MATHS(Q) – TeachGyan

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

Section A: Multiple Choice Questions (1 mark each)

What is the smallest natural number? a. 0 b. 1 c. 2 d. -1
Identify the type of number: -√9 a. Whole b. Integer c. Rational d. Irrational
Which of the following is a prime number? a. 1 b. 2 c. 4 d. 6
Write 25% as a decimal. a. 0.25 b. 0.5 c. 0.75 d. 1
Arrange the numbers in ascending order: -3, 0, 5, -2. a. -3, -2, 0, 5 b. 0, -2, -3, 5 c. -2, -3, 0, 5 d. -3, 0, -2, 5

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

9 is a __________ number.
The sum of a prime number and an even number is always ___________.
The number 2.5 can be written as ____________ in fraction form.
The LCM of 6 and 8 is __________.
The difference between two consecutive whole numbers is always __________.

Section C: True/False (1 mark each)

True or False: Zero is neither positive nor negative.
True or False: The square root of 16 is an irrational number.
True or False: -7 is greater than -5.
True or False: The product of any number and 1 is the number itself.
True or False: The number 0.75 can be written as a fraction in simplest form.

Section D: Match the Following (2 marks each)

Match the following types of numbers with their definitions.

Natural Numbers A. A number that can be expressed as a/b, where a and b are integers and b is not equal to zero.
Whole Numbers B. The set of counting numbers starting from 1.
Rational Numbers C. The set of numbers that includes zero and all the counting numbers.
Irrational Numbers D. The set of all positive and negative integers along with zero.

Section E: Short Answer (2 marks each)

Explain the concept of a prime number.
Represent the number 8,450 in expanded form.
What is the sum of the first 20 natural numbers?
Differentiate between rational and irrational numbers.
If x is a negative integer, what is the value of -x?

Section F: Application (3 marks each)

A shopkeeper gave a discount of 15% on an item originally priced at ₹800. Find the discounted price.
A rectangular garden has a length of 12 meters and a width of 8 meters. Find its area.
The temperature at 6 a.m. was -2°C. If it decreases by 3°C per hour, what will be the temperature at 10 a.m.?
Raj bought a book for ₹350 and sold it at a profit of 20%. Find the selling price.
The sum of two consecutive odd numbers is 44. Find the numbers.

Section G: Problem Solving (4 marks each)

The product of two consecutive integers is 72. Find the integers.
A number is 5 more than three times another number. If their sum is 26, find the numbers.
The sum of three consecutive integers is 48. Find the integers.
A man spent 30% of his monthly salary on rent, 20% on groceries, and the rest on other expenses. If his salary is ₹15,000, find the amount he spent on groceries.
The perimeter of a rectangle is 32 cm. If the length is 10 cm, find the width.
Section H: Crossword Puzzle (5 marks)
Use the clues to fill in the crossword puzzle below:

Clues:
Across:
1. The opposite of positive.
2. A whole number greater than 1 that has no positive divisors other than 1 and itself.
3. The result of multiplying two or more numbers.
4. The process of expressing a number as the product of its prime factors.
Down:
1. The sum of a number and its additive inverse.
2. The result of dividing one number by another.
3. A decimal that repeats indefinitely without terminating.
Section I: True/False Statements (1 mark each)
1. True or False: Every integer is a rational number.
2. True or False: The sum of two rational numbers is always a rational number.
3. True or False: A square number can never be negative.
4. True or False: The least common multiple (LCM) of two numbers is always greater than or equal to the numbers.
5. True or False: The square root of 1 is a rational number.
Section J: Matching (2 marks each)
Match the mathematical term with its definition.
1. Prime Number A. The number at the bottom of a fraction.
2. Numerator B. A number that can be expressed as a/b, where a and b are integers and b is not equal to zero.
3. Denominator C. A number that has exactly two distinct positive divisors: 1 and itself.
4. Composite Number D. The top number in a fraction.
5. Reciprocal E. A number that has more than two positive divisors.
Section K: Word Problems (3 marks each)
1. A train travels 240 km in 3 hours. What is its speed?
2. A rectangular field has a length of 15 meters and a width of 10 meters. Find its area.
3. The sum of three consecutive odd numbers is 63. Find the numbers.
4. A recipe requires 2/3 cup of sugar. If you want to make half of the recipe, how much sugar do you need?
5. A number is 8 more than four times another number. If their sum is 36, find the numbers.
Section L: Critical Thinking (4 marks each)
1. Explain why zero is considered neither positive nor negative.
2. Discuss the importance of prime factorization in mathematics.
3. A square has a side length of 7 cm. If the square is cut into four equal parts, find the perimeter of each smaller square.
4. Suman had some money. She spent 20% on clothes and 30% on books. If she had ₹600 left, how much money did she have originally?
5. Raj is thinking of a number. If he multiplies it by 4 and then adds 7, he gets 31. What is the number?
These additional questions should provide a comprehensive assessment of the students’ understanding of the chapter. Adjust the number of questions based on the time available for the assessment.[/expand]

Chapter 2: Whole Numbers[expand title=”Read More➔” swaptitle=”🠔Read Less”]

A. Identify the Whole Numbers (1-10)

Write the first ten whole numbers.
- ______, ______, ______, ______, ______, ______, ______, ______, ______, ______
Circle the whole numbers in the list below:
- 18.5, 6, 12, 3.2, 7, 0, 14.9, 9
Place the following numbers on the number line:
- $\circ$ 4 $\circ$ 11 $\circ$ 20 $\circ$ 2 $\circ$ 15
Identify the smallest and largest whole numbers from the following:
- 25, 10, 18, 13, 30, 22
Write the next three whole numbers after 48.

B. Operations with Whole Numbers (11-20)

Solve the following addition problems:
- $32 + 15 =$ ______
- $40 + 9 =$ ______
- $58 + 27 =$ ______
Complete the subtraction:
- $75 - 29 =$ ______
- $41 - 18 =$ ______
- $63 - 34 =$ ______
If $a = 24$ and $b = 16$ , find $a + b - 10$ .
If $x = 50$ and $y = 25$ , find $x - y + 15$ .
Calculate $6 \times 9$ .

C. Word Problems (21-30)

There are 60 students in a class. If 25 more students join, how many students are there now?
Mary has 40 books. If she gives 15 books to her friend and buys 12 more, how many books does she have now?
A car travels 120 km in one hour. How far will it travel in 5 hours?
If the temperature is 28°C now and it drops by 10°C, what will be the new temperature?
The sum of two numbers is 85. If one number is 42, what is the other number?

D. True or False (31-40)

$70 - 35 = 35$ (True/False)
$48 + 25 = 75$ (True/False)
$90 - 55 = 35$ (True/False)
$60 + 40 = 100$ (True/False)
$80 - 80 = 0$ (True/False)

E. Fill in the blanks (41-50)

The _______ whole number is zero.
The successor of 30 is _______.
The sum of 18 and 25 is _______.
If $p = 45$ , the predecessor of $p$ is _______.
$14 \times 3 = _______$ .

F. Comparisons and Ordering (51-60)

Compare: $50 > 30$ (True/False)
Order the following numbers from smallest to largest: 15, 27, 10, 35, 20
If $a = 40$ and $b = 60$ , compare $a$ and $b$ using symbols: $�__�$ (Fill in the blank)
Arrange the numbers 18, 25, 13, and 30 in descending order.
If $x = 20$ and $y = 20$ , are $x$ and $y$ equal? (True/False)
G. Multiples and Factors (61-70)
1. List the first five multiples of 7.
2. Find the factors of 36.
3. Is 24 a multiple of 8? (True/False)
4. Identify the common factors of 20 and 30.
5. Determine whether 15 is a factor of 45. (True/False)
H. Patterns and Sequences (71-80)
1. Identify the pattern and fill in the blanks: 10, 20, 30, ___, ___.
2. Write the next three terms in the sequence: 5, 10, 15, ___.
3. Find the missing number: 4, ___, 16, 25, 36.
4. Write the first four terms of the sequence where each term is obtained by adding 8 to the previous term: ___.
5. Identify the rule of the sequence: 3, 6, 9, 12, ___.
I. Practical Application (81-90)
1. If a pencil costs ₹5 and you buy 8 pencils, how much money did you spend?
2. A rectangular garden has a length of 15 meters and a width of 8 meters. What is the perimeter of the garden?
3. Sarah saved ₹30 per week for 4 weeks. How much money did she save?
4. A train travels 120 km in 2 hours. What is its average speed?
5. If a box contains 24 chocolates and 6 chocolates are taken out, how many chocolates are left?
J. Revision and Challenge (91-100)
1. Simplify: $16 - (8 + 5)$ .
2. If $m = 18$ and $n = 24$ , find $m \times n - 12$ .
3. The sum of two consecutive whole numbers is 75. Find the numbers.
4. Solve: $2 \times (7 + 4)$ .
5. If $p = 5$ , find the product of $p$ and its successor.
Ensure that the questions cover a variety of topics and require different levels of thinking. Feel free to adapt these questions to better suit the needs and proficiency level of your students.[/expand]

Chapter 3: Playing With Numbers[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Section A: Multiple Choice Questions (1 mark each)

Which of the following is a prime number? a. 4 b. 7 c. 12 d. 15
Determine the number of factors of 28. a. 4 b. 6 c. 8 d. 10
If a number is divisible by both 4 and 6, it is also divisible by: a. 12 b. 8 c. 16 d. 18
The sum of the first five multiples of 9 is: a. 90 b. 135 c. 180 d. 225
What is the smallest prime number? a. 0 b. 1 c. 2 d. 3
Find the missing number in the pattern: 5, 10, ___, 20, 25. a. 12 b. 15 c. 18 d. 30

Section B: True/False (1 mark each)

True/False: 1 is considered a prime number.
True/False: Every even number is a composite number.
True/False: The sum of two prime numbers is always a prime number.
True/False: If a number is divisible by 9, it is also divisible by 3.

