 7 mm, and its total surface area is 2640 mm². What is the height of the cylinder?
7 One of the parallel sides of a trapezium is thrice the other. If the area of the trapezium is 350 sq. cm and the height is 14 cm, then find the lengths of the parallel sides.
8 Nishant says, “If the length and breadth of a rectangle are the same as the base and height of a parallelogram, then both the shapes have the same area.” Explain whether Nishant’s statement is always, sometimes, or never true.
9 Find the area of the polygons.
10 Find the missing dimensions of the solid shapes.
LSA = 8100
LSA = 88 m2 V = 1728 cm3
11 Look at the figure. Find the difference between the areas of the regions A and C. (PQRS is a square)
12 Square holes of dimensions 1 m × 1 m are cut from all the faces of a cube with edges measuring 4 m. What is the total surface area of the faces of the cube now?
13 The parallel sides of a trapezium are 25 cm and 15 cm. Its non-parallel sides are 13 cm each. Find the area of the trapezium.
14 Three cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. What is the total surface area of the new cube?
15 Look at the image shown below. What is the volume of the cylinder
the given net?
16 A floor is in the shape of a trapezium whose parallel sides are of length 12 m and 15 m, and the distance between them is 8 m. David wants to paint the floor using a 5 L tin of paint costing ₹2899 in such a way that 1 L of paint covers an area of 10 sq. m. If he has ₹5400 to spend on paint, has David got enough money to buy all he paint the needs?
17 A farmer has a field in the shape of a trapezium where the lengths of its parallel sides are 160 m and 240 m. If the distance between the parallel sides is 150 m, and the field produces 6500 kg of wheat per hectare, then find the amount of wheat in kg the field produces. (Hint: 1 hectare = 10,000 sq. m)
18 A brick measures 15 cm × 5 cm × 5 cm. How many bricks will be required for a wall of dimensions 5 m × 1.5 m × 1.5 m?
19 A wooden pipe is in the shape of a hollow cylinder. The internal diameter of the pipe is 28 cm, and its external diameter is 35 cm. The length of the pipe is 48 cm. Find the weight of the pipe if each cm3 of wood weighs 0.8 g.
20 Create a word problem to find the area of a combined shape.
Challenge
1 PQRS is a square with a side 4 cm. The length of ST is 4 cm. PT is equal to RT. What is the area of PST?
2 Decide whether the statements are sufficient to find the area of quadrilateral ABCD.
Statement 1: The sum of the perpendiculars on the diagonal BD from the opposite vertices is 30 cm.
Statement 2: The length of BD is one-third the perimeter of the quadrilateral ABCD. (Perimeter of ABCD = 96 cm)
a Statement 1 alone is sufficient while Statement 2 alone is not sufficient.
b Statement 2 alone is sufficient while Statement 1 alone is not sufficient.
c Both statements together are sufficient.
d Both statements together are not sufficient.
Worksheet 7: Case Study
Theatre Thrills
Mahi’s school organised an annual event, ‘Theatre Thrills’, for the drama and theatre festival. A stage has to be constructed for the event. The stage has a cuboidal shape with dimensions of 5 m by 4 m by 80 cm. Read the questions below and answer.
1 The stage is to be painted. All the faces except the bottom face are to be painted. What is the total area that is to be painted?
2 The cubic-shaped stools are to be placed in the auditorium for the students. The volume of each stool is 2,16,000 cm³. What is the total surface area of the stool?
a 21,000 cm²
c 21,600 cm²
b 21,200 cm²
d 21,800 cm²
3 Many cylindrical dustbins are to be kept at different places. The children are taught to throw away the trash in the dustbins only and not litter at other places to keep the auditorium clean. Mahi is asked to cover the dustbin with coloured paper. How much coloured paper is required by Mahi to cover 8 such dustbins?
14 cm 30 cm
4 An aquarium has to be put outside the gate of the auditorium so that the students learn about different fishes. The aquarium is a cuboid with a length, breadth and height of 120 cm, 50 cm and 1 m, respectively. How much water can the aquarium store (in L) if 1 cm³ = 1 mL?
5 Gift boxes are to be distributed to the winners. Design a gift box for the winner of any one solid shape and find the volume of the gift box.
Exponents and Powers
Worksheet 1: Aligned to NCERT Topic/s: 10.2 Powers with Negative Exponents
1 Expand and find the value of the numbers. a 46 b (−7)−3 c 4 5 3 d -4 -2 3
2 Express the numbers as exponents. a 16 81 b 81 243
3 Express the numbers with negative exponents.
4 Write the expanded form of the numbers using exponents.
45.123 b 541.056 c 107.02356 d 5003.671
5 Which one is larger? a 2⁵ or 5² b 2⁷ or 7²
6 Solve and express your answer with negative exponents.
Challenge
1 Vivan’s school had two branches. After the school’s annual day function, the videos for the events were uploaded on the social media channels of both the branches. Since the time it was uploaded, the online traffic has been monitored. The table shows the number of views the video got each week.
The pattern for the number of views for both the branches continued for few weeks.
a What is the ratio of the growth rates of the number of views for both the branches?
b What is the percentage increase in the number of views for the first branch every week?
c What will be the ratio of the number of views for the second branch in week 2 and week 6?
1 Write the numbers in standard form.
2 Evaluate:
3 Write the numbers in the usual form. a 4.21 × 10⁸
40.857 × 10–2
4 Compare the numbers. a 2.11 × 10², 1.67 × 10–2
5 Solve as directed. Give your answers in standard form. a 6.757869 × 10⁵ + 980.436 × 10³
7.3 × 10–5, 0.7 × 10–8
3.6548 × 10⁸ + 154.142 × 10⁶
6 Find the value of: a (5−9 × 5³) × 15⁵
2 5 –4 × 3 8 –4 × 3 5 4
7 Simplify using laws of exponents. a 72 × 3−6 × 4²
× 16 × 27−2
8 Find the value of x. a 1 2 x = 1 8
b 2x = 32
9 An ant carries a small amount of food that is 2.78 × 10–3 inches long. Another ant carries an amount of food that is 4.56 × 10−5 inches long. How long are the pieces of food carried by the ants altogether?
1 What is the value of 2x + y?
Read the statements and choose the option that correctly answers the question above.
Statement 1: 2x = 8
Statement 2: 2y = 16
a Statement 1 alone is sufficient to answer while statement 2 alone is not sufficient.
b Statement 2 alone is sufficient to answer while statement 1 alone is not sufficient.
c Both statements together are sufficient to answer.
d Both statements together are not sufficient to answer.
e Either of the statements alone is sufficient to answer.
Worksheet
3: Chapter Checkup
1 Write the expanded form of the given numbers using exponents.
a 65.879
b 978.9675
c 4876.9023
2 Identify if the statements are written in standard form or usual form. If the numbers are in standard form, express them in usual form and vice versa.
a The size of a plant cell is 1.275 × 10−5 m.
b The total volume of water on Earth is 1.386 × 109 cu. km.
c The weight of an electron is 0.0000000000000000000000000000911 kg.
3 Which of the following is in usual form? Explain your answer.
a 8.09 × 105
b 0.000000654879
c 9.21 × 10−21
4 Express the given numbers as directed.
a 256 as a power of 2
b 59,049 as a power of 3
c 78,125 as a power of 5
5 Write the reciprocal of the given expressions using exponents.
a 7 9 × 7 9 × 7 9 × 7 9
6 Solve.
7 What power of 49 is equal to 710?
8 Arrange the numbers in ascending and descending orders.
a 210, 323, 642, 128−2, 83
b 310, 273, 7292, 18−2, 93
9 A teacher asked her students to find the multiplicative inverse of x−2. Tanya said the answer is –x2, whereas Sayani said the answer is x−3. Who do you think is right? Explain your answer.
10 Simplify using laws of exponents.
128 × 36 × 4−2 243 × 36 × 27−1
11 Find the value of x in:
12 Simplify: x p + l × x q + p x l + q (x p × x q × x l)2
13 A farm that has 6 × 105 m² of land produces 2.4 × 106 kg of cotton each year. How much cotton is produced per meter square?
