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 sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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What is the sum of the first 20 odd numbers?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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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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What is the square root of 121?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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If x^2 + 4x + 4 = 0, what is the value of x?

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