Section C: Short Answer Questions (2 marks each)

Determine whether 48 is a multiple of 6.
List the factors of 36.
Explain the concept of prime factorization with an example.
Find the LCM of 8 and 12.
Identify the first five prime numbers.
If the product of two numbers is 45, and one of the numbers is 9, find the other number.

Section D: Application Problems (3 marks each)

A rectangular garden has a length of 15 meters and a width of 20 meters. Find the area of the garden.
If the product of two consecutive odd numbers is 143, find the numbers.
Sarah bought 24 candies and wants to distribute them equally among her 8 friends. How many candies will each friend get?
The sum of three consecutive multiples of 5 is 75. Find the numbers.
A number is divisible by 9 and 5. What is the smallest such number?

Section E: Crossword Puzzle

Across

A number that has exactly two distinct positive divisors.

Down

The result of multiplying a number by an integer.

Section F: Reflect and Review

Write a short paragraph explaining how understanding divisibility rules, factors, and multiples can be useful in solving everyday problems.
Section A: Multiple Choice Questions (1 mark each)
1. Which of the following is a composite number? a. 3 b. 7 c. 9 d. 11
2. What is the sum of the first four prime numbers? a. 15 b. 22 c. 20 d. 18
3. If a number is divisible by both 3 and 5, what other number is it divisible by? a. 15 b. 8 c. 10 d. 20
4. Determine the missing number in the pattern: 2, 4, ___, 8, 10. a. 6 b. 5 c. 7 d. 12
5. How many factors does the number 1 have? a. 0 b. 1 c. 2 d. 3
6. If a number is not divisible by 2, it is: a. Prime b. Composite c. Odd d. Even
Section B: True/False (1 mark each)
1. True/False: All prime numbers are odd.
2. True/False: The product of two prime numbers is always a prime number.
3. True/False: The multiples of a number are always greater than the number itself.
4. True/False: If a number is divisible by 10, it is also divisible by 5.
Section C: Short Answer Questions (2 marks each)
1. Determine whether 63 is a multiple of 9.
2. Write down the prime factorization of 24.
3. Explain the concept of co-prime numbers.
4. Find the HCF of 18 and 24.
5. Identify the first five composite numbers.
6. If the product of two numbers is 72, and one of the numbers is 8, find the other number.
Section D: Application Problems (3 marks each)
1. The perimeter of a square is 36 cm. Find the length of each side.
2. The sum of three consecutive even numbers is 72. Find the numbers.
3. Peter has 35 marbles. He wants to arrange them in equal rows. If each row has 5 marbles, how many rows will there be?
4. The product of two consecutive multiples of 4 is 32. Find the numbers.
5. A number is divisible by both 8 and 6. What is the smallest such number?
Section E: Crossword Puzzle
1. Across
  - A number that has exactly three distinct positive divisors.
2. Down
  - The smallest common multiple of a set of numbers.
Section F: Reflect and Review
1. Write a short paragraph explaining how factors and multiples are interconnected and how this understanding can be applied in real-life scenarios.
Feel free to use, modify, or add to these questions based on your preferences and the specific requirements of your class.[/expand]

Chapter 4: Basic Geometrical Ideas[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Multiple Choice Questions:

What is a point in geometry? a) A small dot with no size b) A shape with a defined area c) A straight path
Which of the following has two endpoints? a) Line b) Ray c) Line segment
If two rays share a common endpoint, what is formed? a) Line b) Angle c) Point
How many endpoints does a ray have? a) None b) One c) Two
What is the measure of the amount of turn between two lines called? a) Area b) Perimeter c) Angle

Fill in the Blanks:

A ________ has no size or shape.
A straight path that extends indefinitely in both directions is called a ________.
A part of a line with two endpoints is called a ________.
A line with one endpoint that extends infinitely in one direction is called a ________.
Two rays that share the same endpoint form an ________.

True/False:

A line segment has only one endpoint. (True/False)
An angle is formed when two rays have different endpoints. (True/False)
A point extends infinitely in all directions. (True/False)

Matching:

Match the term to its definition:

Line (i) A part of a line with two endpoints
Ray (ii) A straight path with no endpoints
Point (iii) A line that extends infinitely in one direction

Drawing Exercises:

Draw a line segment PQ where P is the starting point, and Q is the endpoint.
Draw a ray RS where R is the endpoint.
Draw an angle TUV where U is the vertex.

Short Answer:

Explain the concept of a point in geometry.
Differentiate between a line and a line segment.
How is an angle formed?

Problem Solving:

If point A is between points B and C on a line, how many line segments are formed?
If an angle is formed by rays DE and DF, what is the common endpoint?

Application:

Look around your classroom. Identify three examples of points, lines, and angles. Describe their positions.

Reflection:

What challenges did you face in understanding the concepts of this chapter? How did you overcome them?
Multiple Choice Questions:
1. Which of the following is an example of a point? a) Line AB b) Vertex C c) Triangle XYZ
2. If you extend a line segment indefinitely in both directions, what do you get? a) Line b) Ray c) Angle
3. What is the common endpoint of two rays forming an angle? a) Point b) Vertex c) Segment
4. How many rays can be formed from a single point? a) One b) Two c) Infinitely many
5. What is the sum of the angles in a triangle? a) 90 degrees b) 180 degrees c) 360 degrees
Fill in the Blanks:
1. A straight path that extends indefinitely in both directions is called a ________.
2. A line with one endpoint that extends infinitely in one direction is called a ________.
3. Two rays that share the same endpoint form an ________.
4. ________ is the measure of the amount of turn between two lines.
True/False:
1. A line extends infinitely in both directions. (True/False)
2. An angle is formed by three non-collinear points. (True/False)
3. A ray has two endpoints. (True/False)
Matching:
1. Match the term to its definition:
  - Angle Bisector (i) A point where two rays meet
  - Collinear Points (ii) A line that divides an angle into two equal parts
  - Vertex (iii) Points that lie on the same line
Drawing Exercises:
1. Draw a line CD where C is the starting point, and D is the endpoint.
2. Draw a ray EF where E is the endpoint.
3. Draw an acute angle MNO where N is the vertex.
Short Answer:
1. Define a collinear set of points.
2. Explain the concept of an angle bisector.
Problem Solving:
1. If there are four points A, B, C, and D, how many line segments can be formed?
2. If an angle is divided into two equal parts, what is the measure of each part?
Application:
1. In a playground, identify examples of geometric elements. How are they used in the design?
Reflection:
1. Describe how understanding basic geometrical ideas can be useful in everyday life.
Feel free to mix and match these questions or modify them to suit the specific focus and depth you want for your students.[/expand]

Chapter 5: Understanding Elementary Shapes[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Identifying Shapes (1-15):

Identify the shape:
Name the shape with four sides.
Identify a shape with three unequal sides.
What is the name of a shape with six equal sides?
Name a shape with one curved side and no vertices.
Identify the shape with all sides of different lengths.
Name a polygon with eight sides.
What is the name of a shape with exactly five vertices?
Identify the shape:
What is the name of a polygon with five equal sides and angles?
Identify a shape with four right angles and four equal sides.
Name a shape with only one pair of parallel sides.
What is the name of a polygon with nine sides?
Identify the shape:
What is the name of a shape with no parallel sides?

Classifying Shapes (16-30): 16. Classify a shape with four sides and four right angles.

Categorize a shape with exactly three sides.
Place a shape with a curved side into the correct category.
Classify a polygon with six sides.
Identify a shape that is both a polygon and has curved sides.
Classify a shape with five equal sides.
Name a shape that is not a polygon.
Categorize a shape with one curved side and three vertices.
Classify a polygon with eight sides and eight angles.
Identify a shape with four equal sides and four right angles.
Place a shape with no parallel sides into the correct category.
Classify a polygon with seven sides.
Categorize a shape with four sides of different lengths.
Name a shape that is both a triangle and a polygon.
Classify a shape with exactly two parallel sides.

Properties of Shapes (31-45): 31. Find the perimeter of a rectangle with length 12 cm and width 5 cm.