1 Read the statement and choose the correct option.
Assertion (A): (a³ × b³) + 2000 = –1000, where a = 5 and b = –2.
Reason (R): (a³ × b³) = (ab)³ and a0 = 1.
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 Find the value of y if ym + 3 × (y²)m – 1 y³m−9 = 1024
Worksheet 4: Case Study
Elemental Atomic Masses: A Comparative Table
The table shows the mass of an atom for some elements (in kg). Read the data carefully and answer the questions given below.
1 Which of the following is the lightest element?
a Hydrogen b Oxygen
c Gold d Iron
2 Which of the following is correct?
a Carbon is the heaviest element.
b Oxygen is 0.6 times heavier than carbon.
c The mass of all the elements is written in standard form.
d The mass of gold is lighter than iron.
3 Which element is approximately 5 times heavier than carbon?
4 What is the ratio of the weights (approx) of the heaviest element and the lightest element?
× 10–26
Direct and Inverse Proportions
Worksheet 1: Aligned to NCERT Topic/s:
1 Which of the given quantities vary directly from each other? Write Yes/No.
a The speed of a car and the time taken by the car to cover a particular distance.
b The number of men required to construct a wall and the time taken by the men.
2 Observe the tables to find out whether a and b are directly proportional. Also, give the constant of variation in the case of direct proportion.
3 Complete the table if x and y vary in direct proportion.
4 Find the cost of 52 kg of rice if 9 kg of rice costs ₹585.
5 A machine in a chocolate factory makes 450 chocolates in 6 hours. How many chocolates will it make in 4 hours?
6 Kamal can type 1020 words in 15 minutes. How many words will he type in 11 2 hours?
Challenge
Critical Thinking & Cross Curricular
1 In 14 days, the earth picks up 2.8 × 1010 kg of dust from the atmosphere. Rani says it will pick up 5600 × 109 g of dust in approx. 2.8 days, while Dhani says it will need at least 2800 days. Who is correct, Rani or Dhani?
1 Which of the quantities vary inversely with each other? Write Yes/No.
a Distance travelled by a car and time taken by the car.
b Number of men required to paint a house and time taken by the men.
2 If x and y vary inversely, then find the value of a
3 Mohit can finish some work in 6 days. How much work can he do in 1 day?
4 42 women can do a piece of work in 15 days. In how many days can 18 women do the same amount of work?
5 If a box of chocolates is divided among 28 children, they get 6 chocolates each. How many more chocolates would each get, if the number of the children was reduced by 7?
6 A can finish a piece of work in 14 days while B can finish the same work in 21 days. In how much time will they complete the work if they both work together?
Challenge
1 Read the question and statements to decide which of the following options is correct. Kavya and Pulkit together can complete the project in 24 days. How many more days will Suman need to complete the rest of the project after Kavya and Pulkit leave after working for 10 days?
Statement 1. Suman and Kavya, together, can complete the project in 30 days.
Statement 2. Pulkit and Suman, together, can complete the project in 20 days.
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 not sufficient.
d Both statements together are sufficient.
Worksheet 3: Chapter Checkup
1 Identify whether the values are in direct or inverse proportion and find the missing values.
2 A recipe requires 880 g of rice flour for 5 persons. How much rice flour is required if the same recipe is made for 12 persons?
3 A labourer is paid ₹4950 for working for 11 days. How much money will he earn if he works for 30 days?
4 Rohan can do a piece of work in a month. What fraction of work can he do in 6 days?
5 Priya has enough money to buy 35 boxes of chocolates worth ₹120 each. How many more boxes of chocolates can she buy if she gets a discount of ₹20 on each box?
6 If 12 men can plough a field in 7 days, how many men can plough the same field in two days?
7 A societyʹs water tank is filled in 4 hours by 8 tankers. How many tankers are required to fill the tank in 2 2 3 hours?
8 A and B can do a job in 8 hours, while B and C can do the same work in 12 hours. A, B and C together can finish the job in 6 hours. In how much time can A and C finish the job together?
9 Two pipes P and Q can fill a tank in 25 hours and 35 hours, respectively. How much time will it take to fill the tank if both the pipes are opened simultaneously?
10 Krishvi cycles to her school at a speed of 12 km/hr and reaches the school in 20 minutes. One day her speed was reduced by 2 km/hr due to some traffic on her way. If she left her home at 8:00 a.m., at what time did she reach the school?
Challenge
1 Statement I: X and Y together can complete the work in 30 hours.
Statement II: X works for 16 hours and Y finishes the remaining work alone in 44 hours. What is the relationship between the efficiency of X and Y?
2 Read the statements and choose the correct option.
Assertion (A): If 6 men can complete a job in 15 days, then adding 4 more men will reduce the time required to 8 days.
Reason(R): Time taken to complete a task is inversely proportional to the number of men working on it.
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 of A.
d Both A and R are true, and R is not the correct explanation of A.
Worksheet 4: Case Study
Water Conservation and Agriculture
Water is a precious resource, especially for agriculture. Farmers use two types of irrigation systems: traditional flooding and modern drip irrigation. Traditional flooding irrigation wastes a lot of water, while drip irrigation conserves water by delivering it directly to the roots of plants.
A group of farmers decided to switch from traditional flooding to drip irrigation to save water. They found that with traditional flooding, they needed 50 litres of water to irrigate one square metre of land for a day. With drip irrigation, they only needed 20 litres of water for the same area.
1 If a farmer has 100 square metres of land, how much water will he save per day by switching from traditional flooding to drip irrigation?
a 1000 litres b 1500 litres c 3000 litres d 2500 litres
2 If the village has 10 farmers each with 50 square metres of land, how much water in total will they save per day by switching to drip irrigation?
a 10,000 litres b 15,000 litres c 20,000 litres d 25,000 litres
3 If the villageʹs water supply is limited to 50,000 litres per day, how many more square metres of land can be irrigated using drip irrigation compared to traditional flooding?
4 What are some ways you can conserve water at home? Can you think of small changes in your daily routine that could save water?
Factorisation
Worksheet 1: Aligned to NCERT Topic/s:
12.1 Introduction
1 Factorise the expressions by identifying the common monomial using a factor tree. a 3x2 + 9x
4y3 - 2y2
2 Solve to factorise the expressions by identifying the common monomial. a 7x2 - 21xy
3 Factorise the expressions by identifying the common binomial.
(3y + 2) (y - 1) - 2 (3y + 2)
(3x + 2) (2x - 1) - (3x + 2) c (5y - 1) (3y + 2) - 4 (3y + 2)
4 Factorise the expressions by regrouping the terms.
a (2x3 - 3x2 + 4xy - 6y) b (3ab + 6ac - 4cd - 2bd)
c (x2 - 7x - 2xy + 14y)
Challenge
d (2ab + 5ac - 4bd - 10cd)
1 A farmer spent ₹(4x2 + 8xy + x + 2y) on buying plants. If he bought (x + 2y) plants, what is the cost of each plant?
Worksheet 2: Aligned to NCERT Topic/s:
12.2.3 Factorisation using identities
1 Factorise the expressions using the square of a binomial identity.
a a2 + 8a + 16 b x2 + 10x + 25 c b2 + 4b + 4
2 Factorise the expressions using the difference of squares identity.
a a2 − 4 b 25 − x2
c 9b2 − 16 d 49p2 - 16
3 Factorise the expressions using a suitable algebraic identity. a 1 - 8ax + 16a2 x2 b 3x3y - 243xy3
c a4 - b4 d b4 - 81
4 Find the missing term so that the expression can be easily factorised using the square of a binomial identity.
a b2 - 14b + ? b x2 - ? + 9
? - 2cd + d2 d 36 - ? + r2
c
5 What constant must be added to the expressions to create a perfect square?
a a2 + a b - 8y + y2
c 9d2 - 6d
6 Factorise.
d x2 + 5x
a m4 - 16n4 b a2 - b2 - 2b - 1
7 Create a question on factorising an expression using identities.
Challenge
Critical Thinking
1 Oliver wants to install bookshelves in his room. He has a rectangular wall space available with an area represented by the expression (9y2 - 4x2) sq. cm. Factorise the expression of area and separate the factors as the length and breadth. Determine the length and breadth, if x = 2 and y = 3 and the length of the rectangle is more than its breadth.
