742 prompts matching "Structured question: find k so a cubic has a repeated root"
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Common Mistakes: Why a rational number added to an irrational one stays irrational
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Learn: What makes two surds similar
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Worked Example: What makes two surds equal
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Common Mistakes: Expanding the product of two surd brackets
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Learn: Why a surd is never left in the denominator
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Worked Example: Rationalising a denominator that is a single surd
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Learn: The conjugate of a compound surd expression
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Worked Example: Why multiplying by the conjugate clears the surd
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Common Mistakes: Rationalising when both terms of the denominator are surds
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Learn: What a binary operation actually is
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Worked Example: Reading the symbol used for a binary operation
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Common Mistakes: A binary operation that is ordinary addition in disguise
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Learn: What closure means for a binary operation
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Worked Example: Testing the even numbers for closure under addition
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Common Mistakes: Closure on a set of three elements under a stated rule
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Learn: What it means for an operation to be commutative
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Worked Example: Testing a*b against b*a for a given rule
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Common Mistakes: Subtraction as an example of neither law
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Learn: What it means for one operation to distribute over another
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Worked Example: Testing whether star distributes over plus
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