Determine the area of a square with a side length of 9 cm.
Calculate the circumference of a circle with a radius of 7 cm. (Take π as 3.14)
Find the missing angle in a triangle with angles 60° and 80°.
Determine the perimeter of a triangle with side lengths 4 cm, 7 cm, and 9 cm.
Calculate the area of a rectangle with length 15 cm and width 8 cm.
Find the circumference of a circle with a diameter of 10 cm. (Take π as 3.14)
Determine the area of a circle with a radius of 5 cm. (Take π as 3.14)
Calculate the missing angle in a quadrilateral with angles 90°, 110°, and 70°.
Find the perimeter of a square with a side length of 6 cm.
Determine the area of a triangle with a base of 12 cm and a height of 8 cm.
Calculate the circumference of a circle with a radius of 12 cm. (Take π as 3.14)
Find the missing angle in a pentagon with angles 120° and 135°.
Determine the perimeter of a rectangle with length 10 cm and width 6 cm.
Calculate the area of a circle with a diameter of 14 cm. (Take π as 3.14)

Real-Life Application (46-60): 46. Look around your classroom and list three objects with a rectangular shape.

Identify a shape that resembles a clock face. What is its name?
Name a real-life object that has the shape of a triangle.
Find an object in the room that is a circle. What is its purpose?
Identify a polygonal shape in the classroom.
Draw a shape you find in the school building with four equal sides.
Look out of the window and identify a shape in a nearby building.
Find an object with the shape of a hexagon in the classroom.
Name a polygon that has all sides of equal length.
Identify a shape on the school flag, if any.
Draw a shape with exactly five sides that you see around you.
Look for a shape with a curved side in the classroom.
Identify a shape with more than eight sides in the school corridor.
Find a polygonal shape with exactly seven sides.
Name a real-life object that is shaped like a cylinder.

Advanced Problems (61-75): 61. Determine the area of a parallelogram with base 10 cm and height 8 cm.

Calculate the missing angle in a hexagon with angles 120°, 130°, and 140°.
Find the perimeter of a regular octagon with a side length of 6 cm.
Determine the area of a trapezium with bases 5 cm and 8 cm, and height 7 cm.
Calculate the missing angle in a kite-shaped figure with angles 110° and 60°.
Find the circumference of a semicircle with a diameter of 14 cm. (Take π as 3.14)
Determine the area of a rhombus with diagonals 12 cm and 16 cm.
Calculate the missing angle in a cyclic quadrilateral with angles 80° and 100°.
Find the perimeter of an irregular pentagon with side lengths 4 cm, 6 cm, 8 cm, 5 cm, and 7 cm.
Determine the area of a regular hexagon with a side length of 9 cm.
Calculate the missing angle in a concave quadrilateral with angles 85°, 95°, and 120°.
Find the circumference of a quarter circle with a radius of 10 cm. (Take π as 3.14)
Determine the area of a sector of a circle with a radius of 6 cm and a central angle of 60°. (Take π as 3.14)
Calculate the missing angle in a cyclic pentagon with angles 70° and 110°.
Find the perimeter of a composite figure with sides 5 cm, 8 cm, 12 cm, 6 cm, and 10 cm.

Practical Application (76-90): 76. Draw a rectangle with a length of 7 cm and a width of 4 cm.

Construct an equilateral triangle with side length 6 cm.
Draw a circle with a radius of 5 cm. Mark the center and label the radius.
Create a polygon with exactly six sides. Label the vertices and sides.
Draw a quadrilateral with one pair of parallel sides.
Construct a right-angled triangle with legs of 3 cm and 4 cm.
Draw a regular pentagon with side length 8 cm.
Create a shape with three acute angles.
Draw an irregular hexagon with sides of different lengths.
Construct a kite-shaped figure with angles 100° and 80°.
Draw a trapezium with bases 6 cm and 9 cm, and a height of 5 cm.
Create a shape with one obtuse angle and two right angles.
Draw a rhombus with diagonals of 10 cm and 12 cm.
Construct a cyclic quadrilateral with angles 85° and 95°.
Draw a sector of a circle with a radius of 8 cm and a central angle of 45°.

Note: Adjust the difficulty level of the questions based on your students’ understanding and the time available for the assessment. Additionally, you can add diagrams to visualize shapes in the questions.[/expand]

Chapter 6: Integers[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Set of 10 Questions:

Question 1: Represent the following integers on a number line:

a) $- 8, 5, - 3, 0, 7$
b) $2, - 6, 9, - 12, 4$

Question 2: Perform the following operations:

a) $(- 9) + 3$
b) $15 - (- 7)$
c) $(- 4) - 8$
d) $6 + (- 2) + 10$

Question 3: Solve the real-life problems:

a) In a game, a team gained 5 points and then lost 3. Represent this situation using integers.
b) John had $50, and he spent $25. Represent this situation using integers.

Question 4: Compare and order the following integers:

a) $- 10, - 5, 0, 5, 8$
b) $3, - 6, 2, - 9, 7$

Question 5: If $x = - 7$ and $y = 4$ , find the values of $x + y$ and $x - y$ .

Question 6: Create a scenario where the multiplication of two negative integers results in a positive product. Explain the situation.

Question 7: A submarine is diving. If it is at $- 20$ meters and dives $15$ more meters, what will be its new depth?

Question 8: Complete the sentences:

a) The product of two positive integers is ____________.
b) The sum of a positive integer and its additive inverse is ____________.
c) When adding a negative integer, we can rewrite it as ____________.

Question 9: Solve the expression: $(- 3) - (- 5) + 2 - (- 8) + 6$ .

Question 10: Explain, with an example, why understanding integers is crucial in situations involving gains and losses.

Question 11: Calculate the sum of the first 7 positive integers.

Question 12: A car gained 15 meters in elevation and then descended 10 meters. Represent this situation using integers.

Question 13: Evaluate $(- 2) \times 6 - 8$ .

Question 14: Compare the following pairs of integers:

a) $- 15$ and $- 12$
b) $4$ and $4$
c) $- 8$ and $0$

Question 15: If $a = - 6$ and $b = 3$ , find the values of $a \times b$ and $a \div b$ .

Question 16: Represent the following sea depths on a number line: -20 meters, 10 meters, -5 meters, 15 meters.

Question 17: Solve the expression: $2 - (- 6) \times 3$ .

Question 18: Create a word problem involving the multiplication of two negative integers. Solve it.

Question 19: If the temperature is $- 5^{\circ}$ C and it decreases by $3^{\circ}$ C, what will be the new temperature?

Question 20: Discuss, with examples, situations where integers are used to represent the position above and below sea level.

Question 21: Find the additive inverse of the following integers:

a) $9$
b) $- 2$
c) $- 15$

Question 22: A plane takes off from an altitude of $500$ meters and climbs $200$ more meters. Represent this situation using integers.

Question 23: Solve the expression: $3 \times (- 4) + 2$ .

Question 24: Order the following integers from greatest to least:

a) $- 7, 2, - 10, 5, 0$
b) $15, - 8, 12, - 3, 6$

Question 25: If $p = - 9$ and $q = 7$ , find the values of $p + q$ and $p \times q$ .

Question 26: Create a story problem that involves both addition and subtraction of integers. Solve it.

Question 27: If the temperature is $4^{\circ}$ C and it drops by $7^{\circ}$ C, what will be the new temperature?

Question 28: Determine the sign of the product of:

a) Two negative integers
b) One positive and one negative integer
c) Two positive integers

Question 29: Simplify the expression: $(- 2) \times (- 3) \times 4$ .[/expand]

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

Understanding Basics (Q1-Q15):

Define a fraction. Provide an example.
Explain the terms “numerator” and “denominator” with examples.
Represent $3 2$ using fraction strips or drawings.
What does the denominator represent in a fraction?
If the numerator is 3 and the denominator is 4, what fraction is represented?
Express $6 5$ as a decimal.
Write $4 3$ as a percentage.
Identify the proper fraction among $7 5$ , $5 8$ , and $3 3$ .
If the numerator is equal to the denominator, what type of fraction is it?
Can a fraction have a zero in the numerator? Provide an example.
Discuss a real-life scenario where fractions are used.
If you have $2 1$ of a pizza and your friend has $4 1$ , who has more pizza?
Explain why $5 0$ is equal to 0.
Write the fraction for the shaded portion in the given figure.
Solve: $4 3 + 4 2$ .

Classifying Fractions (Q16-Q30):

Classify $3 5$ as proper, improper, or mixed.
Identify the mixed fraction in $2 7$ , $4 9$ , $3 2 1$ .
Convert $4 7$ to a mixed fraction.
List three proper fractions with a numerator less than 5.
Determine the numerator and denominator of $4 3 2$ .
Write an improper fraction that is equal to $3 5 2$ .
Convert $2 2 3$ to an improper fraction.
Identify the type of fraction: $5 10$ .
Write a proper fraction equivalent to $1 3 2$ .
Convert $2 11$ to a mixed fraction.
Classify $6 6$ as proper, improper, or mixed.
Convert $3 4 3$ to an improper fraction.
Identify the proper fraction: $8 8$ , $3 9$ , $5 12$ .
If $b a = 3 2$ and $c b = 5 4$ , find $c a$ .
Write a mixed fraction equivalent to $4 11$ .

