G8_DinoLab_Ebook by Uolo

Acknowledgements

Academic Authors: Muskan Panjwani, Anna Tsoy, Nadezhda Sysonova

Creative Directors: Alena Sizintseva

Book Production: Anastasia Shnip, Anastasia Voitovich

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

This book is sold subject to the condition that it shall not by way of trade or otherwise, be lent, resold, hired out, or otherwise circulated without the publisher’s prior written consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser and without limiting the rights under copyright reserved above, no part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of both the copyright owner and the abovementioned publisher of this book.

Book Title: DinoLab Math Smartbook 8

ISBN: 978-93-89789-46-1

Published by: Uolo EdTech Private Limited

Corporate Office Address:

91Springboard, 3rd Floor 145, Sector 44, Gurugram, Haryana 122003

CIN: U74999DL2020PTC360472

Printed by: Printpro Solutions

All suggested use of the internet should be under adult supervision.

How to get access to DinoLab

Get access to animated interactive courses, Marathons, Olympiads, and much more — all in the Uolo Learn app!

1. Download the "Uolo Learn" app from Google Pay (Android) or AppStore (iPhone).

2. In the app click scanner to scan the QR code below.

Class:

Name:

School:

3. Follow the instruction in the app to access the content.

Welcome to DinoLab!

DinoLab is an AI-powered self-learning platform that helps children learn Mathematics and other subjects step by step, at their own pace. Students can practise and revise every topic digitally and through printed smartbooks.

The DinoLab Mathematics Smartbook is a companion to the digital course. Each exercise has a QR code linking to the Uolo Learn app for continued practice.

Using AI, DinoLab creates a personalised learning path: it explains the concept, gives guided practice, and adapts if mistakes occur — helping students gain clear understanding.

Digital content is presented as interactive flashcards with 50,000+ gamified exercises and animations, making learning engaging and enjoyable.

DinoLab works in Uolo apps and on multiple devices

To use DinoLab on the web, Smartboards, and in computer labs, your school will receive special access for each student and teacher.

Uolo Mobile App SmartboardComputer Lab Smartbooks Tablet and Laptop SMART

How to Use the DinoLab Solution

Once the Uolo Learn app is installed and you are logged in, you can access DinoLab. Our Mathematics course is designed with interactive exercises that help children cover the school syllabus step by step, at their own pace.

1 2 3

Compete and win in Marathons!

• Solve problems and earn points

• Leaderboards of your class, school and all of India

• Get achievement certificates

In this Smartbook, you will find QR codes placed next to the exercises. Simply use the QR scanner inside the app to access the interactive content. QR codes in the smartbook

1 2 3

1. RATIONAL NUMBERS

OPERATIONS ON RATIONAL NUMBERS

1. Fill in the blanks with numbers using the picture. The correct equation should be the result.

2. Put the letters a, b, and c into the circles so that the rule for adding fractions is correct. You can use the same letter more than once.

3. Put x, y, z or + , - signs into the circles so that the rule for subtracting fractions is correct. You can use the same letter more than once.

4. Send the airplanes in the right direction. Connect the airplanes and destinations with lines.

Equal denominators

5. Simplify the expression.

NOT equal denominators

6. Compare the fractions by doing the steps described.

Step 1. Find common denominator and write in the blank

Step 2. Reduce the fractions to a common denominator

Step 3. Compare the fractions you got. Put the same sign into the original expression

7. Place the fractions on the number line.

8. Compare the fractions by doing the steps described.

Step 1. Find common denominator and write in the blank

Step 2. Reduce the fractions to a common denominator

Step 3. Compare the fractions you got. Put the same sign into the original expression

9. Place the fractions on the number line.

10. Choose the 2 correct answer options for each conversation and circle them.

How do you find a common denominator for fractions and ?

To find a common denominator for fractions, you need to find a number that ………………………………………

both 3 and 5

both 1 and 2

both 9 and 4

How do you find a common denominator for fractions and ?

To find a common denominator for fractions, you need to find a number that ………………………………………

both 1 and 4

How do you find a common denominator for fractions and ?

To find a common denominator for fractions, you need to find a number that ………………………………………

both b and d

both b and c can be divided by can be divided by can be divided by divides into divides into divides into

11. Reduce the fractions to the least common denominator.

12. Walk through the maze so that only irreducible fractions appear on your path. Draw the line.

Reduce all the reducible fractions in the maze

Write all the fractions that are greater than one in the boxes

13. Cross out the mistake and write the correct solution below.

14. Simplify the fractions and circle the correct green puzzle piece.

15. Calculate the area of the shaded shape.

How many parts are shaded?

How many parts are there in total?

16. Calculate the area of the shaded shape. Find the side of the shaded rectangle using the picture.

17. Create formulas.

18. Connect the expressions that are equal.

19. Multiply the fractions and simplify them where possible.

20. Find the values that the variable can take in this expression. Tick the correct option.

Any value is OK

21. Welcome to the junk car races! Which car will travel the greater distance before falling apart? Use the data from the table and the formula: S = V × t (where s is distance, v is speed, and t is time). Write the colour of the winning car in the space provided.

The winner is

Speed, V Purple Blue

Red Time, tPath, S=V×t

Answer Answer

22. A waiter needs to divide 4 pizzas into portions. One portion is 2/3 of a pizza. How many portions will there be?

A waiter needs to divide 3 pizzas into portions. One portion is 2/3 of a pizza. How many portions will there be?

23. Put together the rule for dividing fractions.

24. Find and underline the mistakes.

25. Divide.

26. Replace division with multiplication. Fill in the blanks.

27. Connect the expressions that are equal

28. Toddlers at the kindergarten are pouring water into a rubber pool. In 60 seconds, the children fill 1/30 of the pool. What part of the pool will the children fill in:

The pool will be completely filled

The pool will overflow

The pool will be completely filled

The pool will overflow

The pool will be completely filled

The pool will overflow

29. Calculate.

30. Figure out the answers and put them in order from smallest to biggest.

2. SOLVING EQUATIONS IN ONE VARIABLE

SOLVING LINEAR EQUATIONS

1. Write an equation in the blank space.

A game console costs x rupees and a game costs y rupees.

One game console and 2 games cost rupees.

One game console costs rupees more than a game.

The table shows the populations on 3 planets. The population on A-3 planet is the sum of populations on F-9 and S-13

The table shows the populations on 2 planets. The population on H-7 planet is one-third of on TH-5 planet

2. Sort the luggage by the number of variables. Connect with lines.

3. Sort the equations. Connect with lines. x — variable, a, b — some numbers.

4. Is an equation true or false? Mark the correct answer.

If a) Then If b) Then If c) Then If d) Then

5. Select all roots of the equation.

6. Select all the equations with the given root.

The root of the equation is the value of the variable when the equation becomes a true equation the root is8 the root is3

7. Circle the correct answer and find x.

What do you need to do with both parts of the equation to transform x + a into x?

What do you need to do with both parts of the equation to transform –5x + 2 into –5x?

What do you need to do with both parts of the equation to transform –5x into x?

What do you need to do with both parts of the equation to transform into ?

What do you need to do with both parts of the equation to transform into x ?

8. Circle the positive parts of the equation and draw a square around the negative parts.

9. How many roots does the equation have? Mark the correct answer for each equation.

10. Find the value of x using the balancing method.

11. Write the equation and solve it.

12. Choose the correct option and write it in the blank.

How to solve the equation ax = b ?

13. Solve the equations

equals 0?

14. Find the root of the equations.

15. Solve the equations. Write the correct number in the answer field as a decimal fraction.

16. Solve the equation.

17. Solve the problem. The first part of the audiobook is 16 minutes longer than the second. The third part is twice as long as the second. Listening to all three parts takes 40 minutes. How many minutes does the second part last?