Worksheet 3: Aligned to NCERT Topic/s: 12.2.4 Factors of the form (x + a) (x + b)
1 How should the middle term of the expressions given below be split to factorise the expressions?
a x2 - 5x + 4 b 2x2 - 9x + 4
c 6x2 - 11x + 4
4x2 - 17x + 4
2 Which of the expressions has (x + 1) as one of its factors?
a x2 - 13x + 42 b x2 - 12x + 35
c x2 + 11x + 10 d x2 - 9x + 14
3 Factorise the trinomials. a 6x2 - 11x + 3 b 2x2 - 7x + 6
c 2x2 - 5x + 2 d 3x2 - 8x + 4
4 If the area of a rectangle is given by the trinomials, what could the length and breadth of each of these rectangles be?
a 3x2 - 23x + 14 b 5x2 - 37x + 14
c 4x2 - 18x + 14 d 4x2 - 8x + 3
5 Create a word problem on factorising trinomials.
Challenge ................................................................................................................................................................................................................. Critical Thinking
1 Can the trinomials be factorised without taking any monomial term common before splitting the middle term?
a b2c3 + 8bc4 + 12c5 b 3c5 - 18c4 - 48c3
2 A small business owner models the profit of her store on the quadratic trinomial (3x2 - 12x - 15). If each product sold brings equal profit, and (x − 5) products are sold, what is the algebraic expression for her profit?
Worksheet 4: Aligned to NCERT Topic/s: 12.3 Division of Algebraic Expressions
1 Divide the algebraic expressions.
a 15x3 by 3x b 15a2b4 by 5ab2
c 24y4z3 by 6yz
2 Divide polynomials by monomials.
a (2x3 + 4x2 − 6x) by (2x)
d 18x5y 2z by 9xyz2
b (3y4 − 9y3 + 6y2) by (3y)
c (4a5 − 12a4 + 8a3) by (4a)
3 Solve the expressions.
a 225abc (4a − 8) (5b − 15) ÷ 125 (a − 2) (b − 3)
d (6m3 − 18m2 + 12m) by (6m)
b 144ab (a + 5) (b − 4) ÷ 36a (b − 4)
28 (a + 3) (a2 + 3a + 70) ÷ 7 (a+ 3)
117abc (a + b) (b + c) (c + a) ÷ 78ab (b + c) (c + a)
4 Divide the polynomials by the binomials using long division.
(4x3 − 6x2 + 3x − 9) by (x2 − 4)
(3y4 − 9y3 + 6y2 − 12y) by (y2 − 4) c (x5 + 5x4 + 4x3 + 20x2 + 16x) by (x2 + 4)
5 Divide the polynomials by the trinomials using long division.
(3x3 − 5x2 + 2x − 1) by (x2 − 4x+ 4)
(6a4 − 3a3 + 9a2 − 6a) by (a + 2)
c (6a4 − 2a3 + 9a2 − 5a + 3) by (2a2 − a + 1)
(4y4 + 6y3 − 2y2 + 8y − 12) by (2y2 − 3y − 6)
6 What must be multiplied by x − 7 to obtain x3 − 12x2 + 38x − 21?
(x5 − 3x4 + 5x3 − 2x2 − 4x + 8) by (x3 −2x2 x + 2)
7 The total amount of water in a bucket kept in sunlight is (x2 + 5x + 6) litres. The bucket dries up in (x + 3) days due to evaporation. What is the rate of evaporation per day?
Challenge
1 What must be added to 3x3 − 8x to make it perfectly divisible by x − 1?
2 What must be subtracted from (a4 + 2a3 − 2a2 + a − 1) so that the resulting polynomial is exactly divisible by (a2 + 2a − 3)?
Worksheet 5: Chapter Checkup
1 Factorise the expressions by identifying the common monomial using a factor tree.
a 2x2 + 6x b 3ab - 9a
2 Factorise the expressions by taking the binomial term common.
a (x + y) - (x + y)(2x - 11)
3 Factorise the expressions by grouping/regrouping the terms.
a 4a2b - 6ab2 - 2ab + 3b2
4 Factorise the expressions into perfect squares.
a (a2 + 6ab + 9b2)
5x2 - 10xy + 3xy - 6y2
(x2 - 10xy + 25y2)
5 Factorise the expressions by using the difference of two squares identity. a (p2 - 9q2)
(4x2 - 49y2)
6 Factorise the quadratic trinomials.
a 6x2 + 11x - 2 b x2 - 5x + 6
7 Divide the polynomials by the monomials.
a (6x3 + 9x2 − 12x) by 3x
8 Divide the polynomials by the binomials using long division.
a (2x3 + 4x2 - 6x) by (x - 2)
(3x4 - 9x2 + 6x) by (x + 1)
c (4x3 + 12x2 - 3x) by (2x - 1)
9 Divide the polynomials by the trinomials using long division. a (3x3 + 4x2 - 2x + 1) by (x2 - 3x + 2)
(5x4 - 13x3 + 9x2) by (5x + 2)
(2x4 - 5x2 + 3) by (x2 - x - 2)
(6x3 - 8x2 + 2x - 4) by (2x2 - 3x - 2)
(5x3 - 6x2 + 3x - 2) by (x2 + 2x - 1)
10 Lucas wishes to plant flowers in a rectangular garden. He wants the area of his garden to be (64x3 − 25xy2). What are the possible length and breadth combinations of his garden?
Challenge
Critical Thinking
1 What should be subtracted from x4 + 7x3 + 15x2 + 7x – 5 so that the resulting polynomial is exactly divisible by x2 + 4x – 2?
2 Read the statements and choose the correct option.
Assertion (A): The factorisation of x2 + xy + 2x + 2y is (x + 2) (x – y)
Reason (R): Factorisation is defined as breaking or decomposing an expression into a product of two or more expressions which when multiplied together, give the original expression.
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
Urban Art Space
Suhani, who has a passion for art, decided to build an art gallery in the city. She wanted artists from various places to display their work there. The gallery is designed to have two entrances and exit doors. It is also planned that the gallery will have 8 square shaped windows, and the floor will be covered with square tiles. The architect designed the layout and gave all the measurements. Read the questions related to the gallery and answer them.
1 The area occupied by one door can be given as (2ab + 5b2 + 6ac + 15bc) square units. What are the possible length and breadth of each door?
a (2ab + 5b2) units and (6ac + 15bc) units
(ab + 5b2) units and (3ac + 15bc) units
c (b – 3c) units and (2a + 5b) units d (b + 3c) units and (2a + 5b) units
2 The perimeter of one square window can be given as (12a + 20b) units. How much area will each window occupy?
a (4a + 5b)2 square units
c (a + 5b)2 square units
(3a + 5b)2 square units
(12a + 20b)2 square units
3 Suhani planned to cover one of the rectangular walls of the gallery with her creations. If the area and the breadth of the wall is (x3 – x2 – 21x –54) square units and (x – 6) units, respectively, then what is the length of this wall?
4 What will be the cost of fitting one square tile if the area of the floor is (6x4 + 11x3 – 3x2 + 27x – 5) square units, and the total cost of fitting is �(3x2 – 2x + 5)?
Introduction to Graphs
Worksheet 1: Aligned to NCERT Topic/s:
13.1.1 A line Graph
1 State True or False.
a A line graph is used to study how data changes over time.
b When interpreting a double-line graph, if one line is consistently higher than the other, it means that the data represented by that line is always greater.
c Line graphs can also be called histograms.
d In a double-line graph, the two lines must always intersect at some point on the graph.
2 The graph shows the number of shirts sold by a shopkeeper in a week.
Answer the following questions.
a On which day were the most shirts sold?
b On which day were the fewest shirts sold?
c What was the percentage increase in the number of shirts sold from Wednesday to Thursday?
d What is the ratio of the number of shirts sold on Tuesday to the average number of shirts sold on all 5 days?
3 During an intense summer, two cities in the United States, Arizona and Dallas, experienced temperature variations from June to October. To understand the temperature trends, the city planners and residents recorded the temperature in Fahrenheit, as shown in the table below. Represent it as a double line graph.
