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 area of a circle with a diameter of 14 cm?

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

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

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The probability of rolling a sum of 7 with two dice is:

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What is the length of the diagonal of a square with a side length of 7 cm?

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If the perimeter of a square is 40 cm, what is the area of the square?

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

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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

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