Chapter 1: Rational Numbers[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Worksheet: Rational Numbers

Name: __________________________________ Date: ________________

Instructions:

Solve the following problems.
Show all your workings and write the final answers in the space provided.

Questions:

1. Simplify the following expressions:

a) $8 5 + 4 3$

b) $3 2 - 6 1$

c) $5 4 \times 2 3$

d) $10 7 \div 5 1$

2. Identify whether the following numbers are rational or irrational:

a) $9$

b) $2 5$

c) $2$

d) $- 4 3$

3. Place the following rational numbers on the number line:

a) $- 3 2$

b) $4 5$

c) $1$

d) $- 2 7$

4. Solve the following word problems:

a) Sarah had $5 3$ of a chocolate bar, and she ate $4 1$ of what she had. How much of the chocolate bar is left?

b) A rectangle has a length of $8 3$ meters and a width of $2 1$ meters. Find its area.

5. Write the following numbers in decimal form:

a) $25 7$

b) $- 4 3$

c) $3 2$

d) $2 11$

Answers:

a) $8 13$
b) $2 1$
c) $5 6$
d) $2 7$
a) Rational
b) Rational
c) Irrational
d) Rational
(Answers may vary based on the accuracy of the placement on the number line.)
a) $10 3$ of the chocolate bar is left.
b) The area of the rectangle is $16 3$ square meters.
a) $0.28$
b) $- 0.75$
c) $0.67$
d) $5.5$

This worksheet is a general example and may need adjustments based on the specific topics covered in your class and the depth of understanding you want to assess.[/expand]

Chapter 2: Linear Equations in One Variable[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Class 8 Mathematics Worksheet

Name:______________________ Date:______________________ Roll No.:______________________

Section A: Multiple Choice Questions (1 mark each)

What is a linear equation in one variable?
- A. An equation with two variables.
- B. An equation with one variable raised to the power of 2.
- C. An equation with a single variable raised to the power of 1.
- D. An equation with no variables.
Which of the following is a linear equation?
- A. $3 x^{2} + 2 = 8$
- B. $4 x - 7 = 3$
- C. $2 x + 3 = 1$
- D. $2 x^{2} + 5 = 7$
What is the first step in solving a linear equation?
- A. Adding constants on both sides.
- B. Combining like terms.
- C. Isolating the variable.
- D. Dividing both sides by a constant.
If $2 x - 5 = 11$ , what is the value of $x$ ?
- A. $x = 8$
- B. $x = 10$
- C. $x = 6$
- D. $x = 4$

Section B: Short Answer Questions (2 marks each)

Solve for $x$ : $3 x + 7 = 16$ .
If $4 y - 9 = 15$ , find the value of $y$ .
Write down a linear equation and its solution.

Section C: Long Answer Questions (4 marks each)

Solve the following system of equations:
$2 x + 3 y 4 x - 5 y = 12 = 2$
A sum of money is divided among three friends. If the first friend gets $x$ , the second friend gets $2 x$ , and the third friend gets $3 x + 10$ , and the total amount is $75$ , find the value of $x$ and the amount each friend gets.

Section D: Real-World Applications (5 marks each)

A rectangular garden has a length that is $5$ meters more than twice its width. If the perimeter of the garden is $42$ meters, find the dimensions of the garden.
Samantha has twice the amount of money as her brother. If Samantha has $x$ dollars and her brother has $y$ dollars, write down a linear equation representing this situation.

Total Marks: ________

Note: Show all your workings clearly. Be sure to write the final answer with appropriate units where necessary.[/expand]

Chapter 3: Understanding Quadrilaterals[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Worksheet: Understanding Quadrilaterals

Name: _______________________ Class: __________ Roll No: __________

Part A: Multiple Choice Questions (1 mark each)

What is the sum of the interior angles of a quadrilateral?
a) 180 degrees
b) 360 degrees
c) 450 degrees
d) 540 degrees
Which of the following statements is true for a rectangle?
a) Opposite sides are equal and parallel
b) All sides are equal
c) Opposite angles are equal
d) Diagonals bisect each other
A quadrilateral with opposite sides equal and parallel is called a:
a) Rectangle
b) Parallelogram
c) Rhombus
d) Square
In a trapezoid, the non-parallel sides are called:
a) Bases
b) Legs
c) Diagonals
d) Opposite sides

Part B: True/False Questions (1 mark each)

The diagonals of a rhombus are always equal in length. (True/False)
If a quadrilateral is a parallelogram, then its opposite angles are supplementary. (True/False)
All squares are rectangles, but not all rectangles are squares. (True/False)

Part C: Fill in the Blanks (1 mark each)

The sum of all angles in a quadrilateral is __________ degrees.
In a parallelogram, opposite sides are __________ and __________.
A quadrilateral with all sides equal is called a __________.