4 Create a data set to form a double line graph. Challenge .................................................................................................................................................................................................................
1 The graph shows the population of two cities from 2000 to 2004. Read both the statements given below and choose the correct option.
Assertion: City A was most populated in 2004 and least populated in 2001.
Reason: In 2001, the population of City A was 60% of the population of City B.
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, R is false.
d A is false, R is true.
Worksheet 2: Aligned to NCERT Topic/s:
13.2 Some Applications
1 State True or False.
a Every point on the y-axis is of the form (x, 0).
b The graph of every linear equation in two variables need not be a line.
c A point whose y-coordinate is zero and x-coordinate is 5 will lie on the y-axis.
d The coordinates of the origin are (0, 0).
e A point whose x-coordinate is zero and y-coordinate is non-zero will lie on the y-axis.
2 Write the abscissa and the ordinate of each of the following points.
a (9, 4)
c (0, 4)
3 On which axis do the following points lie?
a (0, 1)
c (9, 0)
4 In what quadrants do the following points lie?
a (–8, 8)
c (1, –8)
b (4, –5)
d (–2, –8)
b (–8, 0)
d (0, –5)
b (–9, –2)
d (8, 5)
5 Plot the given points on a graph sheet and verify if they lie in a straight line.
6 Draw a line passing through (4, 4) and (–4, –4). Find the coordinates of the points at which the line meets the x-axis and y-axis.
7 The cost of a notebook is ₹50. Draw a graph after making a table showing the cost of 2, 3, 4, … and so on up to 10 notebooks. Use it to find:
a the cost of 7 notebooks.
b the number of notebooks purchased with ₹550.
8 The Rajdhani Express travels from Mumbai Central (MMCT) to New Delhi (NDLS), covering a total distance of around 1400 km. Below is the dataset with the approximated distance covered at various times during the journey. Plot a graph showing the distance covered by the train over the given time.
1 Simran is visiting a new city and decides to use a taxi to explore different places. The taxi service in this city charges a fixed initial fee plus a variable rate per kilometre travelled. Simran keeps track of her taxi rides to understand how the fare is calculated. The taxi service charges an initial fee of ₹50 per ride. Here is the fare information she noted for her rides:
For a 5 km ride, the fare was ₹150. For a 10 km ride, the fare was ₹250.
a Use the information to form an equation for the given scenario.
b List and plot 5 data points on a graph representing the distance and the fare.
Worksheet 3: Chapter Checkup
1 Write the abscissa, ordinate and the quadrants of the points:
(5, 4)
–18)
2 Draw the points (5, 4) and (4, 5). Do they represent the same point?
–2)
–10)
3 Plot the following on a graph sheet. Verify if they lie on a line.
a A (4, 6), B (4, 2.5), C (4, 2), D (4, 0)
b A (5, 3), B (2, 3), C (2, 5), D (5, 5)
4 Draw a line passing through (1, 3) and (0, 4). Write the coordinates of the point at which this line meets the x-axis and y-axis.
5 The number of electrical appliances manufactured by a factory during five consecutive years is given below.
Draw a line graph representing the above data.
6 Look at the figure and complete the following table:
7 Raman and Ansh were walking on a road. The data was collected for the distance they walked in a particular time.
Draw a double-line graph for the data.
8 The following data represents the interest on deposits Farhan made for a year.
Draw a graph for the above data. Does the graph pass through the origin?
Challenge
1 Mr Gupta owns a company. The graph represents the sales data from 2015 to 2022. The sales in 2022 and 2023 were thrice and twice of that in 2017 and 2016, respectively. The sales in 2024 were at an all time high. Is it possible to draw the graph for the sales from 2015 to 2024?
2 The question consists of a question and two statements, labelled (1) and (2), which contain certain data. You need to decide whether the data given in the statements is sufficient for answering the question.
Question: What is the area of the triangle ΔPQR?
Statement 1: The coordinates of point P are (7,8).
Statement 2: The coordinates of points Q and R are (7,0) and (3,0).
a Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
b Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
c Both statements together are sufficient to answer the question, but neither statement alone is sufficient.
d Each statement alone is sufficient to answer the question.
Worksheet 4: Case Study
Let's Drive with Mariam!
Mariam, a life skills trainer, goes to various cities by car. She often find herself struggling with the travelling time. To manage her schedule efficiently, she tracks the distance travelled by her car in 5 hours. Refer to the given graph and help Mariam by answering the given questions.
1 What is the speed of the car in which Mariam is driving?
a 20 m/hr
c 30 km/hr
b 20 km/hr
d 1km/20hr
2 How many kilometres would Mariam drive in 8 hours, if the same trend follows?
3 How much distance will be travelled by Mariam in 2.5 hours?
a 60 km
c 40 km
b 55 km
d 50 km
4 If Mariam increases her speed by 10 km/hr, how much less time will she take to cover 60 km?
5 Give one tip to ensure safety while driving.
AnswersAnswers
Chapter 1
Worksheet 1
1. a. 0.5 b. -16 c. 35.44 d. 10 7 e. –8 99 f. –103 15
2. a. 12 7 b.13 2 c. 5 9
3. a. 10 11 b.11 39 c.53 60 d. -
4. a. Closure property b. Associative property
c. Subtraction property of zero
5. a. 0; Additive Identity b. 9 16; 5 8; Associative Property
c. 3 5; Subtraction Property of Zero
6. Students will verify using the properties.
7. 1 12 8. 51 200 9. 5 11 feet 12
Challenge 1. Subtract 7 18 , Add 11 18 2. 6.325 L
Worksheet 2
1.
2.
42 25
3. a. -7 48 b. 20 33 c. 9 14 d. -14 5 or - 24 5
4. a. Students will solve using the associative property of multiplication.
b. Students will solve using the associative property of division over subtraction.
c. Students will solve using the commutative property of subtraction.
5. a. 1; Multiplicative Identity b. 11 6 ; Multiplicative Inverse c. 1; Division by 1
6. a. 7 2 b. 19 15 7. a. 11 4 , 4 11 b. 1, 1 8. -56 17 ; 17 -56
9. A = 26,569 25 sq.m or 1062 19 25 10. 55 1m 64 11. 320 pages
Challenge 1. The statement is false, 9
Worksheet 3: Chapter Checkup
1. a. zero b. negative c. 0 d. Zero
2. a. 30 23 b. 51 43 c. 6 43 d. –39 43 e. 56 15 f. 1 9
3. 1489.8sq. m
4. Students will prove using the given values for m,n and o.
5.181 85 or -2 11 85 6. 153 28 7.1 31 8. a. –1 3 b. 7 4
9. 1 82m 4 10. 4 3 4 kg or 4.75 kg
11. Japan; 163 200 trillion dollars 12. 23 6 24 pizza 13. ₹250
14. Answersmayvary.Sampleanswer.
Nitin is filling small containers with water. He has 7 8 of a gallon of water and wants to fill each container with 1 4 of a gallon. How
many containers can Nitin fill?
Challenge 1. 75 2. Option b
Worksheet 4: Case Study
1. b 2. c 3. d 4. ₹2590 5. 19 kg
Chapter
2
Worksheet 1
1. a. 3 b. 1 2.
3. a. 102 b. 12 c. 5
4. 20, 22 5. Answersmayvary.Sampleanswer: 15, 45 6. 2205 square metres.
7. a. 9 cm b. 5 cm 8. 266 square units
9. Answermayvary:Sampleanswer.
a. x + 2 = 7 b. 2x + 3 = x + 8 c. 3x - 5 = x + 5 9. 22
Challenge 1. 22
Worksheet 2
1. a. No b. Yes
2. a.8 27 b. 5 c. 43 14 d. 38 67
3. a. y = 3 b. y = 1 3 4. 11 14 5. 18 12
Challenge 1. Statements 1, 3 and 4
Worksheet 3
1. a. 3x + 5 = 1 2 x - 13 b. 4y + 11 = 2y + 56
c. n + (n + 2) + (n + 4) = 144 d. st = 240; (s + 20)(t – 2) = 240
2. 85, 87, 89, and 91 3. 132, 143, and 154 4. 30°
5. 26 years 6. Rohit - 92 runs, Virat - 204 runs
7. Daughter - ₹15,00,000; Son - ₹10,00,000 8. 1
Challenge 1. 10 notes of ₹5, 82 notes of ₹10
Worksheet 4: Chapter Checkup
1. a. 2 b. 4 2.
