MATHS(Q) – TeachGyan

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

Integer Basics:

Define an integer and provide an example.
Identify three consecutive integers if one of them is $- 5$ .
Write the next three integers after $- 8$ .
Which is greater: $- 12$ or $- 15$ ?
Arrange the integers $- 3, - 7, 0, 2, - 1$ in ascending order.
Identify the opposite of each integer: $6, - 9, 0, 3$ .

Operations with Integers:

Evaluate $- 4 + 7$ .
Compute $- 9 - (- 2)$ .
Simplify $3 - 5 + (- 8)$ .
Add $- 6$ to the opposite of $- 3$ .
Subtract $- 2$ from the sum of $- 5$ and $1$ .
If $x = - 3$ , find $- 2 x$ .

Number Line:

Represent $- 4$ on a number line.
Mark the points $A (- 7)$ and $B (3)$ on a number line. Find $A B$ .
Between which two integers does $- 9$ lie on a number line?
If $- 2$ is 4 units to the right of $P$ , find $P$ .

Word Problems:

John has $- 5$ dollars, and Mary has $8$ dollars. How much money do they have together?
If a submarine is $- 150$ meters below sea level and rises $80$ meters, how deep is it now?
A temperature drops $6$ degrees Celsius. If it was $- 3$ degrees, what is it now?
The elevation of a town is $- 200$ meters. If it goes $50$ meters down, what is the new elevation?

Multiplication and Division:

Find $- 4 \times 6$ .
Calculate $- 3 \times (- 7)$ .
If $x \div (- 4) = 5$ , find $x$ .
Evaluate $3 -15$ .
Simplify $( -4 ) -12$ .

Application Problems:

A plane is $- 500$ meters above sea level. If it descends $300$ meters, what is its new altitude?
Subtract $- 7$ from $4$ , and then multiply the result by $- 2$ .
The temperature was $- 2$ degrees Celsius in the morning. It increased by $5$ degrees. What is the temperature now?
A submarine is at $- 120$ meters. If it rises $80$ meters and then goes $- 30$ meters, what is its final depth?

Challenge Questions:

Explain why the sum of two negative integers is negative.
Provide three examples where the product of two integers is positive.
Create a real-life scenario where subtracting a negative number makes sense.
If $a$ and $b$ are two integers, under what conditions is $a \times b$ negative?
Absolute Value:
1. What is the absolute value of $- 9$ ?
2. If $x = - 12$ , find $∣ x ∣$ .
3. If $∣ a ∣ = 7$ , what are the possible values of $a$ ?
4. True or False: The absolute value of any integer is always positive.
Operations Mix:
1. Evaluate $- 5 + 3 \times (- 2)$ .
2. Simplify $4 - (- 7) \div 2$ .
3. If $x = - 8$ , find $2 x + 5$ .
Comparisons:
1. Compare $- 6$ and $- 10$ .
2. If $a > b$ , is $- a < - b$ always true? Explain.
3. Solve for $x$ : $- 2 x < 10$ .
Multiplying and Dividing by -1:
1. If $x = - 5$ , what is $- x$ ?
2. If $y = 8$ , find $- y$ .
3. Multiply $- 3$ by $- 1$ . What is the result?
Patterns:
1. Find the pattern: $- 4, 1, 6, 11, \dots$ .
2. Complete the series: $3, 0, - 3, - 6, \dots$ .
3. If $n$ is an even integer, what can you say about $- n$ ?
Problem-Solving:
1. The sum of two consecutive integers is $- 10$ . Find the integers.
2. The product of two integers is $24$ , and one of them is $- 8$ . Find the other integer.
3. Solve for $x$ : $- 2 x + 7 = 15$ .
Word Problems:
1. A football team gains $- 5$ yards on one play and $12$ yards on the next. What is their net gain?
2. In a game, a player loses $3$ points, gains $8$ points, and then loses $5$ points. What is the overall result?
3. A submarine is at $- 250$ meters. If it rises $120$ meters, what is its new depth?
Real-Life Scenarios:
1. Provide a real-life scenario where negative numbers are used.
2. Explain how positive and negative integers can represent profit and loss in a business.
Exploring Operations:
1. If $a$ is a positive integer and $b$ is a negative integer, what is the sign of $a - b$ ?
2. Is the product of two negative integers always negative? Justify your answer.
Mixed Review:
1. Simplify $- 3 \times (4 - 6) + 2^{2}$ .
2. Solve for $x$ : $- 2 x - 3 = 11$ .
3. If $m = - 9$ , find $- 2 m + 7$ .
Application Problems:
1. A plane is at $- 300$ meters. If it ascends $150$ meters and then descends $180$ meters, what is its final altitude?
2. If a temperature is $- 5$ degrees Celsius and drops $8$ degrees, what is the new temperature?
3. A submarine is at $- 180$ meters. If it descends $50$ meters and then ascends $30$ meters, what is its current depth?
Challenge Questions:
1. Explain why multiplying two negative numbers results in a positive number.
2. Provide examples where the sum of two positive integers is negative.
3. Can the product of three integers be negative? Explain.
Feel free to adapt these questions to better fit your requirements or ask for specific types of questions.[/expand]

Chapter 2: Fractions and Decimals[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Section A: Fractions

Write the fraction represented by the shaded part of the given figure.
Convert the following improper fractions to mixed numbers: a. $3 7$ b. $4 11$
Represent the following fractions on the number line: a. $5 2$ b. $4 3$
Solve the following: a. $2 1 + 4 3$ b. $8 5 - 3 1$
Express $9 4$ as a decimal.
If $5 3$ of a number is 24, find the number.
Simplify: $25 15$
Write the reciprocal of $7 2$ .
A rectangular field is divided into $4 3$ and $4 1$ parts. If the area of the whole field is 300 square meters, find the area of each part.
If $4 3$ of a number is 45, find the number.

Section B: Decimals

Write the decimal number represented by the model.
Convert the following decimals to fractions: a. 0.75 b. 2.6
Represent the following decimals on the number line: a. 1.2 b. 0.4
Solve the following: a. 3.5 + 2.1 b. 4.8 – 1.3
Express 5.25 as a fraction in simplest form.
If 0.6 of a number is 30, find the number.
Simplify: $1.25 + 0.4$
Write the decimal $0.0072$ in words.
A ribbon is 2.8 meters long. If it is cut into pieces of $0.4$ meters each, how many pieces will you have?
If $2.5$ liters of oil cost $6.25, find the cost of $1$ liter of oil.

Section C: Comparing and Ordering

Compare the following fractions: a. $3 2$ and $5 4$ b. $8 5$ and $8 7$
Order the following decimals from least to greatest: a. 1.6, 0.9, 2.3 b. 0.75, 1.2, 0.6
If $5 3$ is greater than $7 4$ , justify why.
Arrange the following fractions in descending order: $4 3, 6 5, 3 2$
If $0.45$ is subtracted from $1.2$ , which is greater?
Compare $0.25$ and $0.3$ .
If $9 4$ is subtracted from $5 3$ , which is greater?
Order the fractions $5 2, 3 1, 7 4$ from least to greatest.
If $0.6$ is added to $1.2$ , which is greater?
Arrange the decimals $1.25, 1.3, 1.22$ in ascending order.

Section D: Word Problems

A cake is divided into 8 equal parts. If 5 friends eat an equal share each, what fraction of the cake does each friend get?
Maria saved $15.50 each week for 4 weeks. How much money did she save in total?
A bag contains $8 3$ kg of sugar. If $4 1$ kg is used, how much sugar remains?
The length of a rectangle is $5 3$ meters, and the width is $4 1$ meters. Find its area.
In a group of 60 students, $5 3$ are boys. How many boys are there?
A tank is $5 4$ full. If 25 liters of water are poured in, the tank becomes full. Find the capacity of the tank.
The sum of two numbers is $8 7$ , and one of the numbers is $8 3$ . Find the other number.
A car travels $4 3$ of the distance at a speed of 60 km/h and the rest at a speed of 80 km/h. Find the average speed for the whole journey.
If $3 2$ of a number is 18, find the number.
A bag contains $12 5$ kg of rice. If $6 1$ kg is taken out, how much rice remains?

