Essential Maths Textbook Page 207, no 21-30 (show workings) Theory page 208 no 6-15

Page 207, Problems 21-30:

21. Problem: Solve for x: 3x + 7 = 22. Solution:

• Subtract 7 from both sides: 3x = 22 – 7 = 15.
• Divide both sides by 3: x = 15 / 3 = 5.

22. Problem: Solve for y: 4(y – 3) = 32. Solution:

• Distribute the 4: 4y – 12 = 32.
• Add 12 to both sides: 4y = 32 + 12 = 44.
• Divide both sides by 4: y = 44 / 4 = 11.

23. Problem: Solve for z: 2(z + 5) = 18. Solution:
    • Distribute the 2: 2z + 10 = 18.
    • Subtract 10 from both sides: 2z = 18 – 10 = 8.
    • Divide both sides by 2: z = 8 / 2 = 4.
24. Problem: Solve for x: 5 – 2x = 13. Solution:
    • Subtract 5 from both sides: -2x = 13 – 5 = 8.
    • Divide both sides by -2: x = 8 / -2 = -4.
25. Problem: Solve for y: 6y – 4 = 26. Solution:
    • Add 4 to both sides: 6y = 26 + 4 = 30.
    • Divide both sides by 6: y = 30 / 6 = 5.
26. Problem: Solve for z: 3z – 8 = 13. Solution:
    • Add 8 to both sides: 3z = 13 + 8 = 21.
    • Divide both sides by 3: z = 21 / 3 = 7.
27. Problem: Solve for x: 2x – 3 = 11. Solution:
    • Add 3 to both sides: 2x = 11 + 3 = 14.
    • Divide both sides by 2: x = 14 / 2 = 7.
28. Problem: Solve for y: 4(y + 2) = 32. Solution:
    • Distribute the 4: 4y + 8 = 32.
    • Subtract 8 from both sides: 4y = 32 – 8 = 24.
    • Divide both sides by 4: y = 24 / 4 = 6.
29. Problem: Solve for z: 3(z – 4) = 15. Solution:
    • Distribute the 3: 3z – 12 = 15.
    • Add 12 to both sides: 3z = 15 + 12 = 27.
    • Divide both sides by 3: z = 27 / 3 = 9.
30. Problem: Solve for x: 7x + 6 = 27. Solution:
    • Subtract 6 from both sides: 7x = 27 – 6 = 21.
    • Divide both sides by 7: x = 21 / 7 = 3.

Now, let’s move on to the theory problems from page 208:

Page 208, Problems 6-15:

6. Problem: Find the perimeter of a rectangle with length 6 cm and width 4 cm. Solution: Perimeter = 2(length + width) = 2(6 + 4) = 2(10) = 20 cm.
7. Problem: Find the area of a rectangle with length 8 m and width 5 m. Solution: Area = length × width = 8 m × 5 m = 40 square meters.
8. Problem: Find the perimeter of a square with side length 9 cm. Solution: Perimeter = 4 × side length = 4 × 9 cm = 36 cm.
9. Problem: Find the area of a square with side length 12 cm. Solution: Area = side length × side length = 12 cm × 12 cm = 144 square centimeters.
10. Problem: Find the perimeter of a triangle with side lengths 5 cm, 7 cm, and 8 cm. Solution: Perimeter = sum of all side lengths = 5 cm + 7 cm + 8 cm = 20 cm.
11. Problem: Find the area of a triangle with base 6 cm and height 9 cm. Solution: Area = (base × height) / 2 = (6 cm × 9 cm) / 2 = 54 square centimeters.
12. Problem: Find the perimeter of a circle with radius 10 cm. (Use π = 3.14) Solution: Perimeter = 2πr = 2 × 3.14 × 10 cm ≈ 62.8 cm.
13. Problem: Find the area of a circle with radius 7 cm. (Use π = 3.14) Solution: Area = πr² = 3.14 × (7 cm)² ≈ 153.86 square centimeters.
14. Problem: Find the volume of a cube with side length 4 cm.

Solution: Volume = side length × side length × side length = 4 cm × 4 cm × 4 cm = 64 cubic centimeters.

15. Problem: Find the volume of a rectangular prism with length 5 cm, width 3 cm, and height 6 cm. Solution: Volume = length × width × height = 5 cm × 3 cm × 6 cm = 90 cubic centimeters.

These calculations help us understand how to find perimeters, areas, and volumes of different shapes, which are essential concepts in mathematics. Practicing these problems will strengthen your understanding and problem-solving skills.

Understanding Perimeter, Area, and Volume: Essential Maths Concepts for JSS 2 Students 📐

Hello JSS 2 students in Lagos State! Today, we’ll explore important mathematical concepts: perimeter, area, and volume. Let’s dive in:

Perimeter:

What is Perimeter?

Perimeter is the distance around the outside of a shape. We find it by adding up all the sides of the shape.

Example:

If we have a rectangle with length 6 cm and width 4 cm, the perimeter would be 2(6 cm + 4 cm) = 20 cm.

Area:

What is Area?

Area is the amount of space inside a shape. We find it by multiplying the length and width of the shape.

Example:

For a rectangle with length 8 m and width 5 m, the area would be 8 m × 5 m = 40 square meters.

Volume:

What is Volume?

Volume is the amount of space inside a three-dimensional shape. We find it by multiplying the length, width, and height of the shape.

Example:

If we have a cube with a side length of 4 cm, the volume would be 4 cm × 4 cm × 4 cm = 64 cubic centimeters.