Converting Fractions (Q31-Q45):

Convert $2 6 5$ to an improper fraction.
Express $4 16$ as a mixed fraction.
Convert $2 9$ to a mixed fraction.
If $n m = 2 5$ , find $m n$ .
Convert $5 3 1$ to an improper fraction.
If $q p = 4 7$ , find $p q$ .
Convert $3 13$ to a mixed fraction.
If $y x = 4 3$ , find $x y$ .
Convert $4 5 2$ to an improper fraction.
If $d c = 7 6$ , find $c d$ .
Convert $5 17$ to a mixed fraction.
If $f e = 9 8$ , find $e f$ .
Convert $7 4 3$ to an improper fraction.
If $h g = 1 2$ , find $g h$ .
Convert $2 19$ to a mixed fraction.

Operations with Fractions (Q46-Q60):

Simplify $8 6$ to its lowest terms.
Add: $4 3 + 4 1$ .
Subtract: $6 5 - 6 1$ .
Add: $3 2 + 3 1$ .
Subtract: $8 7 - 8 3$ .
Add: $5 4 + 5 2$ .
Subtract: $12 11 - 12 5$ .
Add: $6 5 + 6 2$ .
Subtract: $10 9 - 10 1$ .
Add: $8 7 + 8 3$ .
Subtract: $5 2 - 5 1$ .
Add: $3 1 + 6 1$ .
Subtract: $7 4 - 7 2$ .
Add: $4 3 + 4 2$ .
Subtract: $9 5 - 9 4$ .

Word Problems (Q61-Q75):

James has $4 3$ of a chocolate bar. If he gives $2 1$ to his friend, how much does he have left?
A recipe requires $3 2$ cup of sugar. If you want to make half the recipe, how much sugar do you need?
A ribbon is $6 5$ meters long. If it is cut into three equal pieces, how long is each piece?
A rectangle is divided into $4 3$ and $4 1$ . What fraction represents the smaller part?
A pizza is divided into $8 1$ slices. How many slices are there in the whole pizza?
Mary has $5 4$ of a bag of candies. She gives $5 2$ to her brother. What fraction of candies does Mary have now?
If $b a = 4 3$ and $c b = 5 2$ , find $c a$ .
In a school, $3 1$ of the students are boys, and $5 2$ are girls. What fraction represents the total number of students?
Sara has $5 3$ of a book. If she reads $2 1$ of what she has, what fraction of the book is left?
If $q p = 7 3$ and $r q = 6 5$ , find $r p$ .
A garden is divided into $3 2$ flowers and $3 1$ vegetables. What fraction represents the vegetables?
Tom has $5 4$ of a bag of marbles. If he loses $5 1$ of what he has, what fraction of marbles does Tom have left?
If $d c = 6 5$ and $e d = 3 2$ , find $e c$ .
A rectangle is divided into $4 1$ and $4 3$ . What fraction represents the larger part?
John has $8 7$ of a bag of nuts. If he eats $8 3$ , what fraction of nuts does John have left?

Challenge (Q76-Q90):

If $b a = 4 3$ and $c b = 5 2$ , find $c a$ .
Simplify $18 12$ to its lowest terms.
Convert $3 3 2$ to an improper fraction.
Subtract: $6 5 - 4 1$ .
If $n m = 3 4$ , find $m n$ .
Convert $6 2 3$ to an improper fraction.
Add: $5 2 + 10 3$ .
If $q p = 2 5$ , find $p q$ .
Convert $4 9$ to a mixed fraction.
If $y x = 8 3$ , find $x y$ .
Add: $12 7 + 12 5$ .
If $f e = 6 7$ , find $e f$ .
Subtract: $5 4 - 10 1$ .
If $h g = 4 9$ , find $g h$ .
Convert $2 13$ to a mixed fraction.[/expand]

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

nderstanding Decimals (Questions 1-15):

Write the decimal form for $5 2$ .
Convert 0.6 to a fraction in the simplest form.
Express 5.25 as a mixed number.
Compare the following decimals: 0.3, 0.75, 0.1
Order the decimals from least to greatest: 0.45, 0.32, 0.6
Identify the decimal represented by the point P on the number line: [diagram]
Round 3.874 to the nearest tenth.
Write the place value of 6 in the decimal 4.267.
Express 80% as a decimal.
Simplify: $15 6$ .
If $a = 2.3$ and $b = 1.75$ , find $a + b$ .
Subtract 4.6 from 7.2.
If $x = 0.25$ , find $3 x$ .
Solve: $5.6 - 2.75$ .
Write the decimal and fraction for the shaded part of the figure: [diagram]

Representing Decimals (Questions 16-25):

Draw a number line and represent 1.8 on it.
Locate 0.9 on the number line shown: [diagram]
Represent $10 4$ on a number line.
Draw a figure to represent the decimal 0.75 visually.
Place the decimals 1.2, 0.9, and 1.5 on a number line in the correct order.
Mark the point Q on the number line where $Q = 3.4$ .
Represent 2.25 on a number line with appropriate divisions.
Place the decimals 0.6, 0.45, and 0.8 on a number line in ascending order.
Draw a line segment representing $4 3$ on a number line.
Label the points A, B, and C on the number line where $A = 1.25, B = 1.5, C = 1.75$ .

Addition and Subtraction (Questions 26-45):

Solve: $4.75 + 2.6$ .
If $y = 3.2$ and $z = 1.5$ , find $y - z$ .
What is the result of $7.8 - 3.25$ ?
Find the sum of $5 1 + 0.3$ .
Subtract 0.6 from $5 4$ .
If $p = 2.1$ and $q = 0.9$ , find $p + q$ .
Calculate $5.6 - 2.75 + 1.3$ .
Subtract 0.25 from 2.8.
Add $4 3$ and $5 2$ .
If $a = 1.4$ and $b = 0.75$ , find $a - b$ .
Solve the expression: $3.25 + 1.6 - 0.9$ .
Subtract $3 2$ from 1.8.
If $x = 2.5$ and $y = 0.6$ , find $x - y$ .
Calculate $6.2 + 0.45 - 2.1$ .
Subtract 0.75 from 3.2.
Add $3 1$ to 0.7.
If $m = 1.25$ and $n = 0.8$ , find $m + n$ .
Find the sum of 3.6 and $5 4$ .
Subtract $7 2$ from 0.9.
Solve: $7.25 - 3.4 + 1.1$ .

Real-Life Applications (Questions 46-60):

You have Rs. 45.25. If you spend Rs. 15.75, how much money do you have left?
The length of a table is 6.4 meters. If you cut off 2.5 meters, what will be the length of the remaining part?
A box contains 12.75 kg of rice. If 3.2 kg of rice is taken out, how much remains?
If a train travels 3.5 km in one hour, how far will it travel in 2.5 hours?
You buy a toy for Rs. 18.25 and a book for Rs. 12.5. How much do you spend in total?
A rectangular field is 7.2 meters long and 4.5 meters wide. What is the area of the field?
The temperature was 25.8 degrees Celsius in the morning. If it decreases by 3.5 degrees, what is the new temperature?
A car travels at a speed of 60.5 km/h. How far will it travel in 4 hours?
If you save Rs. 5.25 every day, how much will you save in a week?
A piece of rope is 8.3 meters long. If you cut off 2.6 meters, what is the length of the remaining rope?
You have 2.25 liters of water in a jug. If you pour out 0.8 liters, how much water remains?
The mass of a box is 4.6 kg. If you remove 1.25 kg of items, what is the new mass?
A train travels 150.75 km in 2 hours. What is its average speed?
You walk 3.5 km in the morning and 2.25 km in the evening. How far do you walk in total?
The cost of a pen is Rs. 6.75. If you buy 5 pens, what is the total cost?

Word Problems (Questions 61-75):

A ribbon is 2.5 meters long. If you cut it into pieces, each piece is 0.6 meters long. How many pieces can you get?
If you have Rs. 50 and you spend Rs. 12.5, what percentage of your money is left?
A rectangle has a length of 5.6 cm and a width of 3.75 cm. Find its area.
The speed of a car is 55.5 km/h. If it travels for 3.2 hours, how far does it go?
A tank contains 8.75 liters of water. If 3.6 liters are poured out, what is the volume of the remaining water?
The cost of a shirt is Rs. 450. If you get a 10% discount, what is the final cost?
If you divide 2.5 by 0.5, what is the result?
A rectangular garden is 6.4 meters long and 2.5 meters wide. What is its perimeter?
You save Rs. 7 every day. How much will you save in a month?
A recipe requires 2.25 cups of flour. If you want to make half the recipe, how much flour do you need?
A train travels at a speed of 80 km/h. If it travels for 2.5 hours, how far does it go?
If you have a piece of string that is 3.5 meters long, and you cut off 1.25 meters, what is the length of the remaining string?
The weight of a box is 4.8 kg. If you add 1.2 kg of items, what is the new weight?
You buy a toy for Rs. 15.75 and a book for Rs. 8.6. How much change do you get from Rs. 30?
A rectangle has a length of 4.2 cm and a width of 0.8 cm. Find its area.

