Introduction: This lesson is foundational. Questions on surds appear often, and understanding number sets helps with logic in other areas. Master the simplification of surds to save time and avoid mistakes in algebra and geometry problems.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Define): In your own words, what is the difference between a Rational number and an Irrational number? Give two examples of each.

• Prompt 2 (Identify): Look at the fraction . Without dividing, will its decimal form terminate or recur? Why?

• Prompt 3 (Calculate): Simplify the following basic surds:

  • 35​+65​

  • 83​−3​

• Prompt 4 (Convert): Write 72​ in the form ab​.

• Prompt 5 (Convert): Write 53​ as an entire surd.

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Calculate): Simplify the expression: 38​−50​+218​.

• Prompt 2 (Calculate): Find the product of (42​) and (36​).

• Prompt 3 (Calculate): Simplify: 1520​÷35​.

• Prompt 4 (Method): Rationalize the denominator of 32​8​.

• Prompt 5 (Problem Solve): The length of a rectangle is 45​ cm and its width is 25​ cm. Find its area and perimeter.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Complex Calculation): Simplify the expression: 2​43​​+54​−6​5​.

• Prompt 2 (Problem Solve): The area of a square is 48 cm². Find the length of its diagonal in the simplest surd form.

• Prompt 3 (Explain): Explain why the decimal expansion of 71​ is a recurring decimal, based on the prime factors of its denominator.

• Prompt 4 (Justify): A student simplifies 12​+27​ to 39​. Explain why this is incorrect and provide the correct simplification.

• Prompt 5 (Application): In a right-angled triangle, the lengths of the two shorter sides are 3​+1 cm and 3​−1 cm. Find the square of the length of the hypotenuse.

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Proof): Show that (5​+2)2−(5​−2)2 is a rational number.

• Prompt 2 (Problem Solve): The volume of a cuboid is 150​ cm³. If its height is 3​ cm and its base is a square, find the length of a side of the base.

• Prompt 3 (Challenge): Simplify: 2​+11​+3​+2​1​+4​+3​1​.

• Prompt 4 (Derive): A right circular cone has a base radius of r=2​ cm and a slant height of l=32​ cm. Find its perpendicular height, h, and express the curved surface area (πrl) in terms of π.

• Prompt 5 (Synthesis): A trapezium has parallel sides of length 53​ cm and 73​ cm. Its perpendicular height is 27​ cm. Calculate the area of the trapezium in its simplest form.