Section E: Practical Application

You have a ribbon of length 2.5 meters. If you cut it into pieces of $2 1$ meters each, how many pieces will you have?
A rectangular field has a length of $2.5$ km and a width of $4 3$ km. Find the area of the field.
A recipe calls for $3 2$ cup of sugar. If you want to make $4 1$ of the recipe, how much sugar do you need?
The length of a rectangle is $3.2$ cm, and the width is $2 1$ cm. Find its area.
A shopkeeper sold $5 3$ of his stock. If he had 200 items at the beginning, how many items are left?
A garden is $4 3$ shaded. If the shaded area is $2 1$ acre, find the total area of the garden.
A bottle contains $1.8$ liters of juice. If $3 2$ of the juice is poured into a glass, how much juice is in the glass?
A rectangular box has a length of $4.5$ cm, a width of $3 2$ cm, and a height of $2$ cm. Find its volume.
A map represents a distance of $4.2$ km. If $5 3$ of the distance is a river, how long is the river on the map?
A triangle has a base of $7$ cm and a height of $5 4$ cm. Find its area.
Section F: Advanced Problems
1. Solve the following equation for $x$ : $4 3 x + 5 = 8$
2. A recipe calls for $3 2$ cup of flour, but you want to make 1.5 times the recipe. How much flour do you need?
3. Simplify: $3 2 \times 5 4$
4. In a bag, there are red, blue, and green marbles in the ratio of $5 2 : 8 3 : 10 1$ . If there are 40 marbles in total, how many are green?
5. A rectangular prism has a length of $4 3$ meters, a width of $2 1$ meters, and a height of $6 5$ meters. Find its volume.
Section G: Fractions, Decimals, and Percentages
1. Convert the following percentages to fractions: a. $25%$ b. $80%$
2. Convert the following fractions to percentages: a. $5 3$ b. $8 7$
3. If $3 2$ of a quantity is equal to 60%, find the quantity.
4. A shirt is on sale for $4 3$ of its original price. If the original price was $80, what is the sale price?
5. Express $0.6$ as a percentage.
Section H: Real-Life Applications
1. A garden is in the shape of a rectangle with a length of $6.5$ meters and a width of $4 1$ of its length. Find the area of the garden.
2. A recipe requires $3 2$ cup of sugar for 4 servings. If you want to make 8 servings, how much sugar do you need?
3. A car travels $5 4$ of a journey at a speed of 50 km/h and the rest at a speed of 60 km/h. If the total time taken is 8 hours, find the total distance.
4. A rectangular box has a length of $5.2$ cm, a width of $2 1$ cm, and a height of $4 3$ cm. Find its volume.
5. A solution is $5 2$ alcohol. If you have 500 ml of this solution, how much alcohol is in it?
Section I: Open-Ended Problems
1. Create a real-life scenario where adding two fractions is necessary, and solve it.
2. Invent a word problem that involves converting a decimal to a fraction and solve it.
3. Design a scenario where comparing fractions is crucial, and explain the solution.
4. Formulate a problem where decimals need to be ordered, and provide the solution.
5. Imagine a practical situation requiring the calculation of the area involving both fractions and decimals and solve it.
Section J: Critical Thinking
1. Explain why dividing both the numerator and denominator of a fraction by the same non-zero number does not change the value of the fraction.
2. Justify why the sum of two fractions can be less than both individual fractions.
3. Discuss the importance of understanding fractions and decimals in everyday life, providing at least three examples.
4. Compare and contrast the process of converting a fraction to a decimal with converting a decimal to a fraction.
5. Explain how understanding fractions and decimals can be useful in financial situations.
These questions cover a range of difficulty levels and types, including word problems, conversions, percentages, and critical thinking. Feel free to adapt them based on the specific focus of your class or the CBSE curriculum.[/expand]

Chapter 3: Data Handling[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Multiple Choice Questions (MCQs)

What is the first step in data handling? a. Collecting data b. Organizing data c. Analyzing data d. Representing data
Which of the following is an example of qualitative data? a. Temperature b. Age c. Color d. Weight
In a frequency table, what does the term ‘frequency’ represent? a. Total data points b. Average value c. Number of times a data point occurs d. Range of data
When is a histogram preferred over a bar graph? a. When data is categorical b. When data is numerical c. When comparing categories d. When showing percentages
Which of the following is not a measure of central tendency? a. Mean b. Median c. Mode d. Range

Fill in the Blanks

A ________ graph is used to represent the distribution of numerical data.
The ________ is the middle value in a data set when it is arranged in ascending order.
The process of arranging data in a specific order is called ________.

Short Answer Questions

Explain the difference between a bar graph and a histogram.
Describe a real-life scenario where a line graph would be the most appropriate way to represent data.
What is the purpose of using a tally mark in data collection?

Application-Based Questions

Conduct a small survey in your class about students’ favorite colors. Create a frequency table and a pie chart based on your findings.
Your friend recorded the temperature each day for a week. Create a line graph to represent this data.
Analyze the following data set: 10, 15, 20, 25, 30. Calculate the mean, median, and mode.

Long Answer Questions

Design a survey questionnaire to collect data on students’ hobbies. Include open-ended and closed-ended questions.
You are given data on the heights of students in your class. Create a box-and-whisker plot to represent this data.
Compare and contrast a bar graph and a pie chart. Provide examples of situations where each would be more appropriate.
Multiple Choice Questions (MCQs)
1. Which of the following is an advantage of using a pie chart? a. Shows trends over time b. Compares different categories c. Represents percentages d. Displays individual data points
2. In a line graph, what does the x-axis typically represent? a. Categories b. Frequency c. Time d. Percentage
3. When constructing a bar graph, what should be on the y-axis? a. Categories b. Labels c. Values d. Percentages
4. What is the purpose of outliers in a box-and-whisker plot? a. To show the average value b. To highlight extremes in the data c. To determine the mode d. To calculate the range
5. Which measure of central tendency is most influenced by outliers? a. Mean b. Median c. Mode d. Range
Fill in the Blanks
1. A ________ is a graphical representation of the distribution of a dataset.
2. The value that occurs most frequently in a dataset is called the ________.
3. The range of a dataset is calculated by subtracting the ________ from the ________.
Short Answer Questions
1. Explain the concept of ‘cumulative frequency’ in the context of data handling.
2. Provide an example of a situation where a scatter plot would be an appropriate way to represent data.
3. Differentiate between primary data and secondary data. Give examples of each.
Application-Based Questions
1. You are given the ages of students in your class. Create a histogram to represent this data.
2. Conduct a survey on the mode of transportation used by students to reach school. Represent the data using a suitable graph.
3. Analyze a weather chart for a month and create a composite bar graph showing the temperature variation throughout the month.
Long Answer Questions
1. Discuss the importance of data handling in decision-making processes in various fields.
2. You have collected data on the number of hours students spend on homework each week. Develop a comprehensive data analysis report including relevant graphs.
3. Compare and contrast a bar graph and a line graph in terms of their applications and effectiveness in representing different types of data.
Remember to tailor the questions based on the specific content covered in your class and the depth of understanding you expect from the students.[/expand]

Chapter 4: Simple Equations[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Type 1: Solving Equations

Solve for $x$ : $4 x - 8 = 20$
Solve for $y$ : $3 y + 12 = 27$
Find the value of $a$ in the equation $2 a - 5 = 11$
If $2 b + 7 = 15$ , find $b$ .
Determine the solution for $3 c - 2 = 13$

Type 2: Word Problems

The sum of twice a number and 9 is 25. Find the number.
A number decreased by 6 is 14. Find the number.
If 3 times a number is added to 5, the result is 17. Find the number.
The product of a number and 4 is 28. Find the number.
The perimeter of a square is 24 cm. Find the length of each side.

Type 3: Application Problems

A shopkeeper bought some pens for Rs. 80. He sold each pen for Rs. 12 and made a profit of Rs. 24. How many pens did he buy?
The sum of two consecutive even numbers is 46. Find the numbers.
A number is multiplied by 5, and 7 is subtracted from the result. The final answer is 18. Find the number.
The ages of three friends are in the ratio 3:4:5. If the sum of their ages is 72, find the age of each friend.
The cost of $x$ notebooks is Rs. 120. What is the cost of each notebook if they all have the same price?

Type 4: Forming Equations

Write an equation for the statement: “Six less than twice a number is 14.”
Form an equation for: “The sum of a number and 8 is equal to 20.”
If $x$ represents the unknown number, express the statement: “The product of 7 and a number is 35” as an equation.
Write an equation for the situation: “If 4 is added to a number, the result is 12.”
Form an equation for the sentence: “Three times a number, increased by 2, is 17.”

Type 5: Checking Solutions

Verify if $x = 7$ is a solution for the equation $2 x - 3 = 11$ .
Check if $y = 6$ satisfies the equation $4 y + 5 = 29$ .
Determine if $a = 10$ is a solution to the equation $3 a - 8 = 14$ .
Check the solution $b = 6$ for the equation $2 b + 9 = 21$ .
Verify if $c = 4$ is a solution for the equation $5 c - 2 = 18$ .
Type 6: Multi-step Equations
1. Solve for $x$ : $3 (2 x - 5) = 27$
2. If $2 (3 y + 4) = 22$ , find the value of $y$ .
3. Determine the solution for $2 (a + 3) = 18$ .
4. Solve the equation $4 (b - 2) = 12$ for $b$ .
5. Find the value of $c$ in the equation $2 (5 c - 1) = 21$ .
Type 7: Word Problems with Multi-step Equations
1. The sum of three consecutive odd numbers is 63. Find the numbers.
2. A number is increased by 5, and the result is multiplied by 4. If the final answer is 36, find the original number.
3. The total cost of a shirt and a pair of jeans is Rs. 900. The shirt costs Rs. 350 more than the jeans. Find the cost of each item.
4. The length of a rectangle is three times its width. If the perimeter is 80 cm, find the dimensions of the rectangle.
5. A number is doubled, and 7 is added to the result. The final answer is then multiplied by 3, and the result is 51. Find the number.
Type 8: Forming and Solving Equations from Word Problems
1. A number is 4 more than twice another number. If the sum of the numbers is 24, find both numbers.
2. The sum of three consecutive integers is 51. Find the integers.
3. A number is divided by 3, and 4 is added to the result. The final answer is 9. Find the number.
4. The difference between a number and 6 is equal to twice the number. Find the number.
5. The sum of two numbers is 30. If one number is 5 more than the other, find the numbers.
Type 9: Real-life Applications
1. A recipe calls for 3 times as much sugar as flour. If you need 4 cups of flour, how much sugar do you need?
2. John’s age is 5 years less than twice Mary’s age. If Mary is 14, find John’s age.
3. The sum of the ages of a father and son is 45 years. If the father is 3 times as old as the son, find their ages.
4. A rectangular garden has a length 4 meters more than twice its width. If the area is 56 square meters, find the dimensions.
5. A sum of money is divided among three friends in the ratio 2:3:4. If the smallest share is Rs. 400, find the total sum.
Type 10: Inequalities
1. Solve for $x$ : $2 x - 7 < 11$
2. Determine the values of $y$ that satisfy the inequality: $3 y + 5 \geq 16$
3. Solve the inequality $4 (a - 2) > 12$ for $a$ .
4. Find the solution set for the inequality $2 (b + 3) \leq 10$ .
5. Solve for $c$ : $5 (c - 4) \geq 15$
These questions cover a range of difficulty levels and types, providing a comprehensive set for your students to practice and master the concepts of simple equations.[/expand]

Chapter 5: Lines and Angles[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Section A: Multiple Choice Questions (1-30)

What is the measure of a right angle? a) 45 degrees b) 90 degrees c) 180 degrees d) 360 degrees
In an isosceles triangle, the angles opposite the equal sides are: a) Acute b) Right c) Obtuse d) All of the above
If two parallel lines are cut by a transversal, the alternate angles are: a) Equal b) Supplementary c) Complementary d) None of the above
The angles that share a common side and a common vertex but no common interior points are called: a) Adjacent angles b) Complementary angles c) Vertical angles d) Corresponding angles
If two angles are complementary, and one angle is 40 degrees, what is the measure of the other angle?