Challenge Questions (Questions 76-80):

Solve the following expression: $3 2 + 0.4 - 0.15$ .
A rectangle has a length of 3.75 cm and a width of 1.8 cm. Find its perimeter.
If $x = 1.5$ and $y = 0.25$ , find $x y - 2 x + 0.5 y$ .
Divide 7.5 by $2 1$ .
Solve the equation: $2 a - 0.5 = 4.5$ .

Practical Application (Questions 81-90):

Look around your house and find two objects where you can measure the length in decimals. Measure and represent their lengths in decimal form.
Visit a grocery store and find three items with prices in decimal form. Add the prices to find the total cost.
Measure the dimensions of a book or notebook in your school bag in centimeters and represent the measurements in decimal form.
Find the weight of a fruit or vegetable in your kitchen using a scale and represent it in decimal form.
Calculate the cost of your lunch if you spend Rs. 20.75 on a sandwich and Rs. 12.5 on a drink.
Measure the length of your classroom in meters and represent it in decimal form.
If you have a rectangular tile with dimensions 2.5 cm by 1.8 cm, find its area.
Ask a family member for their height and represent it in decimal form.
Find the average of the following decimals: 3.2, 4.5, 2.75, 5.1.
Calculate the total distance traveled if you walk 1.5 km in the morning, 2.25 km in the afternoon, and 0.8 km in the evening.[/expand]

Chapter 9: Data Handling[expand title=”Read More➔” swaptitle=”🠔Read Less”]

1. Multiple Choice Questions (MCQs):

1.1. Which of the following is an example of raw data? a) Bar graph b) Frequency table c) List of test scores d) Pictograph

1.2. What is the purpose of organizing data in a frequency table? a) To confuse people b) To make it look neat c) To analyze and understand the data better d) To waste time

1.3. In a frequency table, what does the term ‘frequency’ represent? a) The number of times an event occurs b) The average value c) The maximum value d) The minimum value

1.4. Which type of data is represented by tally marks? a) Grouped data b) Raw data c) Qualitative data d) Quantitative data

1.5. What type of graph is suitable for representing categorical data? a) Line graph b) Pictograph c) Histogram d) Pie chart

2. Fill in the Blanks:

2.1. A ____________ is used to represent data graphically using symbols.

2.2. The process of organizing and summarizing data is known as ____________.

2.3. The ____________ of a set of data is the number that appears most frequently.

2.4. In a frequency table, the ____________ column represents the categories or classes.

2.5. A bar graph consists of ____________ that represent different categories.

3. True/False Statements:

3.1. A histogram is a graphical representation of data.

3.2. Grouping data is essential to analyze and interpret it effectively.

3.3. A frequency table is used to represent qualitative data.

3.4. Pictographs are suitable for representing numerical data.

3.5. The mode of a set of data is always unique.

4. Short Answer Questions:

4.1. Explain the difference between raw data and grouped data.

4.2. Why is it important to organize data before representing it graphically?

4.3. How do you create a tally chart from a given set of data?

4.4. Discuss one advantage of using a bar graph over a pictograph.

4.5. Provide an example of a situation where a pie chart would be the most suitable graphical representation.

5. Application-Based Questions:

5.1. Imagine you conducted a survey on students’ favorite colors. How would you represent this data graphically?

5.2. A company collected data on the number of products sold each month. How would you analyze and represent this data to identify trends?

5.3. Your school collected data on students’ heights. How would you represent this data using appropriate graphs?

5.4. Explain how data handling techniques can be applied to solve real-life problems.

6. Match the Following:

Match the correct term to its definition.

6.1. Histogram A. Graphical representation of data using bars 6.2. Median B. The middle value in a set of data 6.3. Data Handling C. Process of organizing and summarizing data 6.4. Qualitative Data D. Non-numerical data, e.g., colors 6.5. Pie Chart E. Represents parts of a whole using sectors

7. Diagram-Based Questions:

7.1. Draw a frequency table for the given data: {12, 15, 18, 12, 15, 20, 18, 15, 12}.

7.2. Sketch a bar graph representing the data in the frequency table:

Range	Frequency
10-15	4
16-20	3
21-25	2

8. Long Answer Questions:

8.1. Explain the steps involved in creating a pictograph. Provide an example.

8.2. Discuss the advantages and disadvantages of using a pie chart as a graphical representation.

8.3. You conducted a survey on students’ favorite subjects and obtained the following data: Math – 15, English – 20, Science – 18, Social Studies – 12. Represent this data using a suitable graph.

9. Critical Thinking:

9.1. Why might it be misleading to only consider the mode when describing a set of data?

9.2. Can data representation through graphs be biased? Provide an example and suggest how to minimize bias in graphical representation.

10. Real-life Application:

10.1. Interview a family member or neighbor about their daily commuting time to work. Create a data set and represent it using an appropriate graph.

10.2. Visit a local store and collect data on the prices of different fruits. Organize and represent the data graphically.

Note: Encourage students to not only solve these questions but also discuss and understand the underlying concepts. This promotes a deeper understanding of data handling and its real-world applications. Adjust the complexity based on the students’ proficiency levels.[/expand]

Chapter 9: Data Handling[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Multiple Choice Questions (MCQs):

What is the primary purpose of data handling in mathematics? a) To confuse students b) To organize, analyze, and interpret data c) To make numbers look interesting d) To create beautiful graphs
In a frequency table, what does the class interval represent? a) The width of the graph b) The range of data values c) The categories of data d) The height of the bars in a bar graph
Which type of data is represented by a histogram? a) Categorical b) Qualitative c) Quantitative d) Raw
What is the central value in a set of data called? a) Mode b) Median c) Mean d) Range
A pie chart is most suitable for representing: a) Frequency distribution b) Parts of a whole c) Qualitative data d) Continuous data

Fill in the Blanks:

A ____________ is a summary of data in tabular form.
In a histogram, the ____________ represents the frequency of each class interval.
The ____________ is the value that separates the higher half from the lower half of a data set.
The process of ____________ involves sorting data into groups or classes.
A pictograph uses ____________ to represent data.

True/False Statements:

A frequency table is used to organize qualitative data.
The mode is the only measure of central tendency that can be applied to qualitative data.
A bar graph is suitable for representing continuous data.
A histogram is a graphical representation of data that is continuous.
In a frequency distribution, the class with the highest frequency is called the mode.

Short Answer Questions:

Explain the difference between ungrouped and grouped data.
How is the median calculated in a set of data?
Provide an example of nominal data.
Why is it important to label the axes in a graph?
What is the advantage of using a frequency table over a list of raw data?

Match the Following:

Histogram A. Non-numerical data
Range B. Represents parts of a whole
Pie Chart C. The middle value in a set of data
Qualitative Data D. Graphical representation of data using bars
Median E. Difference between the highest and lowest values

Diagram-Based Questions:

Draw a pictograph representing the following data: {A – 3, B – 6, C – 4, D – 2}.
Sketch a bar graph using the data in the frequency table:
Range Frequency
1-5 8
6-10 5
11-15 3

Range	Frequency
1-5	8
6-10	5
11-15	3

Long Answer Questions:

Explain the steps involved in creating a frequency table.
Discuss the differences between a bar graph and a histogram.
Provide a real-life example where a pie chart would be an effective means of representation.
Describe how outliers can impact measures of central tendency.

Critical Thinking:

Can a data set have more than one mode? Explain.
Discuss the limitations of using only graphical representations to understand data.

Real-life Application:

Interview three classmates about their favorite genres of books. Represent this data using a suitable graph.
Collect temperature data for a week in your locality. Organize and represent it graphically.

Problem-Solving:

The heights of students in a class are recorded as follows: 120, 125, 130, 135, 140, 145, 150, 155. Find the range.
Solve the following problem: In a survey, students were asked about their preferred mode of transportation to school. Create a bar graph representing the data: Bus – 25, Bicycle – 15, Walk – 10, Car – 5.

Miscellaneous:

What is the purpose of a legend in a graph?
Explain the difference between a bar graph and a double bar graph.
How can data be misleading if the scale on a graph is not appropriately chosen?