3. a. 78 b. 18.5
4. a. 3 b. 4 c. 7 d. 8 5. a. + b. −,+
6. 7 10 7. 1802.25 sq. m
8. 120 goats 9. ₹3000 10. 21 hours
Challenge 1. 9 5 6 hours 2. b
Worksheet 5: Case Study
1. Option c 2. Option b 3. Option c
4. ₹1.5 per km 5. False 6. Answersmayvary.
Chapter 3
Worksheet 1
1. a. heptagon b. 9 c. regular polygon
2. a. True b. False c. True
3. a. Convex polygon. b. Concave polygon.
4. a. Convex polygon. b. Convex polygon.
c. Concave polygon. d. Concave polygon.
5. Convex polygon
6. a. 2, Quadrilateral b. 20, Octagon
7. 5 8. 3 9. Figuresmayvary.Samplefigure.
Challenge 1. Concave polygon. Number of diagonals = 9
Worksheet 2
1. Figuresmayvary.Samplefigures.
a.
b.
2. a. Concave Quadrilateral b. Convex Quadrilateral
c. Concave Quadrilateral
3. x = 9.8°, y = 27° 4. 40 cm, 25 cm
5. 60°, 120°, 60° and 120°.
Challenge 1. Answermayvary.Sampleanswers:
a. PZ & ZR, ZQ & ZS, PQ & PS, RS & QR
b. ∠ QPS & ∠ QRS, ∠ PQR & ∠ PSR, ∠ QSR & ∠ PSQ, ∠ PQS & ∠ RQS
c. Δ QPR ≅Δ SPR, Δ QRS ≅Δ QPS, Δ QZR ≅Δ SZP
d. Yes e. Yes
Worksheet 3
1. a. 360° b. 120° c. quadrilateral d. 20°
2. a. True b. False c. False d. True
3. a. 120° b. 45° c. 30°
4. a. 360° b. 900° c. 1800° 5. a. 261° b. 96°
6. a. 123° b. 70° 7. a. 9 b. 8 c. 6
8. 32°, 16°, 81°, 95°, 27° and 109°
Challenge 1. Convex quadrilateral, 144°
Worksheet 4: Chapter Checkup
1. a. irregular polygon b. 720° c. 5 d. 360°
2. a. True b. True c. False d. False
3. Option c 4. a. Concave polygon b. Convex polygon
c. Concave polygon d. Convex polygon
5. a. 2 b. 27 c. 119 6. Option c
7. a. 90° b. 24° c. 18°
8. a. 103° b. 127° 9. a. 240° b. 150°
10. 53°, 127°, 53°, 127° 11. 92°
12. a. w° = 50°, x° = 125°, y° = 10°, z° = 45° b. x° = 15°, y° = 11°
13. 54 diagonals, 10 non-overlapping triangles
14. 10 bridges, 35 diagonals
Challenge 1. Option a 2. Option d
Worksheet 5: Case Study
1. Option c 2. Option b 3. No 4. Parallelogram
5. Answersmayvary
Chapter 4
Worksheet 1
1. a. 26.55% b. 15.5% c. 63:86 d. 70,800 tonnes
2. a. 13.14% b. 21.37% c. 97:67 d. 217:293 3.
a. 103.3 crores b. 17.217 crores c. 8.97% d. 2016 and 2019
4. a. 400 students b. 66.67% c. 77.78% d. Answermayvary.Sampleanswer. What is the ratio of students who passed in 2018 to those who passed in 2020?
5. a. 48 million b. 5 million c. 20.5 million d. 6 million
Challenge 1. One reason a bar graph is not suitable for displaying this data is that a bar graph is good for showing single values for each category, but the life spans are given as ranges, not single values. A bar graph can't show the full range from the lowest to the highest number for each animal. Yes, we can plot the graph as:
Worksheet 2
1. a. 37.34% b. Fruit c. $11,056 million d. $13,771 million
2. a. 210 tonnes b. 1:1 c. 25% d. 28.57%
3.
Comparison of Ayesha and Ravi's Test Scores
4. a. 8040 runs b. 6940 runs c. 157.14 d. 188:223
Challenge 1. a
Worksheet 3
1. 112.5° 2. 162°
3. No. of workers from various states working in a garment factory Tamil Nadu, 620 Kerala, 300
100 Andhra Pradesh, 340
5.
Worksheet 4
1. Education = 40,000, Arts = 1,00,000, Law = 70,000, Commerce = 1,65,000, Science = 1,25,000
2. a. 2000 cars b. 360 cars c. 1140 cars
3. a. 700 animals b. Tigers; 35 c. 21
4. a. 1500 teenagers b. 15:17
5. a. Coal b. 1:11 c. 19 1 0 0
6. Answersmayvary.Sampleanswer.
a. What is the ratio of consumption of Renewable source of energy to the consumption of coal?
b. Which is the least consumed form of energy?
Challenge 1. a. 21.6° b. 28,800 tonnes
c. June, 1800 tonnes d. 25%
Worksheet 5
1. a. 0 b. 1 c. heads; tails d. 3 2. b 3. 25 26
4. a. 1 2 b. 125 contestants 5. a. 1 6 b. 1 2
6. 1 7. a. 1 6 b. 1 3
8. Answersmayvary.Sampleanswers.
a. What is the probability of getting a prime number?
b. What is the probability of getting a number less than 7?
Challenge 1. a. 18 outfits b. 2 9
Worksheet 6
1. a, b, d 2. 1 6 or 0.16 or 16.67%
3. a. 5 9 or 0.55 or 55.55% b. 40 times 4. 63
5. a. 10 90 or 11.11% b. 53 90 or 58.88% c. 35 90 or 38.88%
d. 27 90 or 30% 6. a. 61 125 or 48.8% b. 64 125 or 51.2%
c. 29 125 or 23.2% d. 25 125 or 20%
Challenge 1. a
Worksheet 7: Chapter Checkup
1. a. 1,04,000 units b. 83,200 units c. 83,200 units d. 5:4 2.
Scale: 1 division = 10 students
A School B
3. a. 3400 cars b. 3600 cars c. 11:14 d. 17.65%
4. a. Items Sold
Others, 36 Rice, 158 Bread, 54
36° 158° Pulses, 67 Spices, 45
b. 54° 72° 80° 90° 64° Sandwiches, 80 Shakes, 90 Burgers, 72 Ice creams, 64 Items Sold Frenchfries, 54
5. No. of Families Owning Pets Others, 16 Rabbit, 12 Dog, 26 Cat, 20 Birds, 6
6. Adventure, 600 Comedy, 760 Books Read Biography, 440 Fantasy, 280 Novels, 320 114° 42° 90° 66° 48°
7. a. Notebooks b. 1 4 c. 15.08% 8. 900 ice creams
9. a. 1 b. 0 c. 1 7 d. 1 e. 1 6
10. a. 1 8 or 0.125 or 12.5% b. 3 8 or 0.375 or 37.5% c. 3 8 or 0.375 or 37.5% d. 1 8 or 0.125 or 12.5%.
11. a. 17 20 b. 3 20
Challenge 1. a 2. a
Worksheet 8: Case Study
1. iii 2. 10,000 3. 3000 4. 84,000
Chapter 5
Worksheet 1
1. a. i. 1 ii. Odd square b. i. 6 ii. Even square
c. i. 1 ii. Odd square d. i. 4 ii. Even square
e. i. 9 ii. Odd square
2. 52 = 25
3. a. 289 b. 1681 c. 1849
4. a. 2401 b. 3481 c. 9604
5. a. 1 + 3 + 5 +
b. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
=
c. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 +
29 + 31 + 33
6. 21, 28, 36, 45; 21 + 28 = 49 = 72, 28 + 36 = 64 = 82, 36 + 45 = 81 = 92
7. a. 25, 24 b. 41, 40 c. 35, 34
8. a. 1624 + 1625 b. 1984 + 1985 c. 2964 + 2965
9. a. 5625 b. 101 c. 9025
10. a. 5775 b. 4352 c. 2600
11. a. (12, 35, 37) b. (16, 63, 65) c. (28, 195, 197) d. (32, 255, 257)
e. (36, 323, 325) 12. 11115556, 1111155556, 333334
13. 9999800001, 999998000001 14. a. 64 b. 289 c. 441
15. a. 22, 32, 42, …, n2 + (2n + 1) = (n + 1)2
b. 22, 32, 42, 52, 62, 72 c. 3136
Challenge 1. Answersmayvary.Sampleanswer.