Part D: Short Answer Questions (2 marks each)

Explain why the sum of the interior angles of a quadrilateral is 360 degrees.
If ABCD is a parallelogram, and angle A measures 120 degrees, what is the measure of angle C?

Part E: Application Problems (3 marks each)

The length of one side of a square is 8 cm. Calculate the perimeter of the square.
In a trapezoid ABCD, if the bases AB and CD are 12 cm and 18 cm, and the height is 10 cm, calculate the area of the trapezoid.

Note:

Show all workings for numerical problems.
Make sure to review your answers before submitting the worksheet.

Feel free to adapt this worksheet as needed for your classroom. Ensure that the difficulty level aligns with the understanding of your students.[/expand]

Chapter 4: Data Handling [expand title=”Read More➔” swaptitle=”🠔Read Less”]

Worksheet: Data Handling

Name: ____________________ Date: ______________ Class: 8th

Part A: Understanding Data

Define: Write the definition of “data handling” in your own words.
______________________________________________________
Examples: List three examples of situations where data handling is used in real life.
a. _____________________________________________________
b. _____________________________________________________
c. _____________________________________________________

Part B: Data Collection

Survey: Conduct a survey among your classmates. Ask them about their favorite color. Record the responses in the table below.
Serial No. Name Favorite Color
1
2
3
4
5
Data Analysis: Use the data collected to create a bar graph representing the favorite colors of your classmates.
(Draw the bar graph on a separate graph paper.)

Part C: Interpreting Data

Interpretation: Analyze the bar graph you created and answer the following questions:
a. What is the most common favorite color among your classmates?
_____________________________________________________
b. How many students prefer the color blue?
_____________________________________________________
c. What is the total number of students surveyed?
_____________________________________________________

Part D: Real-Life Applications

Application: Think of a real-life scenario where data handling is crucial. Explain why data handling is important in that situation.
_____________________________________________________
_____________________________________________________

Part E: Reflection

Reflection: What did you learn from this activity? How can data handling be useful in your daily life?
_____________________________________________________
_____________________________________________________

Feel free to modify or add more questions based on the specific emphasis of the chapter and the needs of your students.[/expand]

Chapter 5: Squares and Square Roots[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Worksheet: Squares and Square Roots

Name: ____________________________________ Class: 8 Roll No: ______

Instructions:

Read each question carefully before attempting it.
Show all your workings clearly.
Circle or underline your final answers.

Section A: Multiple Choice Questions (1 mark each)

What is the square of 9? a) 18 b) 81 c) 27 d) 36
The square root of 64 is: a) 8 b) 4 c) 6 d) 10
If a square has a side length of 5 cm, what is its area? a) 25 sq cm b) 10 sq cm c) 20 sq cm d) 15 sq cm
What is the value of √144? a) 12 b) 16 c) 14 d) 18
If the area of a square is 49 sq units, what is the length of one side? a) 7 b) 14 c) 21 d) 28

Section B: Fill in the Blanks (1 mark each)

The square of 12 is ___________.
The square root of 81 is ___________.
The side length of a square is 6 cm, so its area is ___________ sq cm.
If x^2 = 49, then x is ___________.
√100 = ___________.

Section C: Short Answer Questions (2 marks each)

If the area of a square is 121 sq units, find the length of one side.
Find the value of y if y^2 = 144.
The area of a square is 64 sq cm. What is the length of one side?
If a square has a side length of 10 cm, what is its perimeter?
Determine the value of √169.

Section D: Application Problems (3 marks each)

A rectangular field has a length of 15 m. If the width is equal to its length, find the area of the field.
The square of a number is 256. Find the number.
The area of a square is 144 sq units. If one side is doubled, what is the new area?

Section E: True/False Statements (1 mark each)

√121 = 12 True/False
If the side length of a square is 8 cm, then its area is 64 sq cm. True/False

Section F: Word Problems (4 marks each)

A garden is in the shape of a square with a side length of 12 m. If plants are planted along the perimeter of the garden, how many plants are needed if each plant is placed 1 meter apart?
The area of a square is 36 sq cm. Determine the side length and the perimeter of the square.