Evaluation and Reflection:

Assess the following statement: “Data handling is only about creating graphs.”
Reflect on a situation where you encountered data in your daily life. How was it presented, and could it be improved?
Multiple Choice Questions (MCQs):
What does the range of a set of data represent? a) The spread or dispersion of the data b) The average value of the data c) The mode of the data d) The highest value in the data
In a frequency distribution, what does the width of a class interval indicate? a) The height of the bars in a histogram b) The range of values in a class c) The frequency of each class d) The midpoint of the class interval
Which measure of central tendency is influenced by extreme values? a) Mean b) Median c) Mode d) Range
If a set of data has an even number of values, how is the median calculated? a) By taking the average of the two middle values b) By selecting the middle value c) By adding all values and dividing by the count d) By finding the mode
What is the purpose of the title in a graph? a) To confuse the reader b) To make the graph colorful c) To provide information about the data being represented d) To add extra details
Fill in the Blanks:
A ____________ is a measure of the spread of data around the mean.
The ____________ is the sum of all data values divided by the count.
A line graph is suitable for representing ____________ data.
The ____________ is the value that occurs most frequently in a set of data.
The ____________ of a graph helps in understanding the data without looking at the details.
True/False Statements:
A frequency polygon is a line graph that displays the frequencies of different values.
The mean is always equal to the median in a symmetrical distribution.
A skewed distribution has more than one mode.
The mid-range is calculated as the difference between the highest and lowest values in a set of data.
In a box-and-whisker plot, the box represents the interquartile range.
Short Answer Questions:
How is the mode calculated in a set of data?
Explain why the mean can be affected by outliers.
Differentiate between a histogram and a frequency polygon.
What is the purpose of a scatter plot, and when is it used?
How can you determine if a distribution is positively or negatively skewed?
Match the Following:
Skewness A. Difference between the highest and lowest values
Mean B. Data values arranged in ascending or descending order
Range C. Measure of asymmetry in a distribution
Data Sorting D. Sum of all data values divided by the count
Data Arrangement E. A line graph that displays frequencies
Diagram-Based Questions:
Create a box-and-whisker plot for the following set of data: {12, 15, 18, 21, 24, 25, 30}.
Draw a scatter plot representing the correlation between the hours of study and exam scores for a group of students.
Long Answer Questions:
Discuss the concept of interquartile range and its significance.
Explain how to calculate the mean deviation of a set of data.
Compare and contrast a bar graph, a histogram, and a line graph.
Critical Thinking:
Can a set of data have no mode? Provide an example.
In what situations would it be appropriate to use a logarithmic scale on a graph?
Real-life Application:
Collect data on the ages of people in your neighborhood. Create a frequency distribution and represent it graphically.
Analyze the rainfall data for your city over a month and represent it using an appropriate graph.
Problem-Solving:
Solve the following problem: The heights (in cm) of five students are 120, 125, 130, 135, and 140. Find the mean height.
Given the data set {10, 15, 20, 25, 30}, calculate the mean, median, and mode.
Miscellaneous:
What is the purpose of a stem-and-leaf plot?
How does the scale of a graph affect the interpretation of data?
Explain the concept of a cumulative frequency distribution.
Evaluation and Reflection:
Evaluate the statement: “The mode is the best measure of central tendency.”
Reflect on a situation where you used data handling techniques to solve a problem in your daily life.
Extension and Application:
Conduct a survey on the favorite subjects of students in your class. Organize and represent the data using appropriate graphs.
Research and present a real-world scenario where the analysis of data had a significant impact.
Project-Based Questions:
Design a survey questionnaire on a topic of your choice. Collect data and represent it using various graphical techniques.
Create a project that involves analyzing data from a local business or community organization. Present your findings using graphs and charts.
Collaborative Learning:
Work with a partner to create a composite graph representing different aspects of climate data for a year.
Conduct a class survey on preferred leisure activities. Pool the data and collaborate to create various graphs representing the results.
Cross-Curricular Integration:
Discuss how data handling techniques can be applied in other subjects or real-world scenarios.
Explore the role of data analysis in scientific research and experimentation.
Technology Integration:
Investigate how technology tools such as spreadsheets or graphing software can enhance the process of data handling.
Note: Adapt these questions based on the students’ grade level, and feel free to customize them to suit your teaching style and objectives.[/expand]

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

Section A: Area and Perimeter of 2D Shapes (30 questions)

1-10. For each figure (square, rectangle, triangle), find the area and perimeter given the dimensions.

Square: Side = 6 cm
Rectangle: Length = 8 cm, Width = 5 cm
Triangle: Base = 10 cm, Height = 4 cm
Square: Side = 12 cm
Rectangle: Length = 15 cm, Width = 7 cm
Triangle: Base = 8 cm, Height = 6 cm
Square: Side = 4.5 cm
Rectangle: Length = 12 cm, Width = 9 cm
Triangle: Base = 6.5 cm, Height = 3 cm
Square: Side = 9 cm
Rectangle: Length = 10 cm, Width = 3.5 cm
Triangle: Base = 7 cm, Height = 5 cm

13-20. Real-life Applications: Calculate the area in each scenario.

Garden: Length = 20 m, Width = 12 m
Farm Field: Length = 25 m, Width = 18 m
Room Floor: Length = 7.5 m, Width = 5 m
School Playground: Length = 40 m, Width = 30 m
Patio: Length = 8 m, Width = 4.5 m
Carpet: Length = 6 m, Width = 3.5 m
Wall Poster: Length = 3 m, Width = 2 m
Kitchen Tile: Length = 10 cm, Width = 10 cm

Section B: Volume of 3D Shapes (30 questions)

21-30. For each figure (cube, cuboid), find the volume given the dimensions.

Cube: Side = 4 cm
Cuboid: Length = 10 cm, Width = 6 cm, Height = 3 cm
Cube: Side = 6 cm
Cuboid: Length = 8 cm, Width = 4 cm, Height = 5 cm
Cube: Side = 3.5 cm
Cuboid: Length = 12 cm, Width = 7 cm, Height = 2.5 cm
Cube: Side = 2.5 cm
Cuboid: Length = 5 cm, Width = 3 cm, Height = 4 cm
Cube: Side = 7 cm
Cuboid: Length = 15 cm, Width = 9 cm, Height = 6 cm

31-40. Word Problems: Find the volume in each scenario.

Fish Tank: Length = 20 cm, Width = 15 cm, Height = 10 cm
Gift Box: Length = 12 cm, Width = 8 cm, Height = 5 cm
Juice Carton: Length = 6 cm, Width = 4 cm, Height = 3 cm
Bookshelf: Length = 60 cm, Width = 30 cm, Height = 15 cm
Toolbox: Length = 18 cm, Width = 12 cm, Height = 9 cm
Toy Chest: Length = 25 cm, Width = 20 cm, Height = 18 cm
Storage Bin: Length = 14 cm, Width = 10 cm, Height = 7 cm
TV Stand: Length = 35 cm, Width = 25 cm, Height = 12 cm
Ice Cube Tray: Length = 8 cm, Width = 8 cm, Height = 2 cm
Shoebox: Length = 30 cm, Width = 20 cm, Height = 10 cm

Section C: Application Challenge (30 questions)

41-45. Design and Calculate:

Design a rectangular pool with a length of 15 m and a width of 10 m. Calculate the volume of water it can hold.
Design a square flower bed with a side length of 5 m. Calculate the area for planting flowers.
Design a room with a rectangular floor of length 12 m and width 8 m. Calculate the area of the floor.
Design a cube-shaped gift box with a side length of 3 cm. Calculate the volume of the box.
Design a triangular banner with a base of 6 m and a height of 4 m. Calculate the area of the banner.

46-60. Cost Calculation:

A rectangular field has a length of 30 m and a width of 20 m. If each square meter of the field costs Rs. 50 for maintenance, calculate the total cost.
A square carpet costs Rs. 200 per square meter. If the carpet has a side length of 8 m, find the total cost.
A cuboid-shaped storage box costs Rs. 150 per cubic meter. If the dimensions are 5 m × 4 m × 3 m, find the total cost.
A triangular garden has a base of 12 m and a height of 8 m. If each square meter of the garden costs Rs. 80 for maintenance, find the total cost.
A cube-shaped display stand has a side length of 2.5 m. If the cost per cubic meter is Rs. 300, find the total cost.
61-70. Area and Perimeter:
1. A rectangular garden has a length of 18 m and a width of 12 m. Find its area and perimeter.
2. The side of a square field is 7 m. Calculate its area and perimeter.
3. An isosceles triangle has a base of 9 cm and equal sides of 5 cm each. Find its area.
4. A rectangular room has a length of 15 m and a width of 10 m. Determine the area of the floor.
5. The perimeter of a rectangle is 28 cm, and its length is 8 cm. Find its width and area.
6. A triangular garden has sides of length 6 m, 8 m, and 10 m. Find its area.
7. The side of a square plot is 10.5 m. Calculate its area and perimeter.
8. A rectangle has an area of 45 sq. cm, and its length is 9 cm. Find its width.
9. A right-angled triangle has legs of length 3 cm and 4 cm. Determine its perimeter.
10. The perimeter of a square is 20 cm. Find its side length and area.
71-80. Volume of 3D Shapes:
1. A cube has a volume of 64 cubic cm. Find the length of its side.
2. The volume of a cuboid is 120 cubic cm, and its length is 5 cm. Find its width and height.
3. A cube and a cuboid have the same volume (125 cubic cm). If the cube has a side length of 5 cm, find the dimensions of the cuboid.
4. The volume of a cube is 27 cubic cm. Determine its surface area.
5. The volume of a cuboid is 72 cubic cm, and its dimensions are in the ratio 2:3:4. Find the dimensions.
6. A cube has a surface area of 96 square cm. Find its volume.
7. The volume of a cuboid is 150 cubic cm. If its length is 10 cm, find its width and height.
8. The surface area of a cube is 54 square cm. Find the length of its side.
9. The volume of a cube is equal to the volume of a cuboid. If the side of the cube is 4 cm, find the dimensions of the cuboid.
10. A cuboid has a volume of 180 cubic cm, and its length is 9 cm. Find its width and height.
81-90. Word Problems:
1. A rectangular field has a length of 40 m and a width of 30 m. Find the cost of leveling the field at Rs. 10 per square meter.
2. A triangular banner costs Rs. 5 per square meter. If it has a base of 8 m and a height of 6 m, find the total cost.
3. The cost of painting a cuboid-shaped room with dimensions 7 m × 5 m × 3 m is Rs. 200 per square meter. Find the total cost.
4. The floor of a room needs carpeting. If the room is 6 m long and 4 m wide, and the carpet costs Rs. 300 per square meter, find the cost.
5. A swimming pool is in the shape of a rectangle with a length of 25 m and a width of 15 m. If it costs Rs. 50 per cubic meter to fill the pool, find the total cost.
6. A cube-shaped storage box has a side length of 6 cm. If it costs Rs. 150 per cubic meter, find the total cost.
7. The dimensions of a rectangular room are 12 m × 8 m × 3 m. Find the cost of painting the four walls at Rs. 25 per square meter.
8. A cuboidal tank has a length of 4 m, a width of 3 m, and a height of 2 m. If the cost of filling the tank is Rs. 10 per cubic meter, find the total cost.
9. A triangular flower bed has a base of 10 m and a height of 8 m. If it costs Rs. 30 per square meter to plant flowers, find the total cost.
10. The dimensions of a rectangular table are 1.5 m × 1 m. If it costs Rs. 100 per square meter to cover it, find the total cost.
Feel free to adjust the values or create variations to suit the specific needs of your class and the curriculum.[/expand]