(3, 4, 5); (5, 12, 13); (8, 15, 17); (7, 24, 25)
Worksheet 2
1. a. 3 or 7 b. 4 or 6 c. 2 or 8 d. 1 or 9 e. 2 or 8
2. Length of each side = 4 units
3. a. 12 b. 6 c. 21
4. a. Not a perfect square b. Not a perfect square
c. A perfect square, 86
5. a. 81 b. 94 c. 142 6. a. 3; 162 b. 2; 102 c. 31; 310
7. 144 8. 36 students
Challenge 1. 5
Worksheet 3
1. a. 1 digit b. 2 digits c. 2 digits d. 2 digits e. 3 digits
2. a. 256 b. 278 c. 324 3. a. 12, 38 b. 59, 72 c. 76, 94
4. a. 17, 75 b. 4, 68 c. 24, 418 5. a. 2.65 b. 6.52 c. 8.88
6. a. 304 b. 10.56 7. 25 m
Challenge 1. 8
Worksheet 4: Chapter Checkup
1. a. 1444 b. 2209 2. a. 1769 b. 4355
3. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35
4. (96, 2303, 2305); (24, 143, 145)
5. a. Not a perfect square b. Perfect square, 46
6. a. 2.81 b. 47.56 7. 21; 811 8. 31.62 m
Challenge 1. Option A 2. Option D
Worksheet 5: Case Study
1. Option B 2. Option B 3. 7200 sq. m 4. ₹9,71,407.36
5. Answerwillvary.
Chapter 6
Worksheet 1
1.
2. a. 3375 b. 17,576
3. i. a. 1 b. 0 c. 3 d. 0
ii. Odd cubes: a, c; even cubes: b, d iii. b, c
4. a. 64 343 b.512 729 5. a. 21.952 b. 1.728
6. a. Not a perfect cube. b. Perfect cube; 24
7. a. 4; 12 b. 4; 8 8. a. 9; 4 b. 15; 7
9. 1331, 8000 10. a. 2025 b. 6084
Challenge 1. No, 12 cubes
Worksheet 2
1.
2. a. 20 b. 25 3. a. 3 b. 6 4. a. 32 46 b.28 51
5. a. 84 cm b. 44 cm 6. a. 65; 7 b. 18; 13 7. 42 cm
Challenge 1. 7; 12
Worksheet 3: Chapter Checkup
1. a. 68,921 b. 2197 343
2. The shaded cube shows the cube of number 3.
3. a. Perfect cube; 94 b. Not a perfect cube
4. a. 2197 b. 4356 5. a. 8 10 or 0.8 b.14 20
6. 61 m 7. 45; 14 8. 13; 17 9. 2058 cu. cm
Challenge 1. 38; 57; 95 2. a. 20 metres b. 160 metres
Worksheet 4: Case Study
1. d 2. a 3. 15.625 cubic metres 4. 23.328 cubic metres
Chapter 7
Worksheet 1
1. a. 20% b. 56% c. 0.45 d. 0.135
2. a. 1 250 b. 1 800 c. 5 8 3. a. 21:10 b. 11:2000 c. 131:200
4. a. 200% b. 30%
5. a. 80%, increase b. 55.55%, decrease c. 10.2%, decrease
6. a. ₹228 b. 105 kg 7. ₹275 8. 4% increase
Challenge 1. a. 1500 smartphones b. 600 smartphones
Worksheet 2
1. a. ₹1000; ₹3000 b. ₹800; ₹3200 2. ₹725 3. ₹725, 5% 4. ₹20,000 5. 6.25% 6. 34%
Challenge 1. 55%
Worksheet 3
1. ₹9440 2. ₹49,220 3. ₹14,500 4. ₹13,000
5. ₹16,000
Challenge 1. 12%
Worksheet 4
1. a. ₹112; ₹912 b. ₹2582.86; ₹3486.84 c. 2.5 years; ₹5700
2. $2550, $22550 3. P = ₹4000, R = 5% p.a. 4. ₹74.79
5. Answersmayvary. Sampleanswer.
Ravi deposits ₹12,000 in a savings account at a local bank. The bank offers a simple interest rate of 6% per annum. Ravi plans to keep his money in the account for 4 years. How much interest will Ravi earn after 4 years, and what will be the total amount in his account at the end of 4 years?
Challenge 1. 3.75%
Worksheet 5
1. A = ₹2141.16, CI = ₹541.16 2. P = ₹4000 3. 3 years
4. a. ₹62,720 b. ₹70,246.40 5. ₹24,972.8
6. SI = ₹500, Difference = ₹25 7. CI = ₹9270
Challenge 1. 20%
Worksheet 6
1. ₹720, ₹8720 2. ₹7500 3. 2.5 years 4. 8% p.a.
5. ₹31,932.23
Challenge 1. Option C
Worksheet 7: Chapter Checkup
1. a. 250% b. 16% c. 380% d. 278.9%
2. a. 23:50 b. 1 1250 c. 101 300
3. a. ₹62.5 b. 2 L 4. a. 20% b. ₹1513
5. 2000 students 6. ₹32,450
7. ₹1800 8. ₹20,000 9. ₹1400 10. ₹42,840
11. a. ₹525; ₹4025 b. ₹3200; ₹3592 c. ₹97.2; ₹2797.2
d. 9%, ₹1800
12. a. ₹5940.5, ₹940.5 b. ₹85,753.152, ₹13,753.152
13. ₹600, 15% 14. 13,225 people
Challenge 1. Option C 2. ₹100
Worksheet 8: Case Study
1. Option b 2. Option c 3. 75% 4. 245,000,000
5. Answerwillvary.
Chapter 8
Worksheet 1
1. a. –x2 + 2x + 3; –x2, 2x b. –x2 + 5x + 6; –x2, 5x
c. –x2 + 4x + 2; –x2, 4x d. 2x + 7; 2x
2. Circle a and d; cross out b and c
3. Figure A: 2 xy + Figure B: 2 yx +
4. a. 2 356 xx++ b. 2 353 xx-+
5. a 543 xy b. 2 1033 xyxy+-
c. 2 215 2 54pp -++ d. 128 7 87pqp++
6. a. 2 28 xx+- b. 3 3 61 2 mnn+-
7. a. 3326 x - b. 11732 42 mm-+
8. a. 59843 aa-++ b. 2 161010 xx++
9. 2 151484 pp+- 10. 3 13616hhth -+
11. 2 (29514) mm-+ metres 12. 2 (10431) ss+- metres
13. Answersmayvary.Sampleanswer: Rohit has (5x + 7) fiction books and (x + 3) non-fiction books in his library. How many books does he have in all?
Challenge 1.
Worksheet 2 1. a.
Expression: (−3x + 2y) (2x + 4) Product:
Expression: (3 – 2
. a.
x4y4z5 b. −6a2b2c + 5abc – 7ab
4. a. −56 b. −3885
5. a. 82 5 b. −24 6. a. −30x5y3z sq. units
b. 56 5
x2 + 1723 25 x − 99 5 sq. units
7. a. 72p3q4r4 cubic cm. b. 7 2 p4q5r5 + 7 2 p4q4r 996 5
8. a. 27s3 (stu + 1)3 cu. cm b. −27s6t9u15 cu. cm 9. −19
10. Answersmayvary.Sampleanswer:
Length = (2x + 5) units; Breadth = (x – 3) units
Area = (2x2 – x – 15) square units.
