742 prompts matching "Structured question: find k so a cubic has a repeated root"
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Common Mistakes: Distributivity on a set of three elements
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Learn: What an identity element is
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Common Mistakes: Checking an inverse by working the operation both ways
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Learn: Reading index notation, the base and the exponent
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Worked Example: The law for multiplying powers of the same base
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Common Mistakes: Why the index laws need the bases to match
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Learn: Why any non-zero number to the power nought is one
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Worked Example: Rewriting a negative index as a fraction
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Learn: The definition of a logarithm as the index
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Worked Example: Writing an index statement as a logarithm
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Common Mistakes: Reading a logarithm from a table
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Learn: The law for the logarithm of a product
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Worked Example: The law for the logarithm of a quotient
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Learn: The change of base formula
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Common Mistakes: A logarithmic equation that becomes a quadratic
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Learn: What a sequence is, and what a term means
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Worked Example: Writing out the terms of a sequence from its nth term
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Common Mistakes: The Fibonacci sequence and the rule behind it
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Learn: What makes a sequence an arithmetic progression
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Common Mistakes: An arithmetic progression with a negative common difference
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