18. Solve the problem. The Robo vacuum cleaner cleans an area three times larger than Clean in one hour. Smart cleans 20 m² more than Clean in one hour. Robo and Smart clean equal areas in one hour. What area can Clean clean in one hour?

19. Find the value of x using the cross-multiplication method.

20. Solve the equation.

3. POLYGONS AND QUADRILATERALS

DATA H ANDLIN G

UNDERSTANDING POLYGONS AND QUADRILATERALS

1. Select the correct answers.

What condition must be met for a shape to be a polygon?

The outline must be made of straight line segments

The number of sides must be five or more

Three sides must come out of one vertex

The sides must not cross each other

draw 2 polygons here draw 2 shapes that are not polygons

2. Complete the shape to make a quadrilateral, if possible.

3. Choose the correct option and write it in the blank.

trapezoid parallelogramquadrilateral

rhombus

square rectangle

4. Connect the name of the shape and its description with a line.

trapezoid

quadrilateral

rectangle

parallelogram

rhombus

square

one pair parallel sides

none parallel sides

2 pairs of parallel sides

congruent angles

congruent sides and congruent angles

parallelogram with congruent sides

Answer

5. How many triangles will there be inside a hexagon if you draw all the diagonals from one vertex? Draw and count.

Answer

6. How many triangles will there be inside a 8-gon if you draw all the diagonals from one vertex? Draw and count.

Answer

7. The sum of all interior angles of a convex polygon is 2340°. Find the number of its sides.

Answer

8. What is the sum of all interior angles of a convex 21-gon?

9. Write the numbers in the answer fields in ascending order. Example: 3, 9. What are the side lengths of a parallelogram if one side is 9 cm longer than the other and its perimetre is 66 cm?

Answer

10. Which of the shapes is a trapezoid? Tick it.

11. Which of the shapes is a trapezoid? Tick it.

12. Find the measures of angles M and K in trapezoid TMNK.

13. Choose all correct answers. In which pictures are the legs (non-parallel sides) of the trapezoid highlighted in blue?

14. The diagonals of a rhombus are 10 cm and 24 cm long. Find the area of the rhombus.

4. BAR GRAPHS AND HISTOGRAMS

DATA H ANDLIN G

FREQUENCY DISTRIBUTION OF GROUPED AND UNGROUPED DATA

1. Circle the lower limit of the intervals.

2. Circle the upper limit of the intervals.

3. Write the size of the interval.

4. Find the class mark of the intervals.

5. These are the grades of students for the geography exam. Fill in the frequency distribution table and choose the optimal interval.

6. Find the range between the number of points scored by each basketball team.

Team name

A. Red dragons

B. Fast hawks

C.Brave wolves

Points in games

67,87,58, 93, 54, 97, 56, 74, 61, 55

84,52,49,88, 63, 73, 89, 47,90, 86

Range

68, 54, 92, 80, 46, 65, 55, 48, 81, 70 97 – 54 = 43

7. The given data represents the number of floors on houses in a block: 24, 27, 10, 16, 26, 27, 21, 25, 10, 13, 27, 29, 18, 10, 26, 10, 27, 18, 16, 21. Arrange the data and form a frequency table. Also, find the range of the given data.

8. The picture shows the number of flats in the houses. Analyze the data and make a frequency table. Also find the range of the given data set.

9. During the week, the following number of different types of chocolates were sold in the store.

Milk chocolate: 45, 62, 48, 50, 47, 55, 59

Dark chocolate: 32, 48, 35, 36, 39, 44, 37

White chocolate: 38, 40, 39, 47, 51, 45, 42

Nut chocolate: 65, 70, 58, 67, 59, 62, 61

А. Fill in the table.

B. Determine the range of sales for each type of chocolate.

C. Identify the most and least sold type of chocolate.

D. Calculate the average daily sales for each type of chocolate. Which type has the highest average sales?

1. 1. Milk Milk Milk Dark Dark Dark White White White Nut Nut Nut 2. 2. 2. 3. 3. 3.

The range

10. The boy played the game all week and earned 113 stars. Write his range.

11. The picture shows the discount based on the number of products. Analyze the data and fill in the table.

What kind of discount will the buyer receive if he plans to buy 31 products?

What is the minimum number of products does he need to buy to get a 15% discount?

Answer

12. A group of 11 people wants to go to an amusement park. Together, they weigh 767 kg, and the lowest of them has a height of 143 cm. Write the number of rides that they can all go on.

Answer

13. A girl wants to make pizza. She has 200 grams of flour and 340 grams of cheese. The table shows the amount of these ingredients needed for each pizza. Write down how many types of pizza the girl can make.

14. Circle the correct option.

chart shows how many years different animals live.

many years does a wolf live?

15. Circle the correct option.

The chart shows the length in metres of a football field, basketball, badminton and tennis courts and a swimming track. What is the length of the basketball court?

16. Circle the correct option.

The chart shows how many hours a day different animals sleep.

Which animal sleeps the least? How many hours does it sleep?

17. Circle the correct option.

The chart shows how many tourists visited Chennai in spring and summer. Look, what month was the least number of tourists.

How many tourists came to Chennai this month?

mousesealkoalamonkey

18. Draw the bar to the desired value.

Students marked on the chart the average lifetime of different animals. A rabbit on the average lives 5 years, a cat — 10 years, a horse — 20 years and a lion — 15 years.

19. Draw the bar to the desired value.

The chart shows how much harvest was collected from the third field in a few days.

20. Circle the correct option.

The chart shows the amount of rainfall (in mm) in Mumbai for each month of the year.

How much rainfall was in May?

21. Circle the correct option.

The chart shows the height of the most famous towers in the world: the Leaning Tower of Pisa, the Spassky Tower, the Big Ben and the Tower of Belen in Lisbon. What is the height of the Spassky Tower?

T. of PisaSpassky T.Big BenT. of Belen

22. Draw the bars to the desired value, using the table.

The chart shows how many phones were sold in a few days

23. Draw the bars to the desired value, using the table.

In school there were competitions in mathematics in the spring, summer and autumn. The chart shows how many more students received diplomas than certificates

24. Draw the bars to the desired value, using the table.

The chart shows how many apples were gathered together by the 2nd and 4th teams

25. Draw the bars to the desired value, using the table.

The chart shows how many textbooks the students from different grades used in all three days

26. True or false.

A. The tower of Pisa is higher than the Spassky Tower

B. The lowest tower is the Spassky tower

27. True or false.

A. The wingspan of the albatross is 50 cm larger than of a vulture

B. The wingspan of the marabou is smallest

C. All birds have wingspan of more than 300 cm

28. Label the columns.

The world’s largest fish: whale shark (its length is up to 13 m), belt fish (its length is up to 7 m), blue marlin (its length is up to 5 m)

29. Label the columns.

One of the tallest buildings in the world: «Burj Khalifa» in Dubai — 828 m, the radio tower in Tokyo — 634 m, the Ostankino Tower in Moscow — 540 m

marlin

Graphical representation of Grouped data

30. Average results of the two groups in long jump.

A. What is the result of the Group 2 in June?

B. What is the result of the Group 1 in July?

C. What is the result of the Group 1 and 2 in August?

31. Analyze the histogram and fill in the table.

Visiting the pool

32. Analyze the histogram, fill in the table and answer the questions.

A. Find the day with the maximum number of books issued in each category

B.Calculate the total number of books issued per week

C. What day of the week has the highest demand for books?

D.How many more books were given out on Friday than on Monday?

E. On what day is the difference between the number of books for adults and children minimal?

33. Analyze the histogram and answer the questions.

A. Average company sales per quarter in 2023

B. Average company sales per quarter in 2024

C. The company’s sales in 2023 amounted to

D. The company’s sales in 2024 amounted to

E. Company’s average sales per quarter over 2 years

F. What is the ratio of quarters in which the company’s sales were above average to those in which they were below average?