Total Marks: ________

Feedback: ____________________________________________________________

Please note that this is a sample worksheet, and you may adjust the difficulty level according to your students’ understanding.[/expand]

Chapter 6: Cubes and Cube Roots[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Class 8 Mathematics: Cubes and Cube Roots

Worksheet

Instructions: Solve the following problems. Show all your workings.

Calculate the cube of the following numbers: a. $4^{3}$ b. $7^{3}$ c. $1 0^{3}$
Find the cube root of the following numbers: a. $364$ b. $3125$ c. $3216$
Evaluate the following expressions: a. $5^{3} + 2^{3}$ b. $3^{3} - 2^{3}$ c. $1 1^{3} + 7^{3}$
Solve the following word problems: a. A cube-shaped box has a side length of 6 cm. Calculate its volume. b. The volume of a cube is 343 cubic units. Find the length of its side. c. If the cube of a number is 512, what is the number?
Identify whether the following statements are True (T) or False (F): a. The cube root of 125 is 5. b. $6^{3}$ is a perfect cube. c. The cube root of 64 is 4.

Additional Challenge: 6. Solve the following advanced problem: The sum of two consecutive cubes is 81. Find the two numbers.

This worksheet covers various aspects of the Cubes and Cube Roots chapter, including basic calculations, problem-solving, and conceptual understanding. Adjustments can be made based on the specific requirements of your class or curriculum.[/expand]

Chapter 7: Comparing Quantities[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Worksheet: Comparing Quantities – Exploring Percentages and Discounted Prices

Name:______________________ Class: 8 Date: ______________

Part A: Understanding Percentages

Question 1: Define the term “percentage” and provide an example of a real-life situation where percentages are commonly used.

Question 2: If the price of a shirt is ₹800, and it is discounted by 20%, calculate the discounted price.

Part B: Comparing Quantities

Question 3: A shopkeeper reduces the price of a mobile phone from ₹15,000 to ₹12,000. Calculate the percentage decrease in the price.

Question 4: If the original price of a laptop is ₹40,000, and it is increased by 15%, find the new price.

Part C: Calculating Discounts

Question 5: A pair of jeans is originally priced at ₹1200. If there is a 25% discount, calculate the discounted price.

Question 6: A book is available at a 12% discount. If the discounted price is ₹440, find the original price.

Part D: Real-world Applications

Question 7: During a sale, a watch is available for ₹450 after a 35% discount. What was its original price?

Question 8: If the cost of a mobile phone is ₹10,000 and there is a 10% increase in its price, find the new price.

Part E: Word Problems

Question 9: Maria bought a dress originally priced at ₹2500. She got a 20% discount. How much did she pay after the discount?

Question 10: A laptop’s price increased by 8% to ₹43,200. Find its original price.

Note: Show all workings for numerical calculations.

This worksheet is a starting point and can be adjusted based on the specific topics covered in your class and the depth of understanding you want to assess. Feel free to modify or add questions as needed.[/expand]

Chapter 8: Algebraic Expressions and Identities [expand title=”Read More➔” swaptitle=”🠔Read Less”]

Class: 8th

Subject: Mathematics

Chapter: Algebraic Expressions and Identities

Worksheet

Instructions:

Solve the following algebraic expressions.
Apply the given algebraic identities where applicable.
Show all steps and write the final answer.

Question 1: Simplify the following expressions:

a) $3 x + 2 y - x + 4 y$

b) $5 a - (2 a - 3 b)$

c) $2 (3 x - 7) + 4 (2 x + 5)$

Question 2: Apply the identity $(a + b)^{2} = a^{2} + 2 ab + b^{2}$ to simplify the expressions:

a) $(p + 4)^{2}$

b) $(2 x - 3)^{2}$

Question 3: Apply the identity $(a - b)^{2} = a^{2} - 2 ab + b^{2}$ to simplify the expressions:

a) $(q - 5)^{2}$

b) $(3 y + 2)^{2}$

Question 4: Solve the equations for the given values of $x$ :

a) $2 x + 7 = 15$

b) $3 (2 x - 4) = 18$

Question 5: Word Problems:

The perimeter of a rectangle is given by the expression $2 l + 2 w$ , where $l$ is the length and $w$ is the width. If the length of the rectangle is $5 x + 3$ and the width is $2 x - 1$ , find the expression for the perimeter.