Section B: True/False (31-50)

The sum of the interior angles of a hexagon is always less than 720 degrees. (True/False)
A triangle can have two right angles. (True/False)
The exterior angle of a triangle is equal to the sum of its interior opposite angles. (True/False)
A straight angle measures 180 degrees. (True/False)
Vertical angles are always congruent. (True/False)

Section C: Fill in the Blanks (51-70)

The sum of the angles in a pentagon is __________ degrees.
In a right-angled triangle, the side opposite the right angle is called the __________.
The angles on a straight line add up to __________ degrees.
If two lines are perpendicular, then their slopes are __________.
If ∠A = 40 degrees and ∠B = 60 degrees, then ∠A and ∠B are __________ angles.

Section D: Problems (71-90)

The sum of three angles in a triangle is 180 degrees. If two angles are given as 50 degrees and 70 degrees, find the third angle.
In a parallelogram, one angle is three times the measure of its adjacent angle. Find the angles.
A straight line makes an angle of 120 degrees with one of the arms of an angle. What is the measure of the other arm?
In a quadrilateral, the angles are in the ratio 3:4:5:6. Find the measure of each angle.
The angles in a rhombus measure 80 degrees and 100 degrees. Find the other two angles.
Section A: Multiple Choice Questions (1-30)
1. In a triangle, the longest side is opposite the __________ angle. a) Acute b) Obtuse c) Right d) None of the above
2. If two angles are supplementary, and one angle is 120 degrees, what is the measure of the other angle? a) 60 degrees b) 120 degrees c) 180 degrees d) 240 degrees
3. A straight angle is equal to: a) 90 degrees b) 180 degrees c) 270 degrees d) 360 degrees
4. If ∠PQR = 75 degrees and ∠QPR = 45 degrees, what is the measure of ∠PRQ?
5. In a parallelogram, consecutive angles are: a) Supplementary b) Complementary c) Equal d) None of the above
Section B: True/False (31-50)
1. If two lines are perpendicular, they must intersect. (True/False)
2. The angles of a quadrilateral can be in the ratio 2:3:4:5. (True/False)
3. In an equilateral triangle, each angle measures 60 degrees. (True/False)
4. The diagonals of a rectangle are always equal in length. (True/False)
5. If ∠A and ∠B are adjacent angles, and ∠A measures 60 degrees, what is the measure of ∠B?
Section C: Fill in the Blanks (51-70)
1. In a trapezium, the sum of one pair of opposite angles is __________ degrees.
2. The angles of a rhombus are __________ in measure.
3. If two lines are perpendicular, their slopes are __________.
4. In a right-angled triangle, the side opposite the right angle is called the __________.
5. In a quadrilateral, the sum of the interior angles is __________ degrees.
Section D: Problems (71-90)
1. The measure of an angle is 15 degrees more than twice the measure of its supplement. Find the measure of each angle.
2. The angles in a hexagon are in the ratio 3:4:5:6:7:8. Find the measure of each angle.
3. In a cyclic quadrilateral, if one angle is 80 degrees, find the measures of the other three angles.
4. The angles in a triangle are in the ratio 2:3:4. Find the measure of each angle.
5. The angles in a quadrilateral are in the ratio 5:6:8:9. Find the measure of each angle.
Feel free to continue the sequence, ensuring a balanced coverage of various concepts related to lines and angles. Adjust the difficulty level according to the needs of your students.[/expand]

Chapter 6: The Triangle and Its Properties[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Multiple Choice Questions (MCQs)

In $△ A BC$ , if $A B = BC = A C$ , it is a: a) Scalene triangle b) Isosceles triangle c) Equilateral triangle d) Right-angled triangle
Which of the following is an obtuse-angled triangle? a) $△ X Y Z$ with $∠ X = 7 0^{\circ}$ b) $△ PQR$ with $∠ P = 9 0^{\circ}$ c) $△ L MN$ with $∠ M = 11 0^{\circ}$ d) $△ A BC$ with $∠ A = 6 0^{\circ}$
If $∠ A + ∠ B = 12 0^{\circ}$ , what type of triangle is $△ A BC$ ? a) Acute-angled b) Right-angled c) Obtuse-angled d) Equilateral
In $△ PQR$ , if $PQ = PR \neq = QR$ , it is a: a) Scalene triangle b) Equilateral triangle c) Isosceles triangle d) Acute-angled triangle

True/False Questions

True or False: In any triangle, the sum of the interior angles is $18 0^{\circ}$ .
True or False: An isosceles triangle can also be an obtuse-angled triangle.
True or False: The exterior angle at any vertex of a triangle is equal to the sum of its interior opposite angles.
True or False: A triangle with sides of lengths 3 cm, 4 cm, and 5 cm is an equilateral triangle.

Fill in the Blanks

The sum of angles in a triangle is ________ degrees.
In an isosceles triangle, the angles opposite the equal sides are ________.
A triangle with one angle measuring $9 0^{\circ}$ is called a ________ triangle.
The exterior angle at any vertex of a triangle is equal to the sum of its interior opposite ________.

Short Answer Questions

Explain why the sum of the interior angles of any triangle is always $18 0^{\circ}$ .
If $△ A BC$ is an equilateral triangle, what can you say about the measures of angles $∠ A$ , $∠ B$ , and $∠ C$ ?
Determine the type of triangle formed by the angles $3 0^{\circ}$ , $6 0^{\circ}$ , and $9 0^{\circ}$ .
Can a triangle have two right angles? Justify your answer.

Long Answer Questions

Prove that the base angles of an isosceles triangle are equal.
Derive the formula for the sum of the interior angles of a polygon and apply it to a triangle.
A triangle has angles in the ratio $2 : 3 : 4$ . Find the measures of each angle.
An architect designs a triangular park with angles measuring $4 5^{\circ}$ , $6 0^{\circ}$ , and $7 5^{\circ}$ . Determine the type of triangle formed.

Application-based Questions

A ladder leans against a wall, forming a right-angled triangle. If the base of the ladder is 12 meters and the ladder makes an angle of $6 0^{\circ}$ with the ground, find the height it reaches on the wall.
In $△ L MN$ , if $L N = 6 c m$ , $MN = 8 c m$ , and $L M = 10 c m$ , determine the type of triangle formed.
A triangle has angles measuring $5 0^{\circ}$ , $8 0^{\circ}$ , and $5 0^{\circ}$ . Determine the type of triangle and justify your answer.
An isosceles triangle has a base angle of $4 5^{\circ}$ . If the base is 10 cm, find the length of each equal side.
Multiple Choice Questions (MCQs)
1. In a right-angled triangle, the side opposite the right angle is called: a) Hypotenuse b) Base c) Perpendicular d) None of the above
2. If all angles of a triangle are less than $9 0^{\circ}$ , it is classified as: a) Acute-angled b) Obtuse-angled c) Right-angled d) Isosceles
3. Which of the following statements is true for an equilateral triangle? a) All sides are equal b) All angles are equal c) Both a and b d) None of the above
4. If $△ PQR$ is an isosceles triangle with $PQ = QR$ , then $∠ Q$ is: a) The largest angle b) The smallest angle c) A right angle d) Equal to $∠ P$
True/False Questions
1. True or False: The median of a triangle always bisects the opposite side.
2. True or False: An equilateral triangle is also an isosceles triangle.
3. True or False: The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
4. True or False: A triangle with angles $3 0^{\circ}$ , $6 0^{\circ}$ , and $9 0^{\circ}$ is always an equilateral triangle.
Fill in the Blanks
1. The longest side in a right-angled triangle is called the ________.
2. The sum of the lengths of any two sides of a triangle must be ________ than the length of the third side.
3. In an isosceles triangle, the angle between the equal sides is called the ________.
4. The point where the three medians of a triangle intersect is called the ________.
Short Answer Questions
1. Explain the Pythagorean theorem and its significance in triangles.
2. If two sides of a triangle are equal, can the triangle be a right-angled triangle? Justify your answer.
3. How does the exterior angle of a triangle relate to its remote interior angles?
4. Can an equilateral triangle also be an obtuse-angled triangle? Provide an example or explanation.
Long Answer Questions
1. Prove that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
2. Derive the formula for the area of a triangle and apply it to find the area of a triangle with base 6 cm and height 8 cm.
3. If the measures of the three angles of a triangle are in the ratio $3 : 4 : 5$ , find the measures of each angle.
4. Explain the concept of an exterior angle of a triangle. How is it related to the remote interior angles?
Application-based Questions
1. A flagpole casts a shadow that is 15 meters long when the angle of elevation of the sun is $3 0^{\circ}$ . Determine the height of the flagpole.
2. An isosceles triangle has a base angle of $6 0^{\circ}$ . If the perimeter is 24 cm, find the length of each equal side.
3. A triangle has angles measuring $4 0^{\circ}$ , $7 5^{\circ}$ , and $6 5^{\circ}$ . Determine the type of triangle and justify your answer.
4. An architect designs a triangular park with sides measuring 30 m, 40 m, and 50 m. Determine the type of triangle formed.
Feel free to adapt and rearrange these questions based on your teaching style and the pace of your class.[/expand]

Chapter 7: Congruence of Triangles[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Multiple Choice Questions (1 mark each):

What is the criterion for congruence in triangles when all three sides are equal? a. SAS b. SSS c. ASA d. RHS
If ∠A = ∠B and BC = AC, then which criterion can be used to prove △ABC ≅ △XYZ? a. SSS b. SAS c. ASA d. RHS
In △PQR, if PQ = 4 cm, QR = 6 cm, and PR = 8 cm, what is the type of triangle? a. Acute-angled b. Right-angled c. Obtuse-angled
What is the minimum information required to prove two triangles congruent? a. Two angles b. Two sides c. Three sides d. Three angles

True/False Questions (1 mark each):

True/False: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
True/False: If two triangles are congruent, their corresponding angles are also congruent.
True/False: In an isosceles triangle, the angles opposite to equal sides are equal.
True/False: If two triangles have the same base and the corresponding altitudes are equal, then the triangles are congruent.