11. ₹(24x3 – 26x2 – 19x + 6)
Challenge 1. Option a
Worksheet 3: Chapter Checkup
1. a. Binomial b. Monomial c. Trinomial d. Quadrinomial
2. Circle a and d; cross out b and c
3 a. 2 25 x - b. 2 465 xx -++ 4. a. 2 75mm++
b. 32 921 zzz--+
5. a. 6532 15 53 969 22 zzzzz --+-
b. 42 273 xxx -+ c. 42 5 11 13 4 yy -++
6. a. 33823 sss ++ b. 42 141614 ttt -+
7. 32 9342 xxx++-
8. a. −198x3y6z7 b. 8yz2 + 20yz − 24y + 14z2 +
c. −2p5 + 2p4 + 16p3 + 97p2 + 75p – 45
d. −5s2t2u + 3stu – 9st
9. a. −154 b. 7236
10. a. 2027 30 b. 214
11. a. 56x5y3z sq. units b.
12. a. 4 11 p4q5r5 + 4 11 p4q4r 996 5
cu. cm
b. (14p2r – 7pqr + 98pr – 21q2r + 98qr) cu. cm
13. a. 125s3 (stu + 2)3 cu. cm b. 64s6t9u15 cu. cm
14. 2 (102630) xx+- cm
15. ₹100 (10x2 + x – 3) 16. ₹(34x2 − 7x + 28)
17. Answersmayvary.Sampleanswer:
Sana has (x2 + 2x + 3) pencils and the cost of each pencil is ₹(x3 + 4x – 1) What is the price of all the pencils?
Challenge 1. 2 () 620xx + metres 2 Option c
Worksheet 4: Case Study
1. Option a 2. Option b
3. (–136x2 + 4082x – 26392), �80(– 136x2 + 4082x – 26392)
4. (– 140x2 + 4130x – 26470) m2 5. Answersmayvary.
Chapter 9
Worksheet 1
1. 45,216 sq. m 2. 10 cm 3. 225 tiles 4. 192.5 sq. m
5. a. 471 sq. cm b. 168 sq. cm
6. Both John and David 7. 4 m 8. 32 sq. cm 9. ₹54.656
Challenge 1. 3 8 × 3 8 = 9 64 of the original area.
Worksheet 2
1. a. 477 sq. cm b. 485 sq. cm 2. 9 cm
3. 3.62 sq. m 4. 432 sq. cm 5. 5 cm
6. 24 cm and 36 cm
Challenge 1. Option b
Worksheet 3
1. a. 501 sq. cm b. 9064.28 sq. cm
2. a. 269 sq. cm b. 1913 sq. m
3. a. 9 sq. cm b. 10.2 sq. cm 4. 2147.55 sq. m
5. 585 sq. cm; Yes 6. 450 sq. cm 7. 26.2 sq. cm
Challenge 1. 314 sq. cm
Worksheet 4
1. a. 1156 mm2; 1734 mm2 b. 1764 m2; 2646 m2
2. a. 600 cm2; 792 cm2 b. 2412 cm2; 3252 cm2
3. a. 1056 cm2; 1961.14 cm2 b. 484 m2; 561 m2
4. a. 13,828.57 cm2; 14,658.29 cm2 b. 52,800 cm2; 66,000 cm2
5. a. 7.5 cm b. 10 m 6. 384 cm2 7. 19.09 cm
8. 42,240 cm2 9. 7:9
Challenge 1. Option a
Worksheet 5
1. a. i. 4096 cm3 ii. 13,824 mm3
b. i. 1200 cm3 ii. 22,500 cm3 c. i. 385 cm3 ii. 665.28 m3
2. a. 1771 m3 b. 3630 cm3
3. a. 36 cm b. 42 mm c. 0.35 m d. 11 dm
4. 4000 cm 5. 512 cm3 6. 2,80,000
7. 60 8. 1 237 % 2 9. 1:16 10. 1728 cm3
11. 400 12. Answermayvary.Sampleanswer.
A cylindrical water tank has a diameter of 2 meters and a height of 3 meters. The tank is to be filled with water. How much water (in cubic meters) can the tank hold when it is full?
Challenge 1. Option d
Worksheet 6: Chapter Checkup
1. 29.44 sq. cm 2. a. 600 b. 27
3. a. 3375 litre b. 1500 litre c. 6,03,428.6 litre d. 3326.4 litre
4. 20 cm and 100 cm 5. 16 m 6. 53 mm
7. 12.5 cm and 37.5 cm. 8. Always true.
9. a. 1866 sq. m b. 34,997.5 sq. cm
10. a. 39 m b. 30 cm c. 2.55 m d. 12 cm
11. 44 sq. cm 12. 90 m2 13. 240 sq. cm 14. 486 cm2
15. 154 cm3 16. No 17. 19,500 kg 18. 30,000 bricks
19. 13,305.6 g
20. Answersmayvary.SampleAnswer.
A community park is designed in the shape of a rectangle with a semicircle attached to one of its shorter sides. The rectangular part of the park is 40 meters long and 20 meters wide. Find the total area of the park.
Challenge 1. 4 ² 2 cm 2. Option c
Worksheet 7: Case Study
1. Option b 2. Option c 3. 10,560 cm² 4. 600 L
5. Answersmayvary.
Chapter 10
Worksheet 1
1. a. 4096 b. 1 343 c. 64 125 d. 81 16
2. a. 2 3 4 b. 3 1
3. a. 9 4 8 b. 1 5 4 c. 11 7 5 d. 10 9 6
4. a. 4 × 101 + 5 × 100 + 1 × 10−1 + 2 × 10−2 + 3 × 10−3
b. 5 × 102 + 4 × 101 + 1 × 100 + 0 × 10−1 + 5 × 10−2 + 6 × 10−3
c. 1 × 102 + 0 × 101 + 7 × 100 + 0 × 10−1 + 2 × 10−2 + 3 × 10−3 + 5 × 10−4 + 6 × 10−5
d. 5 × 103 + 3 × 100 + 6 × 10−1 + 7 × 10−2 + 1 × 10−3
5. a. 2⁵ b. 2⁷ 6. a. 3 4 6 b. 10 9 1 c. (43)–1 d. (2)−1
Challenge 1. a. 5 : 4 b. 400% c. 1 : 256
Worksheet 2
1. a. 1.098 × 10⁷ b. 2.3 × 1015 c. 1.0446678 × 101
d. 4.5398785 × 10²
2. a. 16 81 b. 49 169 c. 16 81 d. 4 49
3. a. 421000000 b. 0.40857
4. a. 2.11 × 10² > 1.67 × 10−2 b. 7.3 × 10−5 > 0.7 × 10−8
5. a. 1.6562229 × 10⁶ b. 5.19622 × 10⁸
6. a. 243 5 b. 256 7. a. 8 9 b. 3125 2187 c. 243t2 2 d. 2
8. a.x = 3 b. x = 5 9. 0.0028256 inches
Challenge 1. c
Worksheet 3: Chapter Checkup
1. a. 6 × 101 + 5 × 100 + 8 × 10−1 + 7 × 10−2 + 9 × 10−3
b. 9 × 102 + 7 × 101 + 8 × 100 + 9 × 10−1 + 6 × 10−2 + 7 × 10−3 + 5 × 10−4
c. 4 × 103 + 8 × 102 + 7 × 101 + 6 × 100 + 9 × 10−1 + 0 × 10−2 + 2 × 10−3 + 3 × 10−4
2. a. Standard form, 0.00001275 b. Standard form, 1386000000
c. Usual form, 9.11 × 10−29 kg
3. b since it has not been expressed as k × 10n
4. a. 2⁸ b. 310 c. 57
5. a. 9 7 4 b. 8 3 8 6. a. 1 b. 960 7. 495
8. a. Ascending order: 128−2, 83, 210, 642, 323;
Descending order: 323, 642, 210, 83, 128−2
b. Ascending order: 18−2, 93, 273, 310, 7292
Descending order: 7292, 310, 273, 93, 18−2
9. Neither is correct. The multiplicative inverse of a number a is 1 a .
So, the multiplicative inverse of x–2, is 1 x–2 = x2 .
10. a. 18 b. 1250 c. 1
11. a. x = 3 b. x = 13 8 12. 1 13. 4 kg
Challenge 1. Option d 2. y = 2
Worksheet 4: Case Study
1. a 2. c 3. iron 4. 200 : 1
Chapter 11
Worksheet 1
1. a. No b. No 2. a. NO b. YES; 7 12
3. 88, 228, 304, 209 4. ₹3380 5. 300 chocolates
6. 6120 words
Challenge 1. Rani is correct.