Practice Problems:

1. Perimeter Practice:
   • Find the perimeter of a square with side length 9 cm.
2. Area Practice:
   • Calculate the area of a triangle with base 6 cm and height 9 cm.
3. Volume Practice:
   • Determine the volume of a rectangular prism with length 5 cm, width 3 cm, and height 6 cm.

By understanding these concepts and practicing with examples, you’ll become more confident in solving mathematical problems involving perimeter, area, and volume. Keep practicing, and you’ll master these essential maths skills! 🧮✨

about Perimeter, Area, and Volume:

1. What is perimeter?
   • Perimeter is the distance around the outside of a shape.
2. How do we find the perimeter of a shape?
   • We find the perimeter by adding up all the sides of the shape.
3. What is area?
   • Area is the amount of space inside a shape.
4. How do we calculate the area of a shape?
   • We calculate the area by multiplying the length and width of the shape.
5. What is volume?
   • Volume is the amount of space inside a three-dimensional shape.
6. How do we find the volume of a shape?
   • We find the volume by multiplying the length, width, and height of the shape.
7. What units are used to measure perimeter?
   • Perimeter is measured in linear units such as centimeters, meters, or inches.
8. What units are used to measure area?
   • Area is measured in square units such as square centimeters, square meters, or square inches.
9. What units are used to measure volume?
   • Volume is measured in cubic units such as cubic centimeters, cubic meters, or cubic inches.
10. Can we find the perimeter of a circle?
    • Yes, the perimeter of a circle is called the circumference, and we calculate it using the formula 2πr.
11. Can we find the area of a circle?
    • Yes, we use the formula πr² to find the area of a circle.
12. Can we find the volume of a sphere?
    • Yes, we use the formula (4/3)πr³ to find the volume of a sphere.
13. What is the difference between perimeter and area?
    • Perimeter measures the distance around the outside of a shape, while area measures the space inside the shape.
14. Why is it important to understand perimeter, area, and volume?
    • Understanding these concepts helps us solve real-world problems involving measurement and space.
15. How can I improve my skills in calculating perimeter, area, and volume?
    • Practice regularly with different shapes and dimensions to strengthen your understanding and problem-solving abilities.

Perimeter Examples:

1. Rectangle:
   • Given: Length = 6 cm, Width = 4 cm
   • Perimeter = 2(Length + Width) = 2(6 cm + 4 cm) = 2(10 cm) = 20 cm
2. Square:
   • Given: Side Length = 9 cm
   • Perimeter = 4 × Side Length = 4 × 9 cm = 36 cm
3. Triangle:
   • Given: Side Lengths = 5 cm, 7 cm, 8 cm
   • Perimeter = Sum of all side lengths = 5 cm + 7 cm + 8 cm = 20 cm

Area Examples:

4. Rectangle:
   • Given: Length = 8 m, Width = 5 m
   • Area = Length × Width = 8 m × 5 m = 40 square meters
5. Triangle:
   • Given: Base = 6 cm, Height = 9 cm
   • Area = (Base × Height) / 2 = (6 cm × 9 cm) / 2 = 54 square centimeters
6. Circle:
   • Given: Radius = 7 cm (π ≈ 3.14)
   • Area = π × Radius² = 3.14 × (7 cm)² ≈ 153.86 square centimeters

Volume Examples:

7. Cube:
   • Given: Side Length = 4 cm
   • Volume = Side Length³ = 4 cm × 4 cm × 4 cm = 64 cubic centimeters
8. Rectangular Prism:
   • Given: Length = 5 cm, Width = 3 cm, Height = 6 cm
   • Volume = Length × Width × Height = 5 cm × 3 cm × 6 cm = 90 cubic centimeters
9. Sphere:
   • Given: Radius = 10 cm (π ≈ 3.14)
   • Volume = (4/3) × π × Radius³ = (4/3) × 3.14 × (10 cm)³ ≈ 4186.67 cubic centimeters

Objectives

1. The perimeter of a rectangle is found by adding _____. a) length and width b) length and height c) width and height d) area and volume
2. Area measures the ______ of space inside a shape. a) length b) amount c) distance d) perimeter
3. The volume of a shape measures its _____. a) length b) width c) height d) space
4. Perimeter is measured in ______ units. a) square b) cubic c) linear d) circular
5. To find the area of a rectangle, we multiply its _____. a) length and height b) width and height c) length and width d) perimeter and area
6. The perimeter of a square is found by multiplying the _____. a) side length by 4 b) side length by 2 c) side length by 3 d) side length by 5
7. Area is measured in ______ units. a) linear b) square c) cubic d) circular
8. To find the volume of a cube, we multiply its side length _____. a) once b) twice c) thrice d) four times
9. The area of a triangle is found by multiplying its base by its _____ and dividing by 2. a) length b) width c) height d) perimeter
10. Perimeter is the distance around the ______ of a shape. a) inside b) outside c) bottom d) top
11. The volume of a rectangular prism is found by multiplying its length, width, and ______. a) area b) perimeter c) height d) diameter
12. Area measures the amount of ______ inside a shape. a) space b) air c) water d) sunlight
13. The perimeter of a triangle is found by adding the lengths of its _____. a) angles b) sides c) vertices d) diagonals
14. Volume is the amount of space inside a ______ shape. a) two-dimensional b) three-dimensional c) flat d) linear
15. The area of a circle is found by multiplying π by the square of its ______. a) perimeter b) diameter c) radius d) circumference