Short Answer Questions (2 marks each):

Explain the ASA criterion for proving the congruence of two triangles.
If ∠A = 60° and ∠B = 40°, find ∠C in △ABC.
State the RHS criterion and explain when it can be used to prove triangles congruent.
In △PQR, if PQ = 3 cm, QR = 4 cm, and PR = 5 cm, is the triangle right-angled?

Long Answer Questions (4 marks each):

Prove that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
In △ABC, if ∠A = 50°, ∠B = 70°, and BC = 6 cm, find the measures of ∠C and AC.
Using the SSS criterion, prove that △ABC ≅ △DEF if AB = DE, BC = EF, and CA = FD.
Solve the triangle △PQR, given that ∠P = 40°, ∠Q = 70°, and PQ = 8 cm.

Application-based Questions (5 marks each):

A tower is observed from two points A and B on the ground. If the angles of elevation from A and B to the top of the tower are equal and the distance between A and B is 30 meters, find the height of the tower.
An isosceles triangle has base 10 cm long and each of the equal sides is 6 cm. Find its height using the Pythagorean Theorem.
In a trapezium ABCD, AB || CD, AB = 5 cm, BC = 7 cm, CD = 10 cm, and AD = 6 cm. Is △ABC ≅ △DCB?
A triangle ABC is right-angled at B. If AB = 8 cm and BC = 15 cm, find the length of the altitude from A to BC.
Multiple Choice Questions (1 mark each):
1. In an isosceles triangle, if one of the equal angles is 45°, what is the measure of the other equal angle? a. 45° b. 90° c. 135° d. 180°
2. Which of the following conditions is not sufficient to prove the congruence of two triangles? a. SAS b. AAA c. ASA d. SSS
3. If ∠A = 80° and ∠B = 40°, what is the measure of ∠C in △ABC? a. 60° b. 80° c. 100° d. 120°
4. If two triangles are congruent, what can you say about their corresponding angles? a. They are equal. b. They are supplementary. c. They are complementary. d. They are not related.
True/False Questions (1 mark each):
1. True/False: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
2. True/False: In an equilateral triangle, all three sides are equal but not all angles are equal.
3. True/False: If two triangles are congruent, their corresponding altitudes are also congruent.
4. True/False: If ∠A = ∠C in △ABC, then △ABC must be an isosceles triangle.
Short Answer Questions (2 marks each):
1. State and explain the ASA criterion for the congruence of triangles.
2. In △PQR, if ∠P = 60° and PQ = 5 cm, find the length of PR using the Pythagorean Theorem.
3. If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, what can you conclude about the triangles?
4. Explain why AAA (Angle-Angle-Angle) is not a valid criterion for proving the congruence of triangles.
Long Answer Questions (4 marks each):
1. Prove that the diagonals of a rectangle are congruent using the concept of congruent triangles.
2. In △ABC, if ∠A = 90°, AC = 12 cm, and BC = 9 cm, find the length of AB.
3. Using the SAS criterion, prove that △ABC ≅ △DEF if ∠A = ∠D, AB = DE, and AC = DF.
4. Solve the triangle △PQR, given that ∠P = 30°, PR = 10 cm, and QR = 8 cm.
Application-based Questions (5 marks each):
1. An architect designs a triangular park with sides of lengths 30 m, 40 m, and 50 m. Is the park a right-angled triangle?
2. A ladder leans against a wall at an angle of 60°. If the foot of the ladder is 5 meters away from the wall, find the length of the ladder.
3. In a quadrilateral ABCD, ∠A = ∠B = 90°, AB = 8 cm, and BC = 15 cm. Determine the length of AC using the Pythagorean Theorem.
4. A triangular field has sides of lengths 9 m, 12 m, and 15 m. Is the field an equilateral triangle? Explain.
Feel free to adapt these questions as needed for your specific class and teaching objectives.[/expand]

Chapter 8: Comparing Quantities[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Multiple Choice Questions (MCQs)

What is the percentage decrease if a quantity changes from 80 to 40? a. 40% b. 50% c. 20% d. 100%
If the original price of a book is ₹500 and it is sold at a 10% discount, what is the selling price? a. ₹450 b. ₹510 c. ₹490 d. ₹550
Which formula represents profit percentage? a. $Profit Percentage = Cost Price Profit \times 100$ b. $Profit Percentage = Selling Price Profit \times 100$ c. $Profit Percentage = Profit Cost Price \times 100$ d. $Profit Percentage = Profit Selling Price \times 100$
If the cost price is ₹800 and the selling price is ₹1200, what is the profit percentage? a. 50% b. 25% c. 150% d. 33.33%

Fill in the Blanks

The discount amount is calculated as ________ percent of the marked price.
If the cost price is ₹2000 and the loss percentage is 15%, the selling price is ________.
The selling price is equal to the cost price plus ________.

True or False

True or False: In a discount scenario, the selling price is always less than the marked price.
True or False: The profit percentage is calculated with respect to the selling price.
True or False: Percentage increase is the same as markup percentage.

Word Problems

A smartphone is initially priced at ₹15,000. During a sale, it is marked down by 25%. What is the discounted price?
Mrs. Gupta sold a pair of shoes for ₹1200, incurring a loss of 10%. What was the cost price of the shoes?
A shirt is sold for ₹450 after a discount of 10%. If the original price is ₹500, calculate the discount amount.
The cost price of a refrigerator is ₹8000, and it is sold at a profit of 20%. What is the selling price?
Multiple Choice Questions (MCQs)
1. What is the formula for calculating percentage decrease? a. $Percentage Decrease = Original Value New Value - Original Value \times 100$ b. $Percentage Decrease = Original Value Original Value - New Value \times 100$ c. $Percentage Decrease = Original Value New Value \times 100$ d. $Percentage Decrease = New Value Original Value \times 100$
2. If the marked price of a watch is ₹1200 and it is sold at a loss of 15%, what is the selling price? a. ₹1000 b. ₹1020 c. ₹1140 d. ₹900
3. The profit percentage is 40%, and the cost price is ₹500. What is the selling price? a. ₹700 b. ₹600 c. ₹800 d. ₹750
4. If the profit percentage is 25%, and the selling price is ₹1250, what is the cost price? a. ₹1000 b. ₹1100 c. ₹1200 d. ₹10000
Fill in the Blanks
1. The selling price is equal to the cost price minus ________.
2. If the cost price is ₹1500 and the profit percentage is 20%, the selling price is ________.
3. The discount amount is calculated as ________ percent of the original price.
True or False
1. True or False: Percentage decrease is always calculated with respect to the original value.
2. True or False: In a markup scenario, the selling price is equal to the cost price.
3. True or False: If the selling price is equal to the cost price, there is neither profit nor loss.
Word Problems
1. A laptop is sold for ₹45,000, incurring a loss of 10%. What was the cost price of the laptop?
2. A shopkeeper marked the price of a toy at ₹800 and gave a discount of 15%. What is the discounted price?
3. The cost price of a bicycle is ₹2500, and it is sold at a loss of 12.5%. What is the selling price?
4. A pair of shoes is sold at a profit of 25%, and the selling price is ₹1250. What is the cost price?
  Multiple Choice Questions (MCQs)
  1. If the original price of a TV is ₹20,000 and it is sold at a discount of 15%, what is the discounted price? a. ₹18,500 b. ₹17,000 c. ₹19,500 d. ₹21,500
  2. What is the formula for calculating the discount percentage? a. $Discount Percentage = Marked Price Discount \times 100$ b. $Discount Percentage = Selling Price Discount \times 100$ c. $Discount Percentage = Discount Marked Price \times 100$ d. $Discount Percentage = Discount Selling Price \times 100$
  3. If the cost price of a laptop is ₹30,000 and it is sold at a profit of 20%, what is the selling price? a. ₹36,000 b. ₹32,000 c. ₹28,000 d. ₹34,000
  4. The selling price is ₹500, and the loss percentage is 10%. What is the cost price? a. ₹550 b. ₹600 c. ₹450 d. ₹550
  Fill in the Blanks
  1. If the cost price is ₹1200 and the selling price is ₹1500, the profit is ________.
  2. The selling price is equal to the marked price minus ________.
  3. The loss percentage is calculated as ________ of the cost price.
  True or False
  1. True or False: In a discount scenario, the selling price is always less than the cost price.
  2. True or False: If the selling price is equal to the cost price, there is no profit or loss.
  3. True or False: Markup is the same as the percentage increase.
  Word Problems
  1. A store bought a shirt for ₹800 and sold it at a profit of 25%. What was the selling price?
  2. A mobile phone was originally priced at ₹15,000. It was sold at a discount of 20%. Calculate the discounted price.
  3. Mr. Patel bought a watch for ₹2500 and sold it at a loss of 15%. What was the selling price?
  4. A pair of earrings was marked at ₹1200. The store offered a discount of 10%. What was the final price paid by the customer?[/expand]

Chapter 9: Rational Numbers[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Multiple Choice Questions (1 mark each)

What is the sum of $4 3$ and $5 2$ ? a. $20 11$ b. $20 23$ c. $9 3$ d. $10 7$
Which of the following is an irrational number? a. $4 5$ b. $7$ c. $- 2 3$ d. $0.25$
If $a = - 3 2$ , what is the additive inverse of $a$ ? a. $- 3 2$ b. $3 2$ c. $2 3$ d. $- 2 3$
Arrange the following in descending order: $4 3$ , $- 3 2$ , $6 5$ . a. $6 5$ , $4 3$ , $- 3 2$ b. $4 3$ , $6 5$ , $- 3 2$ c. $- 3 2$ , $4 3$ , $6 5$ d. $- 3 2$ , $6 5$ , $4 3$

Fill in the Blanks (1 mark each)

$8 7 - 8 3 =$
$5 4 \times 3 2 =$
$10 9 \div 5 3 =$
The product of $3 2$ and its reciprocal is \underline{\hspace{1cm}}.