Worksheet 2
1. a. No b. Yes 2. 2 3. 1 6 of the work 4. 35 days
5. 2 chocolates 6. 2 8 5 days
Challenge 1. Option d
Worksheet 3: Chapter Checkup
1. a. Direct Proportion; 65 b. Inverse Proportion; 40
2. 2112 g 3. ₹13,500 4. 1 5 of the work 5. 7 boxes
6. 42 men 7. 12 tankers 8. 8 hours 9. 14 7 12 hours
10. 8:24 a.m.
Challenge 1. X is equally efficient to Y. 2. Option b
Worksheet 4: Case Study
1. Option c 2. Option b 3. 1500 sq. m 4. Answerwillvary.
Chapter 12
Worksheet 1
1. a. 3(3) xx + b. 2 22 ( 1) yy -
2. a. 7(3) xxy - b. 2 5(23) abba - c. 3 4(43) pqpq -
d. 23 6(31) mnmn -
3. a. (32)(3) yy+- b. 2(1)(32) xx-+ c. 5(32)(1) yy+-
d. (25)(4) aa+-
4. a. 2 (2)(23) xyx+- b. (32)(2) adbc -+ c. (2)(7) xyx
d. (2)(25) adbc -+
Challenge 1. ₹(41) x +
Worksheet 2
1. a. (4)2 a + b. (5)2 x + c. (2)2 b + d. (9)2 a +
2. a. (2)(2) aa+- b. (5)(5) xx+- c. (34)(34) bb+-
d. (74)(74) pp+-
3. a. (41)2 ax - b. 3(9)(9) xyxyxy +- c. 22 ()()() ababab ++-
d. 2 (9)(9)(9) bbb+-+
4. a. 49 b. 6x c. c2 d. 12r
5. a. 1 4 b. 16 c. 1 d. 25 4
6. a. 22 (4(2)(2) ) mnmnmn +-+ b. (1)(1) abab--++
c. (2)(2) abcabc -+-- d. 2 xy yx +
7. Answersmayvary.Sampleanswer.
Given the expression 9x2 − 24x + 16, factorise it using the appropriate algebraic identity.
Challenge 1. 13 cm, 5 cm
Worksheet 3
1. a. −4x − x b. –8x − x c. –8x − 3x d. –16x − x 2. c
3. a. (31)(23) xx b. (23)(2) xx c. (21)(2) xx
d. (32)(2) xx
4. a. (32); (7)xx b. (52); (7)xx
c. (414); (1)xx d. (21) x - ; (23) x -
5. Answersmayvary.Sampleanswer.
The area of a rectangular field can be given by the expression x2 + 7x + 10. What is the length and width of the garden?
Challenge 1. a. Yes b. Yes 2. 3(1) x +
Worksheet 4
1. a. 2 5 x b. 2 3ab c. 32 4 yz d. 4 2 xy z
2. a. 2 23xx+- b. 3232 yyy -+ c. 432 32 aaa -+
d. 2 32mm-+
3. a. 36abc b. 4(5) ba + c. 2 4(370) aa++ d. 3 () 2 cab +
4. a. Q = 4x – 6 b. Q = 3y2 – 9y + 18 R = 19x – 33 R = –48y + 72
c. Q = x3 + 5x2 d. Q = 6a3 – 15a2 + 39a – 84 R = 16x R = 168
5. a. Q = 3x + 7 b. Q = 2y2 + 6y + 14 R = 18x – 29 R = 86y + 72
c. Q = 3a2 + a 2 + 13 4 d. Q = x2 – x + 4
R = –9a 4 – 1 4 R = 3x2 + 2x
6. 2 53xx-+ 7. (x +2) litres per/day.
Challenge 1. 5 2. 2 a -+
Worksheet 5: Chapter Checkup
1. a. 2(3) xx + b. 3a(b − 3)
2. a. (x + y)(12 – 2x) b. (x − 2z)(x + y −1)
3. a. b(2a − 1)(2a − 3b) b. (5x + 3y)(x − 2y)
4. a. (a + 3b)2 b. (x − 5y)2
5. a. (p + 3q)(p − 3q) b. (2x + 7y)(2x − 7y)
6. a. (6x − 1)(x + 2) b. (x − 2)(x − 3)
7. a. 2 234 xx+- b. 2 24abcbcd -
8. a. Q = 2x2 + 8x + 10 b. Q = 3x3 – 3x2 – 6x + 12 R = 20 R = – 12
c. Q = 2x2 + 7x + 2 d. Q = x3 – 3x2 + 3x 6 5 –R = 2 R = 12 5
9. a. Q = 3x + 13 b. Q = 2x2 + 2x + 1
R = 31x – 25 R = 5x+ 5
c. Q = 3x + 1 2 d. Q = 5x – 16 R = 19x 2 – 3 R = 40x – 18
10. Length Breadth
x (8x + 5y)(8x − 5y)
(8x + 5y) x(8x − 5y)
(8x − 5y) x(8x + 5y)
x(8x + 5y) (8x − 5y)
x(8x − 5y) (8x + 5y)
(8x + 5y)(8x − 5y) x
Challenge 1. (5 – 7x) 2. option d
Worksheet 6: Case Study
1. d 2. b
Chapter 13
Worksheet 1
1. a. True b. True c. False d. False 2. a. Thursday b. Wednesday c. 125% d. 20:17 3.
4. Answersmayvary.Sampleanswer.
The number of books read by two students Ronak and Priya in 6 months is given below. Draw a double line graph representing the given data.
Challenge 1. Option b Worksheet 2
1. a. False b. False c. False d. True e. True
2. a. Abscissa = 9, Ordinate = 4 b. Abscissa = 4, Ordinate = –5
c. Abscissa = 0, Ordinate = 4 d. Abscissa = –2, Ordinate = –8
3. a. y-axis b. x-axis c. x-axis d. y-axis
4. a. Second b. Third c. Fourth d. First
5. Scale: x-axis = 1 division = 1 unit y-axis = 1 division = 20 units
The points do not lie in a straight line.
6. Scale: x-axis = 1 division = 1 unit y-axis = 1 division = 1 unit
7. Scale: x-axis = 1 division = 1 unit
y-axis = 1 division = 50 units
a. ₹350 b. 11 notebooks
8. Scale: x-axis: 1 division = 200 km
y-axis: 1 division = 2 hours
Challenge 1. a. F= 50 + 20d
b. Graph:
Scale: x-axis: 1 division = 5 km y-axis: 1 division = ₹100
– Fare Graph
Worksheet 3: Chapter Checkup
1. a. Abscissa = 5, Ordinate = 4; first quadrant.
b. Abscissa = −8, Ordinate = –2; third quadrant.
c. Abscissa = −9, Ordinate = −8; third quadrant.
d. Abscissa = –5, Ordinate = –10; third quadrant.
Scale: x-axis: 1 division = 1 unit y-axis: 1 division = 1 unit
3. a. The points lie on a line.
Scale: x-axis: 1 division = 1 unit y-axis: 1 division = 1 unit
b. The points lie on a line.
Scale: x-axis: 1 division = 1 unit y-axis: 1 division = 1 unit
4. Scale: x-axis: 1 division = 1 unit y-axis: 1 division = 1 unit
C(4, 0) and B(0, 4)
5. Scale: x-axis: 1 division = 1 year y-axis: 1 division = 2 thousands
6. a. –2; 1.5; ( –2, 1.5) b. 3; 1; (3, 1) c. 1; –3; (1, –3) d. –3; –2; (–3, –2)
7. Scale: x-axis: 1 division = 5 minutes Y-axis: 1 division = 5 m
8. Scale: x-axis: 1 division = ₹100 Y-axis: 1 division = ₹500
x y Simple Interest
Challenge 1. No 2. Option c
Worksheet 4: Case Study
1. b. 20 km/hr 2. 160 km
3. d. 50 km 4. 1 hour
5. Answermayvary.
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 978-81-982034-4-1
