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

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

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What is the cube of 4?

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If the probability of an event is 1/4, what is the probability of its complement?

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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What is the cube root of 729?

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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 a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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What is the sum of all even numbers between 1 and 50?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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