Answers:

a) $4 y + 2 x$
b) $3 a + 3 b$
c) $14 x + 1$
a) $p^{2} + 8 p + 16$
b) $4 x^{2} - 12 x + 9$
a) $q^{2} - 10 q + 25$
b) $9 y^{2} + 12 y + 4$
a) $x = 4$
b) $x = 6$
$2 (5 x + 3) + 2 (2 x - 1)$ or $14 x + 4$

Note:

Ensure that students show their work and write down all steps.
Encourage them to check their answers by substituting the values back into the original expressions.
Provide additional assistance as needed during the class.[/expand]

Chapter 10: Exponents and Powers[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Worksheet: Exponents and Powers

Name:__________________ Class: _______________ Roll No: _______________

Instructions: Answer the following questions. Show all workings.

1. Define the terms: a. Exponent b. Power

2. Evaluate the following expressions: a. $2^{4}$ b. $5^{2}$ c. $3^{0}$ d. $1 0^{-2}$ e. $8^{3 1}$

3. Simplify the following expressions using the laws of exponents: a. $2^{3} \times 2^{5}$ b. $6 ^{2} 6 ^{4}$ c. $x^{3} \times x^{7}$ d. $y ^{3} y ^{5}$ e. $a^{2} \times a^{-2}$

4. Solve the following problems: a. The population of a town doubles every 10 years. If the current population is 5,000, what will be the population in 30 years? b. A bacteria culture doubles in size every hour. If the initial size is 100 bacteria, what will be the size after 5 hours? c. Simplify: $3^{2} \times 3^{4}$ d. Evaluate: $2^{-3} \times 2^{5}$ e. If $x^{2} = 16$ , find the value of $x$ .

5. Word Problems: a. The side length of a cube is 4 cm. Find the volume of the cube. b. A car depreciates by 15% each year. If the current value of the car is $20,000, what will be its value after 3 years? c. Simplify: $4^{3} \times 4^{-2}$ d. Evaluate: $5^{0} + 6^{1} - 2^{-2}$ e. The area of a square is 49 square units. Find the length of its side.

6. Challenge Problem: a. If $2^{x} = 16$ , find the value of $x$ . b. Solve for $y$ : $3^{2 y - 1} = 27$

Answer Key:

a.
- Exponent: A small raised number that shows how many times a base number should be multiplied by itself.
- Power: The result of raising a base number to an exponent.
a. $16$ b. $25$ c. $1$ d. $0.01$ e. $2$
a. $2^{8}$ b. $6^{2}$ c. $x^{10}$ d. $y^{2}$ e. $1$
a. $40, 000$ b. $3, 200$ c. $3^{6}$ d. $32$ e. $x = \pm 4$
a. $64 cm^{3}$ b. $12, 890$ c. $4$ d. $32.25$ e. $7$
a. $x = 4$ b. $y = 1.5$

Remember to review the answers and explanations with the students during the feedback session. Adjust the difficulty level of questions based on your class’s proficiency in the subject.[/expand]

Chapter 11: Direct and Inverse Proportions[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Worksheet: Direct and Inverse Proportions

Name:____________________ Class: VIII Date: _______________

Instructions: Solve the following problems related to direct and inverse proportions. Show all your workings.

1. Direct Proportion:

a) If 4 bags of candies cost ₹240, how much would 10 bags cost?

b) The time it takes to paint a wall is directly proportional to the area of the wall. If it takes 6 hours to paint an area of 30 square meters, how long will it take to paint an area of 50 square meters?

2. Inverse Proportion:

a) The number of workers needed to complete a construction project is inversely proportional to the number of days it takes to complete the project. If it takes 8 workers 12 days to finish the project, how many workers are needed to complete it in 6 days?

b) The time it takes for a car to travel a certain distance is inversely proportional to its speed. If it takes 4 hours to travel 240 km at a certain speed, how long will it take to travel the same distance at twice the speed?

3. Mixed Proportion:

a) If 5 workers can build a wall in 8 days, how many workers would be needed to build the same wall in 4 days?

b) The cost of printing flyers is directly proportional to the number of flyers printed and inversely proportional to the number of printing machines used. If 5000 flyers cost ₹100 and 4 machines are used, find the cost of printing 8000 flyers using 5 machines.

4. Real-life Scenarios:

a) A car travels 360 km in 4 hours. If the speed remains constant, how long will it take to travel 540 km?

b) If 8 students can finish a project in 10 days, how many students are needed to finish the same project in 5 days?

