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

A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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What is the sum of all even numbers between 1 and 100?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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If the probability of an event is 1/4, what is the probability of its complement?

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What is the sum of the first 50 positive integers?

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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 square root of 144?

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What is the remainder when 5^100 is divided by 3?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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