True/False (1 mark each)

The square root of any positive rational number is irrational. (True/False)
$0 1$ is a rational number. (True/False)

Word Problems (2 marks each)

The length of a rectangle is $4 3$ meters and its width is $5 2$ meters. Find its area.
The sum of two rational numbers is $6 5$ and one of the numbers is $3 1$ . Find the other number.

Application-Based (3 marks each)

A recipe calls for $3 2$ cup of flour. If you want to make half of the recipe, how much flour do you need?
Raj has $5 4$ of a cake, and he gives $4 1$ of his part to his friend. What fraction of the whole cake did his friend receive?
Multiple Choice Questions (1 mark each)
What is the difference between $6 5$ and $3 2$ ? a. $6 1$ b. $3 1$ c. $2 1$ d. $3 2$
If $x = - 5 4$ , what is the value of $- 3 x$ ? a. $5 12$ b. $5 4$ c. $4 3$ d. $5 3$
Which of the following is a rational number? a. $5$ b. $3 7$ c. $- 3$ d. $0.75$
If $2 a = 4 3$ , what is the value of $a$ ? a. $2 1$ b. $2 3$ c. $8 3$ d. $3 2$
Fill in the Blanks (1 mark each)
$6 5 \times 4 3 =$
$3 2 \div 5 4 =$
The reciprocal of $- 9 7$ is \underline{\hspace{1cm}}.
If $b = 5 3$ , what is the additive inverse of $b$ ?
True/False (1 mark each)
Multiplying any nonzero rational number by zero results in zero. (True/False)
$a 0 = 0$ for any nonzero $a$ . (True/False)
Word Problems (2 marks each)
A tank is filled with $5 4$ liters of water. If $5 2$ liters are poured out, how much water remains?
The perimeter of a rectangle is $6 5$ meters. If one side is $4 1$ meters, find the other side.
Application-Based (3 marks each)
A group of friends shared a pizza. If $8 3$ of the pizza was pepperoni, and $2 1$ of the remaining part was vegetarian, what fraction of the pizza was vegetarian?
A car travels $4 3$ of its total distance in the first hour and the remaining $5 1$ in the second hour. What fraction of the total distance is covered in the second hour?
Feel free to mix and match these questions to create a comprehensive set that covers various aspects of the Rational Numbers chapter in alignment with CBSE standard[/expand]

Chapter 10: Practical Geometry[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Multiple Choice Questions (1 mark each)

What is the sum of interior angles in a hexagon? a. 90 degrees b. 360 degrees c. 180 degrees d. 540 degrees
Which of the following is a basic construction using a compass? a. Adding two numbers b. Drawing a perpendicular bisector c. Solving a quadratic equation d. Simplifying a fraction
In a triangle, if one angle is 90 degrees, and another angle is 45 degrees, what is the measure of the third angle? a. 90 degrees b. 45 degrees c. 180 degrees d. 135 degrees
What tool is used to measure the size of an angle? a. Ruler b. Compass c. Protractor d. Set square
If a line is divided into two equal parts, each part is called a: a. Perpendicular bisector b. Parallel line c. Segment d. Ray

Fill in the Blanks (1 mark each)

The ____________ of a triangle is the longest side.
A polygon with eight sides is called an ____________.
The point where the perpendicular bisectors of a triangle intersect is called the ____________.
A triangle with all sides of different lengths is called a ____________.
The process of creating a circle using a compass is known as ____________.

True/False Questions (1 mark each)

True/False: The sum of interior angles in any triangle is always 180 degrees.
True/False: In an isosceles triangle, the angles opposite the equal sides are also equal.
True/False: A square is always a rectangle.
True/False: The perpendicular bisector of a line segment always passes through its midpoint.
True/False: Practical geometry is only concerned with theoretical concepts.

Matching Questions (2 marks each)

Match the geometric tool with its purpose:

Compass A. Measure angles
Protractor B. Draw circles
Ruler C. Draw straight lines
Set square D. Measure length

Short Answer Questions (2 marks each)

Explain the difference between a rhombus and a rectangle.
Define the term “centroid” in the context of triangles.
If the hypotenuse of a right-angled triangle is 10 cm and one leg is 6 cm, find the length of the other leg.
State the Converse of the Pythagorean Theorem.

Long Answer Questions (3 marks each)

Using a compass and straightedge, construct an isosceles triangle with base angles of 45 degrees and a base of 5 cm.
A parallelogram has diagonals of length 8 cm and 15 cm. Determine the area of the parallelogram.
Explain the concept of similar triangles and how it can be used in practical geometry.
In a quadrilateral, if one pair of opposite angles is equal, is the quadrilateral necessarily a parallelogram? Justify your answer.
A rectangular field has a length of 20 meters and a width of 15 meters. Find the perimeter of the field.

Application-based Questions (4 marks each)

A park is in the shape of an isosceles trapezium. If the parallel sides are 30 meters and 40 meters, and the non-parallel sides are both 25 meters, find the area of the park.
Architectural plans for a house show that one room is in the shape of a right-angled triangle with base 8 meters and height 10 meters. Determine the area of the room.
A triangular garden has sides of lengths 15 m, 24 m, and 27 m. Is the triangle acute, obtuse, or right-angled? Justify your answer.
A circle is inscribed in a square of side length 10 cm. Calculate the area of the region between the circle and the square.

Practical Construction Questions (5 marks each)

Using a compass and straightedge, construct an equilateral triangle with sides of length 6 cm.
Given a line segment AB, construct its perpendicular bisector using a compass and straightedge.
Construct a rectangle ABCD where AB = 6 cm and BC = 8 cm.
A triangle has sides of length 9 cm, 12 cm, and 15 cm. Using a compass and straightedge, construct this triangle.
Multiple Choice Questions (1 mark each)
1. What is the sum of interior angles in a pentagon? a. 90 degrees b. 360 degrees c. 180 degrees d. 540 degrees
2. Which of the following is a property of a rhombus? a. All angles are right angles. b. Opposite sides are equal. c. Diagonals bisect each other at right angles. d. All sides are of different lengths.
3. What is the measure of each angle in an equilateral triangle? a. 30 degrees b. 45 degrees c. 60 degrees d. 90 degrees
4. What is the name of the point where the three medians of a triangle intersect? a. Incenter b. Centroid c. Circumcenter d. Orthocenter
5. If two angles of a triangle are 40 degrees and 75 degrees, what is the measure of the third angle? a. 65 degrees b. 85 degrees c. 115 degrees d. 145 degrees
Fill in the Blanks (1 mark each)
1. The ____________ of a polygon is the line segment joining any two non-adjacent vertices.
2. In an isosceles triangle, the angles opposite the equal sides are ____________.
3. The ____________ of a parallelogram is a line segment that connects any two opposite vertices.
4. The sum of the exterior angles of any polygon is always ____________ degrees.
5. The perpendicular bisector of a line segment is also its ____________.
True/False Questions (1 mark each)
1. True/False: All squares are rectangles, but not all rectangles are squares.
2. True/False: The diagonals of a rectangle are equal in length.
3. True/False: In an equilateral triangle, all sides are equal, and all angles are equal.
4. True/False: The medians of a triangle always pass through its circumcenter.
5. True/False: The diagonals of a rhombus are always perpendicular to each other.
Matching Questions (2 marks each)
Match the type of triangle with its description:
1. Scalene triangle A. All sides are equal
2. Equilateral triangle B. Exactly two equal sides
3. Isosceles triangle C. No equal sides
Short Answer Questions (2 marks each)
1. Explain the term “congruent triangles.”
2. If the diagonals of a quadrilateral are equal and bisect each other, what type of quadrilateral is it?
3. What is the sum of interior angles in a regular hexagon?
4. Define the term “altitude” in the context of triangles.
Long Answer Questions (3 marks each)
1. A kite has two pairs of adjacent congruent sides. If one pair of sides is 6 cm each, find the perimeter of the kite.
2. Prove that the diagonals of a rhombus are perpendicular bisectors of each other.
3. Explain the concept of the circumcenter and how it is related to the circumcircle of a triangle.
4. A trapezium has one angle of 90 degrees and the non-parallel sides are equal. Determine the type of trapezium.
Application-based Questions (4 marks each)
1. A rectangular swimming pool has a length of 20 meters and a width of 12 meters. Determine the length of the diagonal of the pool.
2. The diagonals of a rhombus are 10 cm and 24 cm. Find the area of the rhombus.
3. A regular pentagon is inscribed in a circle of radius 8 cm. Calculate the perimeter of the pentagon.
4. A triangular pyramid has a base with sides of length 5 cm, 6 cm, and 7 cm. If the height of the pyramid is 8 cm, find its volume.
Practical Construction Questions (5 marks each)
1. Construct a quadrilateral ABCD where AB = 4 cm, BC = 6 cm, CD = 8 cm, and AD = 5 cm.
2. Using a compass and straightedge, construct an angle of 75 degrees.
3. Construct a square PQRS where PQ = 3 cm.
4. Construct a rhombus XYZW where each side is 4 cm, and one angle is 60 degrees.
Feel free to integrate these questions into your worksheet, and modify them as needed for your specific classroom context.[/expand]

Chapter 11: Perimeter and Area[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Section A: Perimeter

1-10: Multiple Choice Questions (MCQs)

