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

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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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A cube has a side length of 4 cm. What is its volume?

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

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What is the slope of a line passing through the points (2, 3) and (4, 7)?

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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 144?

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If two complementary angles differ by 30°, what are the angles?

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What is the sum of the first 50 positive integers?

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If a person can type 45 words per minute, how many words can they type in 2 hours?

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