AQA · Mathematics · 8300
GCSE Maths: Algebra: completing the square
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Algebra: completing the square (Corbettmaths Video 10), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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When completing the square on x² + 8x + 1, the value of 'a' in (x + a)² is ?.
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4
What is the first step when completing the square on an expression like x² + bx + c?
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Take half of the coefficient of x and square it to form (x + b/2)².
When the coefficient of x² is not 1, what must you do before completing the square?
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Factor out the coefficient of x² from the terms involving x.
How do you expand (x + 3)² − 4 into the form x² + bx + c?
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Expand (x + 3)² to get x² + 6x + 9, then subtract 4 to get x² + 6x + 5.
Why is completing the square useful for finding the minimum point of a parabola y = x² + bx + c?
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It converts the equation to vertex form (x + a)² + b, where (−a, b) is the minimum point.
If x² + px + q = (x − 5)² + 31, what is the value of p?
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p = −10. Expanding (x − 5)² gives x² − 10x + 25, so p = −10.
When solving x² − 6x − 3 = 0 by completing the square, what form should you first write the left side in?
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(x − a)² − b = 0, which allows you to isolate (x − a)² and then take square roots.
What form should 3x² + 18x − 1 be written in when completing the square with a leading coefficient not equal to 1?
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a(x + b)² + c, where a, b, and c are constants.
If y = x² − 10x + 20 is written as (x − a)² − b, what is the equation of the line of symmetry?
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x = a. The line of symmetry passes through the x-coordinate of the vertex.
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