The sum of the lengths of all sides of a polygon is called: a) Diameter b) Perimeter c) Circumference d) Area
What is the perimeter of a rectangle with length 12 cm and width 5 cm? a) 24 cm b) 34 cm c) 44 cm d) 60 cm
If the perimeter of a square is 36 cm, what is the length of each side? a) 6 cm b) 9 cm c) 12 cm d) 18 cm
The perimeter of an equilateral triangle with side length 10 cm is: a) 10 cm b) 20 cm c) 30 cm d) 40 cm
If the perimeter of a polygon is 48 cm and one side is 12 cm, what is the sum of the lengths of the other sides? a) 24 cm b) 36 cm c) 48 cm d) 60 cm
A rectangle has a length of 15 cm and a width of 8 cm. What is its perimeter? a) 21 cm b) 38 cm c) 46 cm d) 60 cm
The perimeter of a regular hexagon with each side measuring 5 cm is: a) 10 cm b) 15 cm c) 25 cm d) 30 cm
The sum of the angles in a rectangle is: a) 180 degrees b) 360 degrees c) 90 degrees d) 270 degrees
If the perimeter of a triangle is 24 cm and two sides are equal, what is the length of each equal side? a) 6 cm b) 8 cm c) 12 cm d) 16 cm
The perimeter of a square is twice the length of one of its sides. What is the length of one side? a) 4 cm b) 6 cm c) 8 cm d) 10 cm

11-20: True/False Statements 11. The perimeter of a rectangle is equal to four times its length. a) True b) False

The perimeter of a square is equal to the sum of the lengths of its sides. a) True b) False
The perimeter of a circle is twice its radius. a) True b) False
The perimeter of an isosceles triangle is the sum of the lengths of its three sides. a) True b) False
In any polygon, the sum of the measures of all interior angles is always 180 degrees. a) True b) False
If the perimeter of a rectangle is 30 cm, the sum of its length and width is 30 cm. a) True b) False
The perimeter of an equilateral triangle is three times the length of one of its sides. a) True b) False
The perimeter of a regular hexagon is six times the length of one of its sides. a) True b) False
The perimeter of a polygon is always an integer. a) True b) False
If the perimeter of a square is 20 cm, the length of one side is 5 cm. a) True b) False

21-30: Fill in the Blanks 21. The ____________ of a polygon is the sum of the lengths of its sides.

The perimeter of a square with side length $s$ is ____________.
If the perimeter of a triangle is 18 cm, and one side is 6 cm, the sum of the lengths of the other two sides is ____________.
The perimeter of a regular pentagon with each side measuring 7 cm is ____________.
The perimeter of a rectangle is twice the sum of its ____________.
The perimeter of a circle is also known as its ____________.
The sum of the interior angles of a triangle is ____________ degrees.
In a parallelogram, opposite sides are ____________ in length.
The perimeter of an isosceles triangle with equal sides of length $a$ and the base of length $b$ is ____________.
The perimeter of a regular octagon with each side measuring 4 cm is ____________.

Section B: Area

31-40: Multiple Choice Questions (MCQs) 31. The space occupied by a two-dimensional figure is called: a) Length b) Perimeter c) Area d) Volume

What is the area of a square with each side measuring 9 cm? a) 18 cm² b) 27 cm² c) 36 cm² d) 81 cm²
If the length of a rectangle is 10 m and the width is 6 m, what is its area? a) 16 m² b) 36 m² c) 60 m² d) 90 m²
The area of a triangle with base 12 cm and height 8 cm is: a) 48 cm² b) 60 cm² c) 72 cm² d) 96 cm²
If the area of a rectangle is 24 cm² and the length is 4 cm, what is the width? a) 2 cm b) 4 cm c) 6 cm d) 8 cm
The area of a circle with radius 5 cm is: a) 25π cm² b) 50π cm² c) 100π cm² d) 125π cm²
The area of a parallelogram with base 8 cm and height 10 cm is: a) 40 cm² b) 64 cm² c) 80 cm² d) 100 cm²
The area of a regular hexagon with side length 6 cm is: a) 36√3 cm² b) 72√3 cm² c) 108√3 cm² d) 144√3 cm²
The area of a trapezium with bases 5 cm and 8 cm and height 12 cm is: a) 78 cm² b) 96 cm² c) 120 cm² d) 144 cm²
The area of a rhombus with diagonals of lengths 10 cm and 12 cm is: a) 40 cm² b) 60 cm² c) 80 cm² d) 120 cm²

41-50: True/False Statements 41. The area of a rectangle is given by the product of its length and width. a) True b) False

The area of a square is given by the formula $A = 4 s$ . a) True b) False
The area of a triangle is half the product of its base and height. a) True b) False
The area of a parallelogram is the product of its base and height. a) True b) False
The area of a circle is given by the formula $A = π r^{2}$ . a) True b) False
The area of a trapezium is the sum of the lengths of its bases. a) True b) False
The area of a regular pentagon with side length $s$ is $5 s^{2} tan (5 4^{\circ})$ . a) True b) False
The area of a rhombus is half the product of its diagonals. a) True b) False
The area of a sector of a circle is given by the formula $A = 2 1 r^{2} θ$ , where $θ$ is the central angle. a) True b) False
The area of a regular octagon with side length $s$ is $2 s^{2} 2 (1 + 2)$ . a) True b) False

51-60: Fill in the Blanks 51. The area of a rectangle is given by the formula $A = \times$ .

The area of a square with side length $s$ is $A = \times$ .
The formula for the area of a triangle is $A = 2 1 \times \times$ .
The area of a parallelogram is $A = \times$ .
The formula for the area of a circle is $A = π \times^{2}$ .
The area of a trapezium is given by the formula $A = 2 1 \times (+) \times$ .
The area of a regular hexagon with side length $s$ is $A = 2 3 3 \times^{2}$ .
The formula for the area of a rhombus is $A = 2 1 \times \times$ .
The area of a sector of a circle is $A = 2 1 \times^{2} \times$ , where $θ$ is the central angle.
The area of a regular pentagon with side length $s$ is $A = 4 1 \times 5 (5 + 25) \times^{2}$ .

Section C: Word Problems

61-70: Word Problems 61. A rectangular field has a length of 15 m and a width of 8 m. Calculate its perimeter and area.

The perimeter of a square garden is 36 m. Find the length of each side. Also, calculate the area of the square garden.
The length of a rectangle is 10 cm, and the width is 6 cm. Calculate the perimeter and area of the rectangle.
The area of a triangle is 24 cm², and the base is 6 cm. Find the height of the triangle.
The perimeter of an equilateral triangle is 30 cm. Find the length of each side.
The radius of a circle is 7 cm. Calculate the perimeter and area of the circle.
The base of a parallelogram is 12 cm, and the height is 8 cm. Determine the perimeter and area of the parallelogram.
The side length of a regular hexagon is 9 cm. Calculate its perimeter and area.
A trapezium has bases of lengths 5 cm and 8 cm, and the height is 12 cm. Find the perimeter and area of the trapezium.
The diagonals of a rhombus measure 10 cm and 12 cm. Determine the perimeter and area of the rhombus.

71-80: Application 71. You have a rectangular room with a length of 6 m and a width of 4 m. Calculate both the perimeter and area of the room.

Imagine you have a triangular garden with sides measuring 9 m, 12 m, and 15 m. Find its perimeter and area.
If the side length of a regular pentagon is 8 cm, calculate its perimeter and area.
You are designing a circular fountain with a radius of 10 m. Determine the perimeter and area of the fountain.
A farmer has a rectangular field with a length of 18 m and a width of 10 m. Calculate the perimeter and area of the field.
An isosceles triangle has equal sides of length 7 cm each, and the base is 10 cm. Find its perimeter and area.
The length of a rectangle is 14 m, and the width is 7 m. Determine the perimeter and area of the rectangle.
A regular octagon has side lengths of 5 cm each. Calculate its perimeter and area.
A trapezium has bases of lengths 6 m and 9 m, and the height is 8 m. Find the perimeter and area of the trapezium.
You are making a circular flower bed with a radius of 6 m. Calculate the perimeter and area of the flower bed.
Question Set 1: Perimeter
1. Find the perimeter of a rectangle with length 12 cm and width 7 cm.
  - a) 38 cm
  - b) 26 cm
  - c) 46 cm
  - d) 24 cm
2. The perimeter of a square is 24 meters. What is the length of each side?
  - a) 4 m
  - b) 6 m
  - c) 8 m
  - d) 12 m
3. An isosceles triangle has sides of length 5 cm, 5 cm, and 8 cm. What is the perimeter?
  - a) 15 cm
  - b) 16 cm
  - c) 18 cm
  - d) 20 cm
4. The length of a rectangle is 15 cm, and its perimeter is 50 cm. What is the width?
  - a) 10 cm
  - b) 5 cm
  - c) 20 cm
  - d) 25 cm
5. A regular hexagon has a perimeter of 36 cm. What is the length of each side?
  - a) 4 cm
  - b) 6 cm
  - c) 3 cm
  - d) 8 cm
Question Set 2: Area
1. Calculate the area of a square garden with a side length of 10 meters.
  - a) 100 m²
  - b) 50 m²
  - c) 120 m²
  - d) 25 m²
2. The area of a rectangle is 56 cm², and its length is 8 cm. What is the width?
  - a) 6 cm
  - b) 7 cm
  - c) 5 cm
  - d) 4 cm
3. Find the area of a parallelogram with a base of 12 cm and a height of 9 cm.
  - a) 108 cm²
  - b) 54 cm²
  - c) 96 cm²
  - d) 72 cm²
4. The length of a rectangle is 10 cm, and the area is 50 cm². What is the width?
  - a) 5 cm
  - b) 10 cm
  - c) 15 cm
  - d) 25 cm
5. A triangular field has a base of 6 m and a height of 8 m. What is the area?
  - a) 24 m²
  - b) 30 m²
  - c) 36 m²
  - d) 48 m²
Question Set 3: Word Problems
1. The perimeter of a square is 32 cm. Find the length of each side.
2. A rectangular room has a length of 15 meters and a width of 10 meters. What is the perimeter of the room?
3. The length of a rectangle is 18 cm, and its width is 5 cm. Calculate the perimeter.
4. A garden is in the shape of an equilateral triangle with sides of length 12 meters. What is the perimeter?
5. The sides of a quadrilateral are 7 cm, 8 cm, 9 cm, and 10 cm. Find the perimeter.
Question Set 4: Application
1. Imagine a square tile with a perimeter of 20 cm. What is the length of each side?
2. You have a rectangular plot with a length of 25 m and a width of 12 m. Find the area of the plot.
3. A swimming pool is in the shape of a rectangle with a length of 20 meters and a width of 10 meters. Calculate the pool’s area.
4. A circular garden has a circumference of 31.4 meters. What is the radius of the garden?
5. A field in the shape of a parallelogram has a base of 14 cm and a height of 10 cm. Find the area of the field.
Question Set 5: Evaluation
1. Explain the difference between perimeter and area.
2. Give an example of a real-life situation where knowing the area is important.
3. How do you calculate the perimeter of an irregular polygon?
4. Why is it necessary to include units when expressing the perimeter or area?
5. If the length of a rectangle is equal to its width, how does this affect the perimeter and area?[/expand]