34. Analyze the histogram and answer the questions.

Number of boxers in competitions in weight categories

number of boxers

A. How many weight categories are shown in the table?

weight category, kg

B. Which weight category has the largest number of boxers?

C. Which weight category has the fewest boxers?

D. Which weight category has the largest number of boxers?

E. Which categories have the same number of participants?

F. How many participants were there in the competition?

G. How many boxers are heavier than 64 kg?

H. What is the ratio of boxers weighing lighter than 69 kg and heavier than 69 kg?

35. The table shows the number of students, depending on the books they read over the summer. Draw a histogram for the given data.

number of students

36. The table shows the number of students, depending on the time it takes them to run 50m. Draw a histogram for the given data, sign the axes.

37. Compare the histograms and answer the questions.

Number of buildings above 100 m in the city A

number of buildings

Number of buildings above 100 m in the city B

number of buildings

The city A has the most buildings with a height of 100-110 m.

The city B has the most buildings with a height of 100-110 m.

There are more 140-150 m tall buildings in city A than in city B

There are fewer 160-170 m high buildings in city A than in city B

There are 30 buildings in the city A with a height of 110-120 m

There are 10 buildings in the city B with a height of 170-180 m

height of buildings, m

G. There are more buildings in city A with a height of 120 to 130 m than in city B.

H. There are more buildings in city A with a height of 130 to 140 m than in city B.

I. There are no buildings between 190 and 200 m high in City A.

J. The number of buildings 160-170 metres high in city A is equal to the number of buildings 130-140 m high in city B

K. There are twice as many buildings in city A that are 150-160 m high as in city B

5. PIE CHARTS

DATA H ANDLIN G

DRAWING AND READING PIE CHARTS

1. Choose the answer to the question in the pie chart. Put a checkmark next to the correct answer. The pie chart shows the number of species belonging to different orders of mammals. Which order has the fewest species?

Insect eating

Primates

Predators

Rodents

Bats

Insect eating

Primates

Predators

Rodents

2. Choose the answer to the question in the pie chart. Put a checkmark next to the correct answer. The pie chart shows the amount of rainfall in spring and summer in the Australian city of Melbourne. Which month has the largest rainfall?

July

June

March

April

May

August

In April

In May

In June

In August

3. Choose the answer to the question in the pie chart. Put a checkmark next to the correct answer. The pie chart shows the area occupied by the world’s largest islands. Which island is larger than Madagascar but smaller than New Guinea?

Greenland

New Guinea

Borneo

Madagascar

Greenland

Borneo

New Guinea

Madagascar

4. Choose the answer to the question in the pie chart. Put a checkmark next to the correct answer. Is it true that it is recommended to eat 4 times more fruits and vegetables than fats?

fruits and vegetables

good carbs

fat

protein

True

False

Not enough information

5. Find the answer on the Pie Chart and write it in the blank space. The pie chart shows how the largest volcanoes on the continents of the Earth are distributed. How many volcanoes are in North and South America?

Answer: volcanoes

6. Find the answer on the Pie Chart and write it in the blank space. The pie chart shows the amount of different nutrients in a 100-gram piece of cake. How much fat is in the piece of cake?

7. Find the answer on the Pie Chart and write it in the blank space. The pie chart shows the number of satellites the giant planets of the solar system have. How many more satellites does Jupiter have than Uranus?

8. Find the answer on the Pie Chart and write it in the blank space. The pie chart shows how the seas are distributed among the four oceans. How many seas do not belong to the Atlantic Ocean?

9. Circle the correct pie chart. The pie chart shows how the countries of the world are distributed across the continents. 50.5% of all countries are in Eurasia, 12.6% — in North America, 6.7% — in South America, 30.2% — in Africa.

Eurasia

North America

South America

Africa

10. Circle the correct pie chart. The pie chart shows the annual rainfall in different natural zones in a year. 5.4 cm falls in the forests, 3 cm — in the prairie, 3.7 cm — in the boreal forest; 2.4 cm — in the cold desert.

prairie forest

boreal forest

cold desert

Indian

Atlantic

Arctic Pacific

11. Circle the correct pie chart. The pie chart shows the area occupied by different oceans in the World Ocean. The Atlantic Ocean covers 92 million km2, the Pacific Ocean 179 million km2, the Indian Ocean 76 million km2, and the Arctic Ocean 15 million km2.

12. Circle the correct pie chart. The pie chart shows the population of the four largest cities in Europe in 2016: St. Petersburg – 5 225 690 people, London – 8 416 999 people, Moscow – 12 330 126 people, Berlin – 3 479 740 people.

London

Moscow

St. Petersburg

Berlin

13. In a class of 30 students, a vote was held to choose a destination for a school trip. The results were:

Sports event: 12

Science Museum: 9

Amusement Park: 6

Nature Park: 3

Color the pie chart. Don’t forget about header and legend.

Sports event

Science Museum

Amusement Park

Nature Park

14. Steve created a pie chart showing how he spent his 24-hour day. However, there are mistakes in the angles.

Sleep: 100°

School: 70°

Homework: 50°

Free time: 70°

Eating and chores: 60°

Add up the angles. Does the total equal 360°? Fix the mistake in the list however you like, as long as the total adds up to 360 degrees. Draw a pie chart.

6. PROBABILITY

UNDERSTANDING PROBABILITY

1. Find the certain and impossible events. Mark certain events with the letter C and impossible events with the letter I.

There will be a full moon on February 31st.

The sum of the angles of a rhombus will be equal to 360 degrees.

Among lottery tickets numbered from 1 to 100, the winning ticket will be the one with number 127.

When rolling a fair die, a number from 1 to 6 will come up.

There exist two lines that intersect at more than one point.

2. Find the elementary events. Mark them with checkmarks.

A red ball will be drawn when taking a ball from a bag containing red and blue balls.

When flipping two fair coins, at least one of them will land heads up.

In a test with 15 questions, a student will answer no more than 7 questions correctly.

When rolling two fair dice, the first die shows 1 and the second die shows 6.

When randomly choosing two integers, the product of the selected numbers will be less than 0.

3. Choose the correct answer.

If a fair die is rolled in a board game, what is the probability that 4 dots will come up?

4. Write your answers in the blanks.

A music teacher plays one note out of seven. What is the probability that this note is C?

A bag contains five balls of different colors: red, yellow, green, blue, and orange. What is the probability of pulling out the green ball?

In a certain random experiment, there are exactly two elementary events. The probability of one of them is 0.57. Find the probability of the second event.

5. Choose the correct answer. A football team has 11 players: 1 goalkeeper and 10 field players. The coach randomly selects one player for an interview after the match. What is the probability that the selected player will be the goalkeeper?

6. Choose the correct answer. In a biology exam, there are 35 tickets in total, and 28 of them include a question on “Zoology.” Find the probability that a randomly selected ticket will contain a question on this topic.

7. Choose the correct answer. A mechanical clock with a 12-hour dial stopped working at some point and stopped moving. Find the probability that the hour hand stopped after reaching the 7 mark but before reaching the 1 mark.

8. Choose the correct answer. When baking a cake, it is weighed to check its mass. We know that: The probability the cake weighs less than 950 grams is 0.99. The probability the cake weighs more than 900 grams is 0.94. Find the probability that the cake’s mass is more than 900 grams but less than 950 grams.

9. Fill in the blanks. Employees at the copying center decided to find out how many sheets with unprinted text the old printer produces in one day. Out of 200 printed sheets, 56 had unprinted text.

The total number of identical trials conducted is _____

The number of trials in which the random event “sheet with unprinted text” occurred is _____

The frequency of the random event “sheet with unprinted text” in this series of trials is _____

10. Fill in the blanks. A bag contains 50 marbles. You randomly draw a marble from the bag, record its colour and then replace it. The table shows the results after 30 draws.