Feel free to adapt this worksheet according to your specific requirements or CBSE guidelines.[/expand]

Chapter 12: Factorisation[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Class 8 Mathematics Worksheet

Chapter 12: Factorisation

Name: ___________________ Class: Date:

Instructions:

Attempt all questions.
Show all steps of your solutions.
Circle or underline your final answers.

1. Define: a) Factorisation b) Common factors

2. Identify the common factors: a) $3 x + 6$ b) $4 y - 8$

3. Factorise the following expressions: a) $6 a + 9$ b) $15 b - 30$

4. Apply the distributive property: Expand and then factorise: a) $4 (x + 3)$ b) $2 (2 y - 6)$

5. Factorise using grouping: $5 m + 10 n - 3 m - 6 n$

6. Factorise using identities: $x^{2} - 25$

7. Solve for $x$ : $3 x - 12 = 0$

8. Simplify: $2 p - 8 4 p ^{2} - 16$

9. Application: The area of a rectangular garden is represented by $A = (x + 3) (x - 2)$ . If the length of the garden is $x + 3$ meters, find the width of the garden.

10. Challenge: Factorise completely: $9 x^{2} - 16$

Evaluation:

Excellent: 9-10 correct
Good: 7-8 correct
Satisfactory: 5-6 correct
Needs Improvement: 4 or fewer correct

Feel free to adjust the difficulty of the questions based on your class’s proficiency. Additionally, include more word problems or application-based questions if you want to focus on real-world scenarios.[/expand]

Chapter 13: Introduction to Graphs[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Class 8 Mathematics Worksheet

Chapter: Introduction to Graphs

Instructions:

Read each question carefully before attempting.
Show all your workings and write answers with proper units.
Use the graph paper provided to draw graphs.

Question 1: Define the following terms:

a) Graph

b) Axes

c) Data point

Question 2: Identify the components of the following graph and explain their significance:

Question 3: Choose the appropriate type of graph for each scenario and draw the graph using the given data:

a) Represent the sales of different products over a month.

Product	Sales (in units)
A	120
B	90
C	150
D	80

b) Represent the percentage distribution of marks obtained by students in a class.

Marks Range	Number of Students
90-100	15
80-89	25
70-79	30
Below 70	20

Question 4: Analyze the given graph and answer the questions:

a) What does the x-axis represent in this graph?

b) Identify the trend in the data represented by the graph.

c) If the trend continues, what would be the expected value on the y-axis for x = 7?

Question 5: Create your own data set related to a topic of your choice. Choose an appropriate type of graph and draw it on the graph paper provided. Label the axes, give a title, and use appropriate scales.

Question 6: Answer the following questions:

a) Why is it essential to label the axes in a graph?

b) Compare and contrast bar graphs and line graphs. Provide examples of situations where each type would be suitable.

Question 7: Solve the following problem:

The temperature (in degrees Celsius) at different times of the day is recorded as follows:

Time (in hours)	Temperature
9 AM	20
12 PM	28
3 PM	35
6 PM	25

a) Draw a line graph to represent the temperature variation throughout the day.

b) What is the highest temperature recorded, and at what time did it occur?

End of Worksheet

Note: This worksheet is a general guide and may need to be adapted based on the specific requirements of the curriculum and classroom.[/expand]

Serial No.	Name	Favorite Color
1
2
3
4
5

Worksheet: Rational Numbers

Class 8 Mathematics Worksheet

Section A: Multiple Choice Questions (1 mark each)

Section B: Short Answer Questions (2 marks each)

Section C: Long Answer Questions (4 marks each)

Section D: Real-World Applications (5 marks each)

Total Marks: ________

Part A: Multiple Choice Questions (1 mark each)

Part B: True/False Questions (1 mark each)

Part C: Fill in the Blanks (1 mark each)

Part D: Short Answer Questions (2 marks each)

Part E: Application Problems (3 marks each)

Worksheet: Data Handling

Part A: Understanding Data

Part B: Data Collection

Part C: Interpreting Data

Part D: Real-Life Applications

Part E: Reflection

Part A: Understanding Percentages

Part B: Comparing Quantities

Part C: Calculating Discounts

Part D: Real-world Applications

Part E: Word Problems

Worksheet

Class 8 Mathematics Worksheet

Chapter 12: Factorisation

Name: ___________________________ Class: ______ Date: ______

Class 8 Mathematics Worksheet

Chapter: Introduction to Graphs

Instructions:

End of Worksheet

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Name: ___________________ Class: Date: