Activity 1
Verification of the Identity (a+b)² = a² + 2ab + b²
Object:
To confirm the given identity.
Apparatus Required:
Cardboard. White chart paper. Two glazed papers of different colours. Scissors. Gum. Pencil. Ruler and geometrical instruments.
Theory:
The square of the sum of two numbers is equal to the sum of the squares of the two numbers and twice their product. This identity can be proved using the area method.
Procedure / Observation:
Draw a square of side . Divide it into one square of side . Again divide it into another square of side . Form two rectangles each of dimensions . Calculate the areas of all the parts.
Result:
The given identity is verified. Precautions: Draw figures neatly. Take correct and precise measurements. Label every part clearly.
Activity 2
Verification of the Identity (a-b)² = a² - 2ab + b²
Object:
To confirm the given identity.
Apparatus Required:
Chart paper. Coloured paper. Scissors. Gum. Pencil. Ruler and geometrical instruments.
Theory:
The square of the difference of two numbers is equal to the sum of their squares minus twice their product.
Procedure / Observation:
Draw a square of side . Remove two rectangles each having area . Add a square of side . Compare the remaining area with the required expression.
Result:
The identity is verified. Precautions: Subtract the areas carefully. Draw straight and clear lines.
Activity 19
Verification of Pythagoras Theore
Object:
To verify Pythagoras theorem. Apparatus Required: Graph paper. Ruler. Pencil. Geometrical instruments.
Theory: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Procedure / Observation:
Draw a right-angled triangle. Construct squares on each of its three sides. Calculate the area of every square. Add the areas of the two smaller squares. Compare the sum with the area of the square on the hypotenuse.
Result:
Pythagoras theorem is verified. Precautions: The right angle must be perfectly accurate. All measurements should be taken carefully.
Activity 25
Total Surface Area of a Cube
Object:
To calculate the total surface area of a cube. Apparatus
Required:
Cube model. Ruler.
Theory: A cube consists of six identical square faces. The total surface area of a cube is .
Procedure / Observation: Measure the length of one side of the cube. Find the area of one face. Multiply the area by six.
Result:
The total surface area of the cube is . Precautions: Measure the side length accurately. Use a proper and correct cube model.
Activity 28
Verification of the Identity a³ - b³ = (a-b)(a² + ab + b²)
Object:
To verify the given identity.
Apparatus Required:
Chart paper. Coloured paper. Scissors. Gum. Pencil. Ruler.
Theory:
The difference of cubes of two numbers can be expressed as a product of one linear factor and one quadratic factor.
Procedure / Observation:
Draw suitable geometrical shapes. Represent and . Find the difference between the areas. Compare it with the product .
Result: The identity is verified. Precautions: Draw clean and neat diagrams. Take accurate measurements.