Find the experimental probability of drawing a red marble

Answer

Predict the total number of the red marbles in the bags

Answer

11. Choose and circle the correct answer. Over a 24-hour period, a parking attendant randomly recorded the color of each arriving car. A total of 80 observations were made, out of which 32 cars were white and the rest were black.

a) What is the experimental probability that the next arriving car will be black?

b) How many white cars would you expect among the next 90 arriving vehicles?

7. SQUARES AND SQUARE ROOTS

SQUARE OF A NUMBER

1. Fill in the blanks in the table of squares.

2. Sort expressions into carts. Connect with lines.

3. Circle the negative numbers and draw a square around the non-negative numbers.

4. Choose a word from the given options and write it in the blank. You may use the same word more than once.

Positive number squared is

Negative number squared is

Zero squared is

Any number squared is

5. Circle the numbers that can be squares of another number.

6. Calculate the side length from the figure and then calculate the area of the square.

7. Calculate. m 1m

8. Put a checkmark next to the correct statements.

Positive number squared is negative

6 is greater than the square of 2

3 squared is equal 9

The square of a number is always less than the number

9. Guess how to get the second and third rows of the table from the first row, then fill in the blanks.

10. Find the following products using the rule.

SQUARE ROOTS

11. Find the side of the square.

64m² m

How to find the length of one of the sides? m

The area should be divided by the number of sides

Find the number which square is equal to the area

Divide the area by two

12. Find the side of the square.

121m² m

13. Find a,b,c. m

14. Calculate the expressions.

15. Choose a number from the given options and write it in the blank.

= 2.25

16. Choose a number from the given options and writeit in the blank.

= 169

17. Choose a number from the given options and write it in the blank.

a) 5.0625

18. Find the square roots of the following decimal numbers.

b) 33.64

c) 92.16 2 4 3 A

19. One of the numbers √5, √8, √11, √14 is marked on the number line at point A. Which number is it?

20. One of the numbers √10, √15, √19, √26 is marked on the number line at point A. Which number is it?

21. The length and breadth of a rectangular room are 12 m and 5 m, respectively. What is the length of the longest straight line that can be drawn on the floor of the room? 2 4 A 3

DATA H ANDLIN G

8. CUBES AND CUBE ROOTS

CUBE OF A NUMBER

1. What is the length of a cube if the width and height are 2 cm?

2. Find the volume of each box. Choose which box is more spacious.

3. А wooden block was cut into cubes with an edge length of 1 cm.

Write down the dimensions of the cube:

A. Length cm

B. Width cm

C. Height cm

D. Fill in the table

1cm

4. How many small cubes will this cube make?

5. Fill in the blanks and solve the examples.

a) 1³ + 2³ + 3³ + 4³ + 5³ = (1 + 8 + + + 125) = 225 = ( )²

b) 1³ + 2³ + 3³ + 4³ + 5³ + 6³ = (1 + + + + + = = ( )²

c) 1³ + 2³ + 3³ + 4³ + 5³ + + = (1 + + 27 + + 125 + + = 289 = = ( )²

6. Find the difference.

35³ – 34³

B. 58³ – 57³

C. 92³ – 91³

7.Find the cube.

A. –9³ –17³ –5³ –100³

C. (1.6)³ (0.25)³ (1.42)³ (15.2)³

8. Check the numbers are perfect cubes using prime factorisation .

12673 42875

1009875 238328

9.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.

10.Find the smallest number by which the number should be divided to get the perfect cube in each case.

11. How many packages of light bulbs 3cm x 4cm x 2cm, can fit into a shipping box, which is a perfect cube with sides of 50 cm.

A. 108

B. 250

A. 1024

B. 2592

cube root of a number

12. Which of these figures represents the cube of a number in each row.

13. Shade the side to show the cube root.

А. Of 27

B. Of 125

D. Of 343

C. Of 1000

14. Connect the missing shapes to make a perfect cubes.

15. Find the cube root.

16. Find the cube root.

17. Fill in the gaps.

18. Fill multicolored gaps and find the cube root using prime factorisation.

A. 5832

4096

13824

19. Find the cube root of the numbers using successive subtraction.

A. 64

B. 512

C. 3375

20. 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. 9520

B. 131

C. 5000

D. 1200

21. Find the smallest number that must be added to each number to make it a perfect cube. Also, find the cube root.

A. 29650

B. 11925

C. 6500

C. 4448

22. A set of expensive dishes was placed in a wooden box with a volume of 39,304 cm³, which needs to be taken to another city. Will it fit in an empty car trunk if its length is 1040 cm, height is 480 cm, and width is 1080 cm?

23. A box with a vaccine, the volume of which is 10,648 cm3, should be placed in the thermobox for medicines. Will it fit if the side of a cubic thermobox is 25 cm?

24. A shipping box is an ideal cube. Its volume is 64cm³. It is now 75% loaded with boxes that represent perfect cubes, with a length of 1 cm. How many boxes do I need to load to fill the cube completely?

9. PERCENTAGE AND ITS APPLICATIONS

percentaGe and percentaGe chanGe

1. The cost price of computer is ₹90,000. What is the profit if the selling price is:

A. ₹1,70,000

B. ₹2,20,000

C. ₹3,10,000

2. The cost price of grocery basket is ₹1000. What is the loss if the selling price is:

A. ₹456

B. ₹743

C. ₹899

3. Car dealership sold the car. Write down SP if:

CP = ₹2,53,000 Profit 24%

D. CP = ₹15,00,000 Profit 7%

B. CP = ₹9,00,000 Profit 40%

C. CP = ₹12,00,000 Profit 60%

4. Mark sold the smartphone for ₹12,000.

A. What was its cost price if the loss was 7%

B. What was its cost price if the loss was 26%

C. What was its cost price if the loss was 57%

5. Combine the cost and the selling price to get the profit 5%.

6. Combine the cost and the selling price to get the loss 15%.

7.A shopkeeper sells two laptops for ₹80,000 each. On one laptop, he makes a profit of 15%, and on the other, he incurs a loss of 15%. What is the cost price of each laptop, and what is his total profit or loss percentage?

8. The owner of a stationery store bought 200 pens at a price of ₹2.5 per piece. Unfortunately, 12 handles turned out to be defective during transportation and had to be written off. The remaining pens were sold for ₹3.2 a piece. Calculate the percentage of profit or loss.

9. When selling household appliances for ₹2,38,000, the seller incurs a loss of 12%. At what price do you need to sell this equipment to make a profit of 7%?

10. Jane has a family-owned jam business. She made jam with a total cost of 8500 rupees. They sold half of the entire batch (1/2) at a loss of 10%. Misha wants to get a total profit of 25% on all the jam. At what profit percentage should the rest be sold?

11. The marked price of a TV is ₹2,40,000. Find the discount and the selling price if the rate of discount is given.

A. Discount 15%

Discount 8%

12. Find the selling price, if marked price ₹18,350.

13. Find the percentage of the discount, if marked price was ₹32,000?

14. Tickets for the tour were sold at a 15% discount, and on the day of the tour they cost another 15% cheaper. What was the regular ticket price if the tourists bought them for ₹4700 on the day of the tour?

15. The kettle was sold for a third of the price, but due to a scratch on the case, the seller made another 20% discount. What is the discount percentage and the regular price of the kettle if Robin bought it for ₹1200, including all discounts.

A. Discount offered ₹5370

B. Discount offered ₹3490

16.Dishwasher costs ₹56,000. What amount should Anny give to the shopkeeper if the GST is 23%?

17. Dan bought a laptop for ₹56,340 that included GST of 14%. Find the price of the laptop before the GST was added.

18. Arash bought a lawn mower for ₹1,32,750 that included GST of 7%. Find the GST in rupees.

19. Find GST if the radio receiver cost ₹34,500 before paying the tax, and after ₹37,260.

20. Ravi got a discount of 15% on the computer he bought. The marked price was ₹1,55,000 for the computer. How much did he pay?