Chapter 11: Algebra[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Section A: Basic Concepts

Define algebra and explain its importance in mathematics.
Distinguish between constants and variables.
What is the coefficient of $3 x$ in the expression $2 + 3 x - 4$ ?
If $a + 6 = 15$ , find the value of $a$ .

Section B: Solving Equations

Solve for $x$ : $2 x + 7 = 15$ .
If $4 y = 28$ , find the value of $y$ .
The sum of a number $n$ and 10 is 25. Find the value of $n$ .
Solve for $p$ : $3 p - 5 = 16$ .

Section C: Word Problems

Mary has $m$ chocolates. She gives 4 chocolates to her friend and now has 8 chocolates left. How many chocolates did Mary have initially?
The perimeter of a rectangle is 34 cm. If the length is $l$ and the width is 8 cm, find the value of $l$ .
If twice a number $q$ increased by 5 is 17, find the value of $q$ .
The sum of three consecutive odd numbers is 51. Find the numbers.

Section D: Applications

Express the statement “five less than twice a number $x$ ” as an algebraic expression.
If $2 n + 3 = 11$ , find the value of $n$ .
The area of a square is given by $A = s^{2}$ . If $s = 6$ , find the area.

Section E: Advanced Problem Solving

Solve the equation $5 (x - 3) = 20$ .
If $2 (a + 4) = 18$ , find the value of $a$ .
The sum of two consecutive even numbers is 28. Find the numbers.

Section F: Exploring Patterns

Identify the pattern: 2, 6, 10, 14, …
Extend the pattern: 3, 8, 13, 18, …

Section G: True/False

True or False: In the equation $3 x - 2 = 13$ , $x = 5$ .
True or False: The solution to $2 c + 3 = 11$ is $c = 4$ .

Section H: Multiple Choice

If $4 k = 28$ , what is the value of $k$ ? a) 5 b) 7 c) 6 d) 8

Section I: Matching

Match the expression to its verbal description:

$2 p + 5$ A. Twice a number $p$ increased by 5.
$4 - m$ B. Four less than a number $m$ .
$3 q$ C. The product of 3 and a number $q$ .

Section J: Fill in the Blanks

The sum of twice a number $x$ and 7 is $________$ .
If $5 + m = 12$ , then $�=________$ .
Section K: Critical Thinking
1. Explain why it is important to check the solutions of algebraic equations.
2. Consider the equation $2 x - 3 = 11$ . How would the solution change if you added 3 to both sides first?
Section L: Equation Manipulation
1. Simplify the expression $3 (2 x - 5)$ .
2. Solve for $y$ : $4 y = 3$ .
Section M: Real-world Applications
1. The cost of $c$ chocolates is given by $c \times 12$ . If the cost is $36, find the value of $c$ .
2. Express “ten more than a number $n$ ” as an algebraic expression.
Section N: Problem Solving
1. The sum of two consecutive odd numbers is 44. Find the numbers.
2. A rectangle has a length of $l$ and a width of $w$ . If $2 l + 2 w = 30$ , find the length.
Section O: Expressions and Equations
1. If $2 x + 6 = 18$ , find the value of $x$ .
2. Write an equation to represent the statement: “The product of 4 and a number $m$ is 24.”
Section P: Application in Geometry
1. The area of a rectangle is $A = lw$ . If the length is $5$ and the area is $20$ , find the width.
Section Q: Fractional Equations
1. Solve for $a$ : $2 a + 3 = 7$ .
2. If $2 b = 3 12$ , find the value of $b$ .
Section R: Evaluating Expressions
1. If $n = 8$ , evaluate the expression $3 n - 2$ .
2. Evaluate $5 p - 4$ when $p = 7$ .
Section S: Inequalities
1. Solve the inequality: $2 x + 5 < 15$ .
2. If $3 y + 7 \geq 16$ , find the possible values of $y$ .
Section T: System of Equations
1. Solve the system of equations:
$2 x + 3 y 4 x - 2 y = 13 = 14$
Section U: Graphical Representation
1. Graph the equation $y = 2 x - 4$ on a coordinate plane.
Section V: Factorization
1. Factorize the expression $4 x - 8$ .
2. If $6 p = 18$ , express $p$ as a product of prime factors.
Section W: Word Problems
1. The sum of two consecutive even numbers is 30. Find the numbers.
2. A number is multiplied by 5 and then added to 8; the result is 33. Find the number.
This should provide you with a comprehensive set of questions that cover various aspects of the Algebra chapter. Adjust the difficulty level based on your students’ proficiency and the learning objectives.[/expand]

Chapter 12: Ratio and Proportion[expand title=”Read More➔” swaptitle=”🠔Read Less”]

Understanding Ratios (1-15)

Define the term “ratio” and provide an example.
Express the ratio $3 : 7$ in its simplest form.
If a box contains 15 apples and 25 oranges, what is the ratio of apples to oranges?
If $a : b = 4 : 5$ , find the value of $a$ when $b = 15$ .
Convert the ratio $5 : 8$ to a decimal.
If the ratio of boys to girls in a class is $2 : 3$ , and there are 24 girls, how many boys are there?
If $p : q = 1 : 2$ and $q : r = 3 : 4$ , find the ratio $p : r$ .
The length of a rectangle is in the ratio $3 : 4$ to its width. If the width is 12 cm, find the length.
Express the ratio $2 : 3$ as a percentage.
In a bag of candies, the ratio of red to green candies is $5 : 3$ . If there are 40 candies in total, how many are green?
Solve for $x$ in the proportion $4 : x = 6 : 9$ .
If the ratio of milk to water in a mixture is $2 : 1$ and there are 24 liters of the mixture, find the quantity of water.
If $a : b = 3 : 4$ , find the value of $b$ when $a = 9$ .
The ratio of the salaries of two persons is $5 : 8$ . If the second person earns Rs. 40,000, find the salary of the first person.
If $x : 8 = 6 : 12$ , find the value of $x$ .

Exploring Proportions (16-30)

Determine whether the ratios $2 : 5$ and $4 : 10$ are proportional.
If $x : 8 = 6 : 12$ , find the value of $x$ .
In a rectangle, if the ratio of the length to the width is $3 : 2$ , and the width is 6 cm, find the length.
If $a : b = 2 : 5$ , find the value of $b$ when $a = 6$ .
A solution is prepared by mixing sugar and water in the ratio $3 : 2$ . If there are 15 liters of the solution, how much is water?
The ratio of boys to girls in a class is $4 : 5$ . If there are 36 girls, find the number of boys.
The ratio of the number of white balls to red balls in a bag is $2 : 3$ . If there are 15 white balls, find the number of red balls.
If $2 : 5 = x : 15$ , find the value of $x$ .
A rectangular field is 30 m long. If the length to width ratio is $2 : 3$ , find the width of the field.
A recipe requires mixing flour and sugar in the ratio $4 : 7$ . If you want to use 2 cups of flour, how many cups of sugar do you need?
If the speed of a car is in the ratio $3 : 4$ to the speed of a bike, and the bike is traveling at 20 km/h, find the speed of the car.
If the ratio of the ages of two persons is $5 : 3$ , and the sum of their ages is 40 years, find their ages.
In a group of 100 students, the ratio of boys to girls is $3 : 2$ . How many boys are there?
If $a : b = 3 : 4$ , and $b : c = 5 : 6$ , find the ratio $a : c$ .
A mixture contains alcohol and water in the ratio $2 : 3$ . If there are 15 liters of the mixture, find the quantity of water.