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

Section A: Simplification (Questions 1-30)

$3 x + 4 y - 2 x + 5 y$
$5 a - 2 a + 6 b - 3 b$
$2 m + 3 n - 4 m + n$
$7 x - 3 y + 2 x - 5 y$
$6 a + 2 a - 4 b + 7 b$
$4 m - 2 n + 5 m + 3 n$
$8 x + 2 y - 3 x - 4 y$
$3 a - 5 a + 8 b - 2 b$
$2 m - 3 n + 6 m - 2 n$
$9 x - 4 y + x + 6 y$

Section B: Evaluation (Questions 31-60)

Evaluate $4 x - 2 y$ for $x = 2, y = 3$
Evaluate $3 a + 5 b - 2 a$ for $a = 4, b = 1$
Evaluate $2 m - 4 n + 3 m$ for $m = 5, n = 2$
Evaluate $5 x + 3 y$ for $x = 1, y = 2$
Evaluate $a + 2 b - 3 a$ for $a = 3, b = 2$
Evaluate $m - 2 n + 4 m$ for $m = 2, n = 1$
Evaluate $6 x - 5 y$ for $x = 3, y = 2$
Evaluate $2 a + 3 b - 4 a$ for $a = 2, b = 5$
Evaluate $3 m - n + 2 m$ for $m = 4, n = 1$
Evaluate $7 x - 2 y$ for $x = 2, y = 1$

Section C: Word Problems (Questions 61-75)

The sum of twice a number and five.
Three more than the product of a number and four.
The difference between seven times a number and two.
The product of a number and three less than another number.
Four less than twice a number.
Five more than three times a number.
The sum of a number and its square.
Six less than the product of a number and two.
Eight more than half of a number.
Ten less than three times a number.

Section D: Equations (Questions 76-90)

Solve for $x$ in $2 x + 5 = 11$ .
Solve for $y$ in $3 y - 7 = 8$ .
Solve for $m$ in $4 m + 2 = 14$ .
Solve for $x$ in $3 x - 2 = 7$ .
Solve for $y$ in $2 y + 4 = 10$ .
Solve for $a$ in $5 a - 3 = 22$ .
Solve for $x$ in $2 x - 6 = 10$ .
Solve for $b$ in $4 b + 7 = 19$ .
Solve for $m$ in $2 m + 8 = 18$ .
Solve for $a$ in $3 a - 5 = 10$ .
Section E: Mixed Practice (Questions 91-105)
1. Simplify: $2 x + 3 y - x + 5 y$
2. Evaluate: $5 a - 2 b$ for $a = 3, b = 2$
3. Translate into an expression: Three less than twice a number.
4. Solve for $x$ in $4 x - 7 = 9$ .
5. Simplify: $3 m + 2 n - 4 m + n$
6. Evaluate: $2 a + 4 b - 3 a$ for $a = 5, b = 1$
7. Translate into an expression: The sum of a number and eight.
8. Solve for $y$ in $3 y + 5 = 20$ .
9. Simplify: $7 x - 3 y + 2 x - 5 y$
10. Evaluate: $4 a + 2 b - 3 a$ for $a = 2, b = 4$
Section F: Advanced Practice (Questions 106-120)
1. Simplify: $6 x - 4 y + 3 x - 2 y$
2. Evaluate: $3 a - 2 b + 4 a$ for $a = 1, b = 2$
3. Translate into an expression: Seven more than twice a number.
4. Solve for $m$ in $2 m - 5 = 7$ .
5. Simplify: $4 m - 2 n + 5 m + 3 n$
6. Evaluate: $8 x - 2 y + 3 x$ for $x = 4, y = 1$
7. Translate into an expression: Four times the difference between a number and six.
8. Solve for $b$ in $2 b + 8 = 18$ .
9. Simplify: $8 x + 2 y - 3 x - 4 y$
10. Evaluate: $3 a - 5 b + 8 a$ for $a = 3, b = 2$
Feel free to use or modify these questions based on the specific needs of your students or the depth of understanding you wish to assess.[/expand]

Chapter 13: Exponents and Power[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Objective Type Questions:

What is the value of $2^{5}$ ? a. 25 b. 32 c. 64 d. 128
Evaluate $3^{4}$ . a. 81 b. 12 c. 64 d. 27
Write the expression $5^{3}$ in standard form.
Simplify: $2^{3} \times 2^{4}$ .
Find the value of $x$ in $4^{x} = 256$ .

Fill in the blanks:

$62=6×_____$ .
$90=_____$ .
$28÷25=2____$ .

True/False:

$1 0^{3}$ is equal to $10 \times 10 \times 10$ . a. True b. False
Any number to the power of 0 is 1. a. True b. False

Match the following:

Match the following expressions with their values.
- $2^{4}$
- $3^{3}$
- $5^{2}$
a. 9 b. 25 c. 16

Long Answer Type:

If $a^{2} = 36$ , find the value of $a$ .
Explain the concept of exponents and their importance in mathematics.

Application-Based:

If you have a rectangular box with sides of length $2^{3}$ cm, $2^{2}$ cm, and $2$ cm, what is the volume of the box?
A population of bacteria doubles every hour. If there are initially 10 bacteria, how many will there be after 5 hours?
Objective Type Questions:
1. What is the value of $1 0^{1}$ ?
2. If $a^{3} = 125$ , what is the value of $a$ ?
3. Evaluate $2^{-3}$ .
4. If $b^{2} = 16$ , find the value of $b$ .
5. Write $4^{2}$ as a power of 2.
Fill in the blanks:
1. $31=3×_____$ .
2. $70=_____$ .
3. $54÷52=5____$ .
True/False:
1. $2^{6}$ is equal to $2 \times 6$ . a. True b. False
2. $3^{-2}$ is the same as $3 ^{2} 1$ . a. True b. False
Match the following:
1. Match the following expressions with their values.
  - $6^{2}$
  - $2^{-2}$
  - $3^{4}$
  a. 36 b. 1/9 c. 16
Long Answer Type:
1. Explain the zero exponent rule and provide an example.
2. If $c^{3} = 27$ , find the value of $c$ .
Application-Based:
1. A cell divides into two cells every 3 hours. If there are initially 4 cells, how many cells will there be after 12 hours?
2. A rectangular field has a length of $2^{2}$ meters and a width of $2^{3}$ meters. What is the area of the field?
Feel free to use, modify, or rearrange these questions to suit your needs![/expand]

Chapter 14: Symmetry[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Section A: Multiple Choice Questions (1 mark each)

What is the definition of symmetry? a) A type of shape
b) A repeating pattern
c) A figure that can be divided into two identical parts
d) None of the above
How many lines of symmetry does the letter ‘O’ have? a) 0
b) 1
c) 2
d) Infinite
Which of the following figures has rotational symmetry? a) Square
b) Rectangle
c) Triangle
d) Circle
What is the line of symmetry in an isosceles triangle? a) Base
b) Altitude
c) Median
d) No line of symmetry
Identify the symmetrical figure from the given options. a) [Figure A]
b) [Figure B]
c) [Figure C]
d) [Figure D]

Section B: True/False (1 mark each)

The letter ‘Y’ has two lines of symmetry. (True/False)
A rhombus has exactly one line of symmetry. (True/False)
The capital letter ‘D’ has rotational symmetry. (True/False)
A square has four lines of symmetry. (True/False)
A hexagon can have either 0, 1, or 6 lines of symmetry. (True/False)

Section C: Short Answer Questions (2 marks each)

Explain what rotational symmetry is. Provide an example.
Determine the number of lines of symmetry in the following figures: a) Parallelogram
b) Trapezium
c) Rhombus
Draw a symmetrical figure with exactly three lines of symmetry.
What is the difference between line symmetry and rotational symmetry?

Section D: Application Problems (3 marks each)

A rectangular flag has a length of 10 meters and a width of 6 meters. Determine if the rectangle has a line of symmetry. If yes, draw it.
Priya has a design that she wants to put on her notebook cover. The design is shown below. Determine the lines of symmetry in the design. [Insert Design Image]
A regular hexagon has how many lines of symmetry?
A triangle has one line of symmetry. Can it have rotational symmetry?