A. If he had to pay a tax of 12% on the price at which he bought it

B. If he had to pay a tax of 9% on the price at which he bought it

21. The furniture factory produces wooden chairs and sells them at a price of ₹4290 per piece, including 7% GST. At the same time, the manufacturer makes a profit of 25% of the sale price without GST. Determine the production cost of one chair.

22. Sabyasachi decided to upgrade his home office and bought:

Office desk for 95,000 rupees

Executive chair for 45,000 rupees

Filing cabinets for 75,000 rupees

All of these products are subject to a GST of 8%. Calculate the total amount that Sabyasachi has to pay for the entire purchase, including tax.

23. The cost of 20 cups of coffee without tax is equal to the selling price of 16 cups of coffee with tax. What is the tax percentage?

24. The family wants to buy household appliances. Calculate the purchase amounts in both stores. Compare which store is more profitable to do this if the VAT on household appliances is 20%.

10. COMPOUND INTEREST

1. Fill the table.

2. If Mattew wants to make a profit of ₹300 in 3 years. Which deposit should he choose?

3. Amar plans to place a deposit of ₹15,000 in Summa Bank for a period of 2 years. The Bank offers an interest rate of 3.75% per annum under the simple interest rate Calculate:

A. The amount of interest you will receive for the entire period.

B. The total amount in the account at the end of the deposit period.

4.The client deposited ₹4200 in the bank on February 15, 2023 at 8% per annum. Calculate the amount of accrued interest.

A. by May 10, 2023.

B. by July 17, 2023.

5. Find the amount and the compound interest on ₹98,500 for 4 years at 7% per annum, compounded annually.

6. Raj borrowed ₹9000 from his brother and returned after 3 years the amount of ₹10,300 , along with accrued interest. What annual interest rate did Raj pay his brother?

7. Which will earn more interest, and how much?

A. ₹25,000 lent at 10% per annum compounded annually for 2 years.

B. ₹25,000 lent at 10% per annum compounded semi-annually for 2 years.

8.The bank offers several deposit options with different interest accrual conditions. Compare the profitability of each option over 3 years with an initial contribution of ₹2,00,000.

9. Researchers have recorded that the population of a small resort town is growing at an annual rate of 8%. If 850,000 people live in the city now, what will the population be like in 2 years while maintaining this growth trend?

10. Amit bought commercial real estate for ₹30,00,000 Market analysts predict an annual increase in prices for such facilities by 7%. Find what the cost of the property will be in 4 years, while maintaining the current price growth trend.

A. 986440

A. 38,32,388

C. 39,32,388

D. 36,32,388

B. 37,32,388

C. 991440

D. 901440

B. 891440

11. The company bought musical equipment for ₹9,50,000 in 2021. The management plans to sell it in 2024. The depreciation rate of the equipment is 35% per year. Find at what price the company will be able to sell the equipment in 2024, taking into account depreciation.

12. Choose the correct option.

Assertion (A): Priya invests ₹2,50,000 at 8% per annum compounded annually for 3 years. She will receive ₹3,14,928 after 3 years.

Reason (R): The amount after compound interest is calculated as principal multiplied by (1 + rate) raised to the power of time.

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

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

A is true, but R is false.

A is false, but R is true.

A. 2,70,894

C. 2,60,894

D. 2,60,894

B. 2,50,894

11. ALGEBRAIC EXPRESSIONS

DATA H ANDLIN G

addition and subtraction of alGebraic expressions

1. Fill the table.

2. Look at the given algebraic tiles. Write algebraic expressions for the tiles.

3. Sort the expression as monomials, binomials, trinomials, quadrinomials.

Monomials

Trinomials

Binomials

Quadrinomials

4. Find and connect the pairs of like terms.

5. Combine a numerical and a literal expression.

A. The square of the difference between m and n, reduced by the tripled product of these variables.

В. The sum of the square of x and the triple of y, increased by the product of x and y.

C. The difference between triple the product of m and n, quadruple m, and n.

D. The quotient of the sum of p and q divided by triple the sum of these same numbers.

E. The product of the sum of p and q and their difference.

F. The quotient of the product of m and n divided by triple the product of these same numbers.

6. Add or subtract the following algebraic expressions.

7. Add or subtract the expressions vertically.

8. Simplify the expressions.

9. Find the missing expression and connect with the lines.

a) 1)

b) 2)

c) 3)

multiplication of alGebraic expressions

10. Finish drawing algebraic tiles to find the product of the given polynomials.

11. Find the area of the rectangular painting.

12. Find the area and verify the result for the values of the variables.

14. Imagine that you are an architect designing an unusual amusement park. It is planned to build a magic cube in the center of the park, the size of which depends on the number of visitors on different days of the week.

The length of the magic cube is determined by the formula:

(x + y + z) metres, where:

x — number of children under 12 years of age

y — number of teenagers aged 12-18

z — number of adult users

Cube width: (2x – y + 3z) metres

Cube height: 5xy metres

Task:

A. Create a formula to calculate the volume of the magic cube

B. Calculate the volume if on Saturday:

Children under 12 years old: 100 people

Teenagers: 50 people

Adults: 200 people

C. Calculate the volume if on:

Children under 12 years old: 200 people

Teenagers: 130 people

Adults: 170 people

15. In the future, humanity is building a cuboid-shaped space station. The size of the station is determined by special parameters depending on the number of research laboratories.

Station length: (3a + 2b) kilometres, where:

a — number of physical laboratories

b — number of biological laboratories

Station width: (a2 – b + 5) kilometres

Station height: 4ab kilometres

Station Features:

Each physical laboratory occupies a volume of 1000 km³

Biological laboratory — 1500 km³

The station also has living quarters and recreation areas.

Task:

A. Create a formula to calculate the total volume of the station

B. Calculate the volume of the station if:

Physical laboratories: 5

Biological laboratories: 3

C. Determine how many laboratories can be placed at the station

D. Find the volume that will remain for the living quarters

12. AREA OF POLYGONS

area of fiGures made with polyGons

1. A shape is formed by a trapezoid with bases 8 cm and 14 cm and height 5 cm, and a semicircle constructed on the longer base of the trapezoid as its diameter. Find the total area of the shape. (Use π ≈ 3.14.).

2. A right triangle with legs 6 cm and 8 cm is attached to a rectangle measuring 8 cm × 5 cm, such that the 8 cm leg coincides with one side of the rectangle. A semicircle is constructed outwardly on the triangle’s hypotenuse. Find the total area of the composite shape. (Use π ≈ 3.14.).

3. A shape consists of a rectangle with sides 10 cm and 6 cm, with an isosceles triangle on top. The triangle has a base of 10 cm and a height of 4 cm. Find the total area of the shape.

4. A circle is cut out from a square with side length 12 cm. The diameter of the circle equals the side of the square. Find the area of the remaining part of the shape. (Use π ≈ 3.14.).

5. Calculate the area of the shapes.

The area of this square is 1

6. Complete the triangles to form rectangles and calculate their areas using subtraction.

The area of this square is 1

7. Is there enough information to calculate the area of the shape? Mark the right answer.

8. Calculate the area of the shapes above, where possible.

9. Calculate the area of the shapes. Round the answer to the nearest whole number

13. SURFACE AREA AND VOLUME OF SOLIDS

SURFACE AREA

1. Find the surface area of a rectangular prism (parallelepiped) if the length of the base is 6 centimetres, the width is 4 centimetres, and the height is 3 centimetres.

2. Find the lateral surface area and total surface area of a cylinder if radius and height of the cylinder are 2 cm and 5 cm respectively (Take π= 22/7).

