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 remainder when 5^100 is divided by 3?

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What is the cube of 4?

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A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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If the sum of three consecutive integers is 96, what are the integers?

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If x - y = 5 and x + y = 15, what is the value of x?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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