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

If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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If the sum of the angles of a polygon is 1080°, how many sides does the polygon have?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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

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What is the square root of 0.25?

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What is the value of log₃(27)?

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What is the HCF of 72 and 120?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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