Solving Problems Involving Ratios (31-45)

The ratio of boys to girls in a school is $5 : 4$ . If there are 360 students, how many boys are there?
If the ratio of the ages of A and B is $3 : 4$ , and the sum of their ages is 28 years, find their ages.
In a bag, there are red, blue, and green marbles in the ratio $2 : 3 : 5$ . If there are 40 marbles in total, find how many are blue.
The ages of A and B are in the ratio $4 : 5$ . If A is 20 years old, find the age of B.
A mixture contains milk and water in the ratio $3 : 2$ . If there are 15 liters of the mixture, find the quantity of water.
The ratio of the present ages of A and B is $5 : 6$ . If A is 25 years old, find the age of B.
In a mixture, the ratio of sugar to salt is $3 : 2$ . If there are 15 kg of salt, find the quantity of sugar in the mixture.
If $a : b = 2 : 3$ and $b : c = 4 : 5$ , find the value of $c$ when $a = 8$ .
A bag contains 80 red balls, 60 blue balls, and 40 green balls. What is the ratio of red to blue to green balls?
The ratio of the incomes of A and B is $5 : 3$ . If A’s income is Rs. 25,000, find B’s income.
In a school, the ratio of boys to girls is $2 : 3$ . If there are 300 girls, find the number of boys.
The ratio of the present ages of A and B is $2 : 3$ . If B is 18 years old, find the age of A.
A mixture of fruit juice contains apple juice and orange juice in the ratio $3 : 2$ . If there are 15 liters of the mixture, find the quantity of apple juice.
In a class, the ratio of boys to girls is $3 : 5$ . If there are 24 boys, find the number of girls.
The ratio of the areas of two squares is $4 : 9$ . If the area of the smaller square is 36 sq units, find the area of the larger square.

Applying Ratios to Real-life Situations (46-60)

If you spend Rs. 300 on 5 kg of rice, what is the cost per kilogram?
A recipe calls for 2 cups of flour and 3 cups of sugar. If you want to make half the recipe, what is the ratio of flour to sugar?
A mixture contains alcohol and water in the ratio $2 : 1$ . If there are 15 liters of the mixture, find the quantity of alcohol.
If the ratio of the lengths of two ropes is $3 : 4$ , and the length of the shorter rope is 15 meters, find the length of the longer rope.
The ratio of the speeds of two cars is $5 : 3$ . If the first car is traveling at 60 km/h, find the speed of the second car.
A recipe requires mixing lemon juice and water in the ratio $1 : 4$ . If you want to make 2 liters of lemonade, how much water do you need?
If the ratio of the prices of two books is $2 : 5$ , and the first book costs Rs. 150, find the cost of the second book.
The ratio of the heights of two buildings is $3 : 5$ . If the first building is 15 meters tall, find the height of the second building.
In a group of 120 students, the ratio of boys to girls is $4 : 5$ . How many girls are there?
A mixture contains milk and water in the ratio $4 : 7$ . If there are 21 liters of the mixture, find the quantity of water.
The ratio of the weights of two objects is $2 : 5$ . If the first object weighs 8 kg, find the weight of the second object.
If the ratio of the ages of A and B is $3 : 4$ , and A is 24 years old, find the age of B.
A rectangular field is 40 m long and 30 m wide. If its length to width ratio is maintained, find the width of a similar field with a length of 60 m.
The ratio of the number of boys to girls in a class is $7 : 4$ . If there are 28 girls, find the number of boys.
If the ratio of the principal to the interest for 2 years is $5 : 2$ , and the interest is Rs. 400, find the principal.

Problem-solving with Proportions (61-75)

If $3 : 5 = x : 15$ , find the value of $x$ .
The ratio of the areas of two circles is $4 : 9$ . If the radius of the smaller circle is 3 cm, find the radius of the larger circle.
If $a : b = 2 : 3$ , and $b : c = 4 : 5$ , find the value of $c$ when $a = 8$ .
The ratio of the incomes of A and B is $5 : 3$ . If B’s income is Rs. 15,000, find A’s income.
If the ratio of the speeds of two trains is $3 : 4$ , and the first train is traveling at 90 km/h, find the speed of the second train.
A mixture of fruit juice contains apple juice and orange juice in the ratio $2 : 3$ . If there are 10 liters of the mixture, find the quantity of orange juice.
If $2 : 5 = x : 15$ , find the value of $x$ .
The ratio of the number of girls to boys in a class is $3 : 2$ . If there are 20 boys, find the number of girls.
If $a : b = 3 : 4$ , and $b : c = 5 : 6$ , find the value of $c$ when $a = 9$ .
The ratio of the present ages of A and B is $2 : 3$ . If A is 20 years old, find the age of B.
If $3 : 7 = x : 21$ , find the value of $x$ .
The ratio of the ages of A and B is $4 : 5$ . If B is 25 years old, find the age of A.
In a mixture, the ratio of sugar to salt is $4 : 3$ . If there are 21 kg of sugar, find the quantity of salt.
If $a : b = 2 : 5$ , find the value of $b$ when $a = 10$ .
The ratio of the present ages of A and B is $5 : 6$ . If B is 15 years old, find the age of A.

Advanced Problem-solving and Application (76-90)

In a group of 150 students, the ratio of boys to girls is $3 : 4$ . If there are 40 more girls than boys, find the number of boys.
The ratio of the areas of two rectangles is $2 : 3$ . If the area of the smaller rectangle is 18 sq units, find the area of the larger rectangle.
If $a : b = 3 : 5$ , and $b : c = 4 : 7$ , find the value of $c$ when $a = 9$ .
A mixture of nuts and raisins contains nuts and raisins in the ratio $5 : 2$ . If there are 35 nuts, find the quantity of raisins.
If $2 : 3 = x : 15$ , find the value of $x$ .
A rectangular field is 50 m long and 20 m wide. If its length to width ratio is maintained, find the length of a similar field with a width of 40 m.
The ratio of the lengths of two ropes is $5 : 4$ . If the shorter rope is 10 meters long, find the length of the longer rope.
In a group of 200 students, the ratio of boys to girls is $2 : 3$ . How many girls are there?
If $a : b = 4 : 5$ and $b : c = 3 : 2$ , find the value of $c$ when $a = 8$ .
A solution is prepared by mixing juice and water in the ratio $3 : 2$ . If there are 25 liters of the solution, how much is juice?
If the ratio of the prices of two items is $3 : 7$ , and the first item costs Rs. 90, find the cost of the second item.
The ratio of the speeds of two bikes is $4 : 3$ . If the first bike is traveling at 36 km/h, find the speed of the second bike.
A rectangular garden is 24 m long. If the length to width ratio is $3 : 2$ , find the width of the garden.
If the ratio of the ages of A and B is $3 : 4$ , and the sum of their ages is 35 years, find their ages.
A mixture of coffee and milk contains coffee and milk in the ratio $2 : 1$ . If there are 30 liters of the mixture, find the quantity of milk.

Remember to adapt these questions based on the specific needs of your students and the curriculum requirements. You can also create variations of these questions to reinforce different aspects of the chapter.[/expand]

A. Identify the Whole Numbers (1-10)

B. Operations with Whole Numbers (11-20)

C. Word Problems (21-30)

D. True or False (31-40)

E. Fill in the blanks (41-50)

F. Comparisons and Ordering (51-60)

G. Multiples and Factors (61-70)

H. Patterns and Sequences (71-80)

I. Practical Application (81-90)

J. Revision and Challenge (91-100)

Section A: Multiple Choice Questions (1 mark each)

Section B: True/False (1 mark each)

Section C: Short Answer Questions (2 marks each)

Section D: Application Problems (3 marks each)

Section E: Crossword Puzzle

Section F: Reflect and Review

Section A: Multiple Choice Questions (1 mark each)

Section B: True/False (1 mark each)

Section C: Short Answer Questions (2 marks each)

Section D: Application Problems (3 marks each)

Section E: Crossword Puzzle

Section F: Reflect and Review

Multiple Choice Questions:

Fill in the Blanks:

True/False:

Matching:

Drawing Exercises:

Short Answer:

Problem Solving:

Application:

Reflection:

Multiple Choice Questions:

Fill in the Blanks:

True/False:

Matching:

Drawing Exercises:

Short Answer:

Problem Solving:

Application:

Reflection:

Set of 10 Questions:

Multiple Choice Questions (MCQs):

Fill in the Blanks:

True/False Statements:

Short Answer Questions:

Match the Following:

Diagram-Based Questions:

Long Answer Questions:

Critical Thinking:

Real-life Application:

Problem-Solving:

Miscellaneous:

Evaluation and Reflection:

Multiple Choice Questions (MCQs):

Fill in the Blanks:

True/False Statements:

Short Answer Questions:

Match the Following:

Diagram-Based Questions:

Long Answer Questions:

Critical Thinking:

Real-life Application:

Problem-Solving:

Miscellaneous:

Evaluation and Reflection:

Extension and Application:

Project-Based Questions:

Collaborative Learning:

Cross-Curricular Integration:

Technology Integration:

Section A: Basic Concepts

Section B: Solving Equations

Section C: Word Problems

Section D: Applications

Section E: Advanced Problem Solving

Section F: Exploring Patterns

Section G: True/False

Section H: Multiple Choice

Section I: Matching

Section J: Fill in the Blanks