Answer

3. 30 identical circular discs, each with a radius of 15 cm and a height (thickness) of 1.5 cm, are stacked vertically to form a solid cylinder. Calculate the total surface area of the resulting cylinder, including both circular bases and the lateral surface.

4. The edge of a cube is 8 cm.A cardboard net of this cube needs to be made, with a 1 cm glue flap added to each side of every face where joining is required. A cardboard sheet measuring 40 cm × 25 cm is available. Will the net of the cube (including all glue flaps) fit on this sheet?

5. Find the area of the shaded shape (blue).

Answer

6. Find the surface area of a cube with a given volume.

Answer

7. Calculate the height of a tower made of 4 cubes, knowing the volume of each cube.

8. A ladybug is crawling on a cube. Its path is shown in the picture in red. Calculate how far it has crawled.

DATA H ANDLIN G 14. EXPONENTS AND POWERS

exponents

1. Help the scientist choose the substance with the largest number of particles. Circle the correct flask

2. 1) Write down the numbers in expanded form using powers of 10:

A. 234.56

B. 7089.004

C. 0.12345

D. 6000.0078

E. 9876.54321

Additional tasks:

2) For each number, determine the sum of all the coefficients.

A. 234.56

B. 7089.004

C. 0.12345

D. 6000.0078

E. 9876.54321

3) Find the number with the most significant digits.

4) Determine which number has the largest power of 10.

3. Replace the fraction with a power with a negative integer exponent.

4. Replace the power with a negative integer exponent with a fraction.

5. Calculate.

6. Calculate.

7. Calculate.

8. By what number should be divided to get a quotient of 25?

9. By what number should be multiplied to get a quotient of 225? 4

10. Write it in the standard form and determine which planet is more distant.

11. Exponentiate the fraction.

12. Simplify the expression.

13. Write the missing number.

14. Find the unknown.

15. Calculate.

15. DIRECT AND INVERSE PROPORTIONS

PROPORTIONS

1. Calculate the ratio of the numbers of floors in the blue building to the the numbers of floors in the pink building.

2. Fill in the blanks using numbers from previous task.

There are times more floors in the blue building than in the pink one

3. Write the ratio of the number of motorcycles to the number of cars.

: : 3 == 3

4. Calculate the ratio of the numbers of floors in the blue building to the the numbers of floors in the pink building.

Number of flowers takes of number of cacti : 7 : 4 == 4 3

5. Correct a mistake using numbers from previous task and fill in the blank with a decimal number.

6. Circle the right picture.

7. Choose the right picture. Fill in the blanks with the letter corresponding to the correct answer.

Case1. There are 3 times more glasses with orange juice than with apple juice

Case 2. There are 2 times more glasses with orange juice than with apple juice

8. Choose the right ratio of glasses with orange juice to number of glasses with apple juice. Use the cases from the previous task.

9. Mark all correct answers.

The ratio of glasses with orange juice to number of glasses with apple juice is

10. Mark all correct answers.

The ratio of glasses with orange juice to number of glasses with apple juice is

Case 1. Case 2.

11. Calculate the ratio: the mass of the burger to the mass of the french fries.

12. Fill in the blanks using numbers from previous task.

Burger is times heavier than the french fries

13. Calculate the ratio: the mass of the burger to the mass of the ice-cream.

14. Fill in the blanks using numbers from previous task.

Burger is times heavier than the ice-cream

15. Choose the correct answers from the options provided and fill them in the blanks.

What is the ratio of the number of bagels to the number of cupcakes?

2:41:41:32:3

16. Mark the correct answer.

The height of the Sphinx to the height of the Pyramid of Cheops is

Pyramid of Cheops Sphinx

17. Mark the right statement.

The weight of the panda to the weight of the koala is 137 : 15

The panda is times heavier than koala

The panda is kg heavier than koala

18. Check Direct Proportionality and complete the Table.

a) Determine whether the quantities x and y are directly proportional. If they are, state the constant of proportionality.

Direct proportionality: T / F

Constant of proportionality: ______

b) The variables x and y are directly proportional, and the constant of proportionality is 2.5. Complete the missing values in the table.

19. Check Inverse Proportionality and Find Missing Values.

a) Decide whether the quantities m and n are inversely proportional. If yes, write the constant of proportionality.

Inverse proportionality: T / F

Constant of proportionality: ______

b) The variables p and q are inversely proportional. It is known that when p = 8 , q = 9 .

Use this information to complete the table.

20. 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.

21. Complete the table if x and y vary in direct proportion.

22. Manish can type 960 words in 15 minutes. How many words will he type in 2 hours?

Answer

23. A cyclist covers 72 kilometres in 4 hours. How many kilometres will he cover in 7 hours at the same speed?

Answer

24. Ravi can complete a job in 20 minutes. He works alone for 5 minutes, and then Meena takes over and finishes the remaining work in 15 minutes. How long would it take for Ravi and Meena to complete the entire job if they worked together from the start?

Answer

25. Pipe X can fill a pool in 24 hours. Pipe Y can fill the same pool in 12 hours. Meanwhile, Pipe Z can empty the full pool in 48 hours. If all three pipes are opened simultaneously, how long will it take to fill the pool?

16. FACTORISATION AND DIVISION OF ALGEBRAIC EXPRESSIONS

factorisation of alGebraic expressions

1. What is the greatest factor that can be factored out? Choose the correct answer.

2. Factor out the common factor. Write the answer as a digit and a Latin letter.

3. Factorise the expressions by identifying the common binomial.

4. Factor out the common term from the parentheses.

5. Answer three questions about the problem.

The width of the plot is x metres, and its length is 4 metres more than the width. A fence is being built around the plot, and two additional partitions parallel to the width (each x metres long) are installed to divide the plot into three parts

1) Write an expression for the total length of the fencing

2) Simplify the expression and write it as a polynomial

3) Factor out the greatest common factor

6. Factorise the expressions by regrouping the terms.

7. Express the trinomial as a product of two identical factors:

8. Fill in the blank by choosing a monomial so that the trinomial can be written as the square of a binomial.

9. Find the value of the expression when a = 4.

11. Find the value of the expression when a = 1. 1) 2) 3)

10. Find the value of the expression when a = 3.

12. Simplify the expressions.

13. Fill in the blanks.

14. Calculate, using the difference of squares formula.

15. Factor the polynomial. Mark the correct answer option.

16. Divide the monomials by the monomials. Simplify your answers completely.

17. Divide the polynomials by the monomials.

16. LINEAR GRAPHS

DATA H ANDLIN G

line Graphs and linear Graphs

1. Mark the point and complete the water level graph.

The graph shows the water level in the Ganga River during major floods.During the flooding in 1986, the water in the Ganga River rose to a level of 2.6 m

2. Mark Anusha’s height at 5 years and complete the graph.

At 4 years, Anusha’s height was 1 m, at 5 years — 1.1 m, in 6 years — 1.15 m, at 7 years — 1.2 m. When she was 8 years old, her height was 1.25 m

5. Answer the questions using the graph.

The graph shows how the price on sandals changed for several months. How much did sandals cost in September?

6. Answer the questions using the graph.

Parth showed on the graph how the length of the shadow of the metre column changed over time. What was the length of the shadow at 12 o’clock?

7. Answer the questions using the graph.

The graph shows how the altitude of the helicopter varied during the flight. How many minutes after the flight began, the helicopter reached the highest altitude?

8. Answer the questions using the graph.

Hydrologists noted on a graph the change in the water level in the Ganga River. What is the highest level of water in the river?

9. Is the statement true.

The graph shows the population of France in the first half of the 20th century

A. In 1930, the population of France was 45 million people.

B. In 1920 in France lived the least people.

C. The population of France in 1910 and 1930 was the same. True False True False

10. Answer the questions using the graph.

The graph shows the water temperature in the Black Sea during the holiday season. The water temperature in the Mediterranean Sea in July is 5°C higher than in the Black Sea. What is the water temperature in the Mediterranean Sea in July?

