Topic Details (Notes format)

How to Use Completing the Square Technique

Subject: Mathematics

Book: Maths Mastery

Completing the square rewrites a quadratic ax² + bx + c into a(x – h)² + k form. For instance, x² + 6x + 5 → (x² + 6x + 9) – 9 + 5 → (x + 3)² – 4. This reveals the vertex or allows direct factoring. It’s also vital in derivations (quadratic formula), geometry (circle equations), and calculus (integrals of certain forms). Mastering it fosters deeper insight into parabola properties and simplifies many otherwise cumbersome algebraic tasks.

Practice Questions

What is the HCF of 72 and 120?

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What is the HCF of 48 and 180?

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If sin(A) = 1/2 and A is acute, what is the value of A?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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If a number is divisible by 9, it is also divisible by which of the following?

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What is the sum of the interior angles of a hexagon?

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How many diagonals does a pentagon have?

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What is the sum of all odd numbers from 1 to 99?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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