Section E: Long Answer Questions (5 marks each)

Consider the capital letter ‘Z.’ Explain why it has rotational symmetry but no line of symmetry. Provide a detailed explanation.
Discuss the importance of symmetry in architecture. Provide examples.
An irregular quadrilateral has two lines of symmetry. Can you draw such a quadrilateral? If yes, provide one example and explain why it has two lines of symmetry.
Elaborate on the concept of bilateral symmetry in living organisms. Provide examples.
Section A: Multiple Choice Questions (1 mark each)
1. What is the line of symmetry in the letter ‘A’? a) Horizontal line
  b) Vertical line
  c) Diagonal line
  d) No line of symmetry
2. Which of the following has rotational symmetry? a) Rectangle
  b) Pentagon
  c) Hexagon
  d) Rhombus
3. The number of lines of symmetry in a regular octagon is: a) 4
  b) 6
  c) 8
  d) 12
4. Identify the symmetrical figure from the given options. a) [Figure E]
  b) [Figure F]
  c) [Figure G]
  d) [Figure H]
5. A scalene triangle can have: a) 0 lines of symmetry
  b) 1 line of symmetry
  c) 2 lines of symmetry
  d) 3 lines of symmetry
Section B: True/False (1 mark each)
1. Every equilateral triangle has rotational symmetry. (True/False)
2. The letter ‘X’ has both line symmetry and rotational symmetry. (True/False)
3. A regular pentagon has no lines of symmetry. (True/False)
4. A square has a greater number of lines of symmetry than a rectangle. (True/False)
5. The word “LEVEL” has rotational symmetry. (True/False)
Section C: Short Answer Questions (2 marks each)
1. Explain what reflection symmetry means in the context of symmetry.
2. Determine the lines of symmetry for each of the following: a) Trapezoid
  b) Kite
  c) Regular hexagon
3. If a figure has exactly two lines of symmetry, what type of figure could it be? Provide an example.
4. Can a figure have both rotational symmetry and line symmetry simultaneously? Justify your answer.
Section D: Application Problems (3 marks each)
1. A designer is creating a logo and wants it to have rotational symmetry. Design a simple logo with at least three lines of rotational symmetry.
2. A circular table has a diameter of 120 cm. Determine if the table has a line of symmetry. If yes, draw it.
3. A student claims that an irregular pentagon can have 5 lines of symmetry. Evaluate the statement and explain your reasoning.
4. Two friends are discussing a shape. One says it has line symmetry, and the other says it has rotational symmetry. Can they both be correct? Justify your answer.
Section E: Long Answer Questions (5 marks each)
1. Discuss how symmetry is applied in creating patterns. Provide examples from art or design.
2. Investigate and explain why a regular heptagon (7 sides) has only 2 lines of symmetry.
3. Compare and contrast line symmetry and rotational symmetry. Provide examples to illustrate the differences.
4. Design a unique figure that has both line symmetry and rotational symmetry. Explain your design choices.
This set adds more variety to the question types, ensuring a comprehensive understanding of symmetry for the students.[/expand]

Chapter 15: Visualising Solid Shapes[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Creating a set of 90 questions involves a considerable number of questions. Below, I’ll provide a diverse set of questions covering various question types as per the CBSE standards.

Class 7 Mathematics Question Set

Chapter 15: Visualising Solid Shapes

Name: _______________________________________ Roll Number: _______

I. Multiple Choice Questions (1 mark each)

What is the defining characteristic of a 3D shape?
- A. Length
- B. Width
- C. Height
- D. Volume
How many faces does a cuboid have?
- A. 4
- B. 6
- C. 8
- D. 10
What is the shape of the base of a cone?
- A. Square
- B. Circle
- C. Triangle
- D. Rectangle
How many edges does a sphere have?
- A. 0
- B. 1
- C. 2
- D. Infinite
Which of the following is an example of a pyramid?
- A. Dice
- B. Football
- C. Book
- D. Coin
What is the total number of vertices in a triangular prism?
- A. 3
- B. 6
- C. 9
- D. 12
A cylinder has how many curved edges?
- A. 0
- B. 1
- C. 2
- D. 3
Which 3D shape has all faces as triangles?
- A. Cube
- B. Sphere
- C. Cone
- D. Tetrahedron
The net of a cube consists of __________.
- A. 4 squares
- B. 6 squares
- C. 8 squares
- D. 12 squares
If the volume of a cube is 125 cubic units, what is the length of each side?

II. True/False Statements (1 mark each)

A cylinder has two parallel circular bases. (True/False)
All faces of a prism are rectangles. (True/False)
The number of vertices of a pyramid is always less than the number of its edges. (True/False)
A cone has a curved surface. (True/False)
The net of a 3D shape can always be folded to form the shape. (True/False)
A sphere has no edges. (True/False)
A cuboid and a rectangular prism are the same. (True/False)
A pyramid can have a square base. (True/False)
A cylinder has three faces. (True/False)
A cube has more edges than vertices. (True/False)

III. Short Answer Questions (2 marks each)

Explain the concept of a net in the context of 3D shapes.
Calculate the surface area of a cube with a side length of 4 cm.
Differentiate between a pyramid and a prism.
If the height of a cylinder is 8 cm and the radius is 3 cm, find its volume. (Use $π = 7 22$ )
Define the term “vertex” in the context of 3D shapes.
If the volume of a rectangular prism is 60 cubic units and its length is 5 units, find the product of its width and height.
Identify a 3D shape commonly found in packaging.
How does a cone differ from a cylinder?
Calculate the total surface area of a cylinder with a radius of 5 cm and a height of 10 cm. (Use $π = 7 22$ )
What is the difference between a cube and a cuboid?

IV. Application-Based Questions (3 marks each)

Real-life Applications: Describe three real-life scenarios where knowledge of 3D shapes is essential.
Problem Solving: A rectangular prism has dimensions 6 cm, 8 cm, and 10 cm. Calculate its volume.
Practical Understanding: Explain how to find the surface area of a cylinder.
Visualization Skills: Draw the net of a triangular pyramid.
Critical Thinking: Can a cuboid have all its faces as squares? Justify your answer.
Math in the Environment: How does the shape of a water tank affect its capacity?
Geometry in Architecture: Identify and describe the 3D shapes present in a common building structure.
Word Problem: Mary has a cylindrical jar with a radius of 4 cm and a height of 12 cm. What is the volume of the jar? (Use $π = 7 22$ )
Logical Reasoning: Can a pyramid have a circular base? Provide reasoning for your answer.
Creative Application: Design a box that can be folded from a single sheet of paper, with a square base and a height of 6 cm.
V. Matching Questions (1 mark each)
1. Match the 3D shape with its number of vertices.
- A. Cube
- B. Cylinder
- C. Cone
- D. Sphere
i. 8 vertices ii. 0 vertices iii. 1 vertex iv. 2 vertices
1. Match the 3D shape with its number of curved edges.
- A. Cone
- B. Sphere
- C. Cylinder
- D. Prism
i. 0 curved edges ii. 1 curved edge iii. 2 curved edges iv. 3 curved edges
1. Match the 3D shape with its base shape.
- A. Cuboid
- B. Pyramid
- C. Cylinder
- D. Sphere
i. Rectangle ii. Triangle iii. Circle iv. Square
1. Match the 3D shape with its net.
- A. Cube
- B. Pyramid
- C. Cylinder
- D. Sphere
i. $□ □ □ □ □$ ii. $□ □ □ □$ iii. $□ □ □ □ □$ iv. $□ □ □ □$
VI. Diagram-Based Questions (2 marks each)
1. Draw and label the net of a cube.
2. Identify and label the vertices, edges, and faces of a cylinder.
3. Sketch a pyramid with a square base and label its dimensions.
4. Draw a rectangular prism and indicate the length, width, and height.
VII. Descriptive Questions (3 marks each)
1. Critical Analysis: Explain why a sphere is considered a 3D shape even though it has no faces.
2. Comparative Analysis: Compare and contrast a cone and a pyramid.
3. Real-life Connections: Discuss how understanding 3D shapes is important in fields like architecture or engineering.
4. Problem-Solving Challenge: A cylindrical tank has a radius of 6 m and a height of 10 m. Calculate the volume of water it can hold. (Use $π = 7 22$ )
5. Application of Formulas: Explain how to find the surface area of a cuboid.
6. Generalization: Can all 3D shapes have a net? Justify your response.
7. Math in Nature: Provide examples of objects in nature that can be represented by 3D shapes.
8. Practical Application: Describe a situation where knowing the volume of a 3D shape is crucial.
9. Extended Problem Solving: Create a real-life scenario where you need to find the surface area of a composite 3D shape.
10. Reflective Thinking: How does learning about 3D shapes contribute to your understanding of spatial relationships?

[/expand]

Integer Basics:

Operations with Integers:

Number Line:

Word Problems:

Multiplication and Division:

Application Problems:

Challenge Questions:

Absolute Value:

Operations Mix:

Comparisons:

Multiplying and Dividing by -1:

Patterns:

Problem-Solving:

Word Problems:

Real-Life Scenarios:

Exploring Operations:

Mixed Review:

Application Problems:

Challenge Questions:

Section A: Fractions

Section B: Decimals

Section C: Comparing and Ordering

Section D: Word Problems

Section E: Practical Application

Section F: Advanced Problems

Section G: Fractions, Decimals, and Percentages

Section H: Real-Life Applications

Section I: Open-Ended Problems

Section J: Critical Thinking

Multiple Choice Questions (MCQs)

Fill in the Blanks

Short Answer Questions

Application-Based Questions

Long Answer Questions

Multiple Choice Questions (MCQs)

Fill in the Blanks

Short Answer Questions

Application-Based Questions

Long Answer Questions

Type 1: Solving Equations

Type 2: Word Problems

Type 3: Application Problems

Type 4: Forming Equations

Type 5: Checking Solutions

Type 6: Multi-step Equations

Type 7: Word Problems with Multi-step Equations

Type 8: Forming and Solving Equations from Word Problems

Type 9: Real-life Applications

Type 10: Inequalities

Multiple Choice Questions (MCQs)

True/False Questions

Fill in the Blanks

Short Answer Questions

Long Answer Questions

Application-based Questions

Multiple Choice Questions (MCQs)

True/False Questions

Fill in the Blanks

Short Answer Questions

Long Answer Questions

Application-based Questions

Multiple Choice Questions (MCQs)

Fill in the Blanks

True or False

Word Problems

Multiple Choice Questions (MCQs)

Fill in the Blanks

True or False

Word Problems

Multiple Choice Questions (MCQs)

Fill in the Blanks

True or False

Word Problems

Multiple Choice Questions (1 mark each)

Fill in the Blanks (1 mark each)

True/False (1 mark each)

Word Problems (2 marks each)

Application-Based (3 marks each)

Multiple Choice Questions (1 mark each)

Fill in the Blanks (1 mark each)