11. Answer the questions using the graph.

The graph shows how many minutes you need to wait for a bus at the stop at different times of the day. You need to wait for a tram 5 minutes less. How many minutes do you need to wait for a tram at 17 o’clock?

12. Select the answer using the graph lines.

The graph shows how the altitude of the helicopter varied during the flight. Selected all the times when the helicopter was at an altitude of more than 900 m.

13. Select the answer using the graph lines.

The graph shows how the population of the Earth changed in the second half of the 20th century.

How much has the population of the Earth increased from 1960 to 2000?

14. Select the answer using the graph lines.

The graph shows how the car route between two cities. How many kilometres did the car pass from 14:00 to 16:00?

15. Is the statement true.

from Mumbai, km

The graph shows the route the bus Mumbai — Delhi — Mumbai.

A. After 2 hours of travel, the distance to Mumbai was 25 km more than after 5 hours.

B. From the first to the fifth hour of the journey, the distance to Mumbai only increased.

16. Is the statement true.

Hydrologists made a graph of the water level of a small river in India.

A. The water level in the river in April and October was the same.

B. The lowest water level in the river was in May.

17. Is the statement true.

The graph shows how the population of the Earth changed in the second half of the 20th century.

A. The population of the Earth grew by 0.8 billion from 1970 to 1980.

B. From 1980 to 2000, the population of the Earth continued to grow.

The graph shows how many people visited the web site each month.

A. The number of visitors increased from November to January.

B. In October, the site was visited by more people than in any other month.

19. Is the statement true.

The graph shows how the temperature of the air changed for three days.

A. It was 3 °C colder on first day at 12:00 than on the second day at the same time.

B. The lowest temperature was on the second day at 0:00.

The graph shows how the eucalyptus grows during its lifetime. How tall is it at the age of 25? temperature, oC

20. Answer the question using the graph.

ANSWERS

1. Rational Numbers (p. 1 - 16)

4. equal: not equal: 5.

can be divided by both 9 and 4 can be divided by both b and d 11.

numerator of the dividend

denominator of the dividend × ×

numerator of the divisor

denominator of the divisor

The pool will be completely filled 15 min 3 min 30 min

21. Winner is blue

22. 6,4

2. Solving Equations in One Variable (p. 17 - 26)

1 variable: more than 1 variable:

other ax + b = 0 ax = b a) , , , b) c) d) e)

One root Infinite roots No roots No roots

x = 3 x = 1

= 3 x = 2 6.

4. True True True False 5. x

15. 0.5, 1.5, 2.0

16.

k = –2

17.

6 min

18.

10 m²

19.

20. a) 16, b) 1.5, c) -2, d) any number

e) no solution, f) 4.75, g) 4.5, h)

3. Polygons and Quadrilaterals (p. 27 - 32)

The outline must be made of straight line segments

The sides must not cross each other 2.

4. Bar Graphs and Histograms (p. 33 - 52)

1. A. 1 B.10 C. 21 D. 50

2. А. 5 B. 19 C. 36 D. 199

3. A. 5, B. 9, C. 5, D. 4, E. 25, F. 20

4. А. 4 B. 37.5 C.60.5 D.79

6. A. 43 B. 43 C. 46

7.The range: 19

8. A.

B. 1. Milk: 17 2.Dark: 16 3.White: 13 4.Nut: 12.

C. 1.Milk: 366 2.Dark: 2613. White:292 4.Nut: 442.

D. 1.Milk: ≈ 52.29 2.Dark: ≈ 37.29 3.White: ≈ 41.71 4.Nut: ≈ 63.14. Chocolate with nuts has the highest sales.

9. Diamond

10. A. В. 3% C. 81

29. A. 230 B.190 C. Groupe 1 200, Groupe 2 240

Adults: Friday (180 books) Children: Friday (70 books)

Answers (pages 48 - 53)

32. A. 32.5 B.35 C.130 D.140 E.33.75 F. 1

33. A. 8 B. 64−69kg C. 45−49kg and 81−86kg D. 64−69kg E. 45−49kg and 81−86kg, 49−52kg and 75−81kg F. 120 G. 45 H. 7

36. A. True B. False C. True D. False E.False F. False G. True H. False I. True J. False K. False.ц

5. Pie charts (p. 53 - 60)

Predators

May

False

N/A

N/A 1. CIICC

6. Probability (p. 61 - 64)

2. A red ball will be drawn when taking a ball from a bag containing red and blue balls.

When rolling two fair dice, the first die shows 1 and the second die shows 6.

, , 0.43

9. 200, 56, 0.28

10. 0.2, 10

10. 6396, 2499, 3591, 8084, 875

11. 8,8

Find the number which square is equal to the area

7. Squares and Square Roots (p. 65 - 72)

11. a) 0.6, b) 36 1.

2. equal zero: 0², 0

positive: –3+5, –(–16), (–3)²

negative: –4

4. Positive Positive Zero Non-negative

5. 6, 14, 1.44, 0, 25, , 0.001

6. 5m, 25m²

7. 289, 1681, –1849, ,

8. 6 is greater than the square of 2, 3 squared is equal 9

12. 11,11

13. c = 16, b = 9, a = 81

14. 4,5,8, ,7

15. 1.5

16. 13

17. 0.09

18. 2.25, 5.8, 9.6

19.

20.

21. 13

8. Cubes and Cube Roots (p. 73 - 88)

1. 2

2. а) 27cm³, 125cm³, 64 cm³, the second box is the most spacious.

b) 343cm³, 64cm³, 512cm³, 216 cm³, the third box is the most spacious

3. A. Length 1cm, B. Width 1cm, C. Height 1cm. D 1-4, 2-16, 3-64, 4-256, 5-1024, 6-4096

4. 64

5. A. 1³+2³+3³+4³+5³=(1+8+27+64+125= =225=15²

В.1³+2³+3³+4³+5³+6³=(1+8+27+64+125+ + 216)=441=21²

C.1³+2³+3³+4³+5³+6³+7³=(1+8+27+64 + + 125+216+343)=784=28²

6. А. 3571. В. 9919. C.25117

7. А. −4913; −125; −1000000.

В.

C. 4.096; 0.015625, 2.863288; 3511.808.

8. А. 12673 is not a perfect cube; 42875 perfect cube; 8778 is not a perfect cube В. 1009875 is not a perfect cube; 238328 perfect cube; 343 is not a perfect cube

9. A. multiply by 2, the new number is 6

B. multiply by 4, the new number is 10

10. A. It must be divided by 2. The new number is 8.

B. It must be divided by 12. The new number is 6.

11. 52

14. A 4, B 3, C 1, D 2.

15.

A. 4; 16; 7;

B. C. .

16. A. -3; -0.3; -21; B. -24; -110; -144

A. 5832 B. 4096 C. 13824

19. A. 4, B.8, C 15.

20. A. 259, 21.

B. 6, 5.

C. 87, 17.

D. 200, 10.

21.

A. The number to add is 141 Cube root: 31

B.The number to add is 242 Cube root: 23

C. The number to add is 359 Cube root: 19

22. Yes, the box will fit in the trunk

23. Yes, the vaccine box will fit in a thermobox.

24. 16 1. A. ₹80,000

B. ₹1,30,000

C. ₹2,20,000 2. A. ₹544

₹257

₹101 3. A. ₹3,13,720

B. ₹1,260,000

C.₹1,920,000

D. ₹16,05,000 4. A. ₹12,903 B. ₹16,216

C. ₹27,907

5. А. 2, В.4, C.3, D.1. 6. A. 3, B.4, C.2, D. 1.

9. Percentage and Its Applications (p. 89 - 100) Answers (pages 88 - 97)

7. CP1 = ₹ 69,565 CP2 = ₹94,118

Total profit or loss 2,25%

8. 20.32%

9. ₹2,89,192

10. 60%

11.

A. Discount: ₹36,000 SP: ₹2,04,000

B. Discount: = ₹19,200 SP =₹2,20,800

12. A. SP ₹17,060; B.₹15,350

13. A. 16.78%; B. 10.88%

14. ₹6499

15. Regular price: ₹4500. Discount: 73.33%

16. ₹68,880

17. ₹49,421

18. ₹8685

19. ₹2760, 8%

20. A. ₹1,47,560; B. ₹1,43,607.5

21. ₹3,000

22. ₹2,32,200

23. 25%

24. 20,004 (Store 2) <20,868 (Store 1)

10. Compound Interest (p. 101 - 106)

A. Simple interest ₹33, Amount ₹583.

B. Rate 18%, Amount ₹1,290.

C. Time 2 years, Amount ₹1,830.

D. Principal ₹10,480, Amount ₹11,200.

2. Matthew should choose deposit B

A. The amount of interest for the entire period is ₹1125.

B. The total amount in the account at the end of the deposit period is ₹16,125.

4. A. The amount of accrued interest by May 10, 2023 is ₹76,98.

B. The amount of accrued interest by July 17, 2023 is ₹140,09.

5. Amount ₹1,29,171. Compound interest ₹30,671

6. 4,8%

7. Option B will bring more interest by ₹137.66

Option A: 2,38,203 rupees

Option B: 2,38,023 rupees

Option C: 2,37,420 rupees

Option D: 2,36,937 rupees

The most profitable option is deposit A

9. A

10. C

11. C

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

11. Algebraic Expressions (p. 107 - 118)

A. –X² + 2x + 3

В. –2X² + 3x + 4

C. –3X² + 2x

D. 6x + 12

Monomials:

2pqr; w8x²y²

Binomials:

10ab + 18;

xy + 5xc; xy²– 10; ab + abc²

Trinomials:

7c – 9ab – 90;

abc – 6a +5; a²bc – a +7

Quadrinomials:

a2 + 5abc – za² – 10;

a² + 5a2b² + 6b² – 6c; 2ab + abc – 3c – 4

1. 10ab + 18 4ab + 4;

2. 4ab 6ab;

3. 5ab² +8 7ab² + 7;

4. 7a²b – 9 10a²b + 18;

5. 10b + 18y + 9 7b + 3y – 5; 6. 2ab² – 8b + 3 10ab² – 7b – 18.

A. (m−n)²−3mn

B. x²+3y+xy

C. 3mn−4m+n

D. (p+q)/3(p+q)

E. (p+q)(p−q)

F. mn/3mn

A. 10x + y + 9.

B. 3x² + 13x + y + 9

C. 2x + 14y − 19

D. 3x² − 3x + 10y − 13

A. 6x + 7

B. 14x + 8y − 5

C. −x² + 5y + 4

D. −7x + 3y + 16

E. −4x² − 2y − 18

A. −y − 46

B. 46n + 3m

C. −4y² + y + 6

D. 3m² + 19m − 46

A. 2y² − 5y + 12

B. 2y² − 2y − 2

C. −y² + 8y − 10

D. 3y² − 2y − 6

10.

11.

A. 24xy + 9y − 32x − 12

В. 4a²b − 2a² + 8b² + 16b − 10

C. z⁴ − z³ + 4z² + 20z

D. 9p⁴ − 55p³ − 59p² + 21p

12. А. 55; В. 40; C. 2; D. 28

13. A. +30ac − 4bc + 9b²

B. 70a²bc + 11b²c − 12bc − a²c + ab³ + + 4ab²

C. a³ − 6a² − 2ab² + 12b² + 9ac + + 18abc − 5a − 54c − 9bc + 30.

D. −6a³ − 9b³ + 20ab − 15ac + 6bc

14.

А. V = (x + y + z) × (2x − y + 3z) × 5xy

В. 6562500000

C. 50700000000

15.

A. (3a + 2b) × (a² − b + 5) × 4ab

B. 34020 km³

C. 8

D. 24520 km³

12. Area of polygons (p. 119 - 124)

1. 131.93 cm²

2. 103.25 cm²

3. 80 cm²

4. 30.96 cm²

5. 27, 36

6. 12, 11.5

7. No, yes, yes

8. -, 650, 800

9. A. 357, B. 2153, C. 29, D. 414, E. 427, F. 429, G. 2072, H. 131, I. 344, J. 14.

13. Surface Area and Volume of Solids (p.125 - 128)

1. 108

2. , 88

3. 1800

4. no

5. 25

6. 6

7. 8

8. 40 cm

14. Exponents and Powers (p.

A. 2⁶>6²

B. 5⁹>9⁵

C. 4⁷>7⁴

1) A. 2 × 10² + 3 × 10¹ + 4 × 10⁰ + 5 × × 10⁻¹ + 6 × 10⁻²

B. 7 × 10³ + 0 × 10² + 8 × 10¹ + 9 × × 10⁰ + 0 × 10⁻¹ + 0 × 10⁻² + 4 × 10⁻³

C. 1) × 10⁻¹ + 2 × 10⁻² + 3 × 10⁻³ + 4× × 10⁻⁴ + 5 × 10⁻⁵

D. 6 × 10³ + 0 × 10² + 0 × 10¹ + 0 × × 10⁰ + 0 × 10⁻¹ + 0 × 10⁻² + 7 × 10⁻³+ + 8 × 10⁻⁴

E. 9 × 10³ + 8 × 10² + 7 × 10¹ + 6 × × 10⁰ + 5 × 10⁻¹ + 4 × 10⁻² + 3 × 10⁻³+ + 2 × 10⁻⁴ + 1 × 10

A.20

B.28

C.15

D.21

E.45

3) E (9 numbers)

4) B, D or E

3. a) 5⁻²; b) 10⁻¹; c) x⁻⁶; d) a⁻¹; e) 23⁻⁴

4. 5.

6. a) 3; b) ; c) 10000; d)

7. a) ; b) ; c) 453; d) –7

8. A

9. B 10.

A: 5.6 × 10⁷ < 5.7 × 10⁸

B: 9.5 × 10⁶ < 8.9 × 10⁸

C: 3.2 × 10⁸ < 7.0 × 10⁸

15. Direct and Inverse Proportions (p. 137 - 144)

1. 6:3

2. 6:3 = = 2

3. 4:6

4. 7:4

5. 1.75

B. 2. C.

Case1 3:1

Case2 2:1

9. 10. , 11. 300:60

12. 300:60 = = 5

5 times heavier

13. 300:100

14. 300:100 = = 3

3 times heavier

15.

16. 17.

The panda is times heavier than koala

18.

a) false

b) 10, 6, 40, 14 19.

a) true, 120

b) 6, 12, 4

20. False, True, 21.

22. 7680

23. 126 km

24. 10 min

25. 9 hours 36 minutes

16. Factorisation and Division of Algebraic Expressions

(p. 145 - 152)

1. 6, 8, 15

2. 4x, 2x, 2x 3. 20:139

4. 1 column: 2 column:

17. Linear Graphs (p. 153 - 162)

8. 25, 1, 16 9. 40 10. 31 11. 9

12. 6x, 5x, 4x

13. 120, 180, 160 14. 15. 4x³y²

–5a²b³c

–4m³n²

–4p³q²

16.

2x² – 3x + 5

2z⁴ – 3z² + 4

5m²n + 3m – 2n²

2a²bc – 3ac² + 4b²

3p² – 2pqr + r²

year 17261752189819771986

600

10. 22

11. 10

12.

13. 300 million

14. 100 km

15. А. True B. False

16. А. True B. False

17. А. True; B. True

18. A. True; B. False

19. A. True; B. False

20. 70

9. А. False, B. True, C. True

3; 4; 5; 7