755 prompts matching "Structured question: intersection of a line and a circle"
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Final Revision: Deciding whether a given rule really is a binary operation
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Learn: What closure means for a binary operation
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Final Revision: Why closure is checked before any other property
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Learn: What it means for an operation to be commutative
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Final Revision: Why brackets matter when an operation is not associative
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Learn: What it means for one operation to distribute over another
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Final Revision: Why distributivity links two operations rather than one
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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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Common Mistakes: Why the index laws need the bases to match
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Final Revision: Evaluating a numerical expression using the index laws
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Learn: Why any non-zero number to the power nought is one
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Common Mistakes: Writing a root as a fractional index before simplifying
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Learn: Solving an equation by writing both sides to the same base
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Common Mistakes: An indicial equation solved by substitution
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Final Revision: Checking an indicial solution by substitution
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Common Mistakes: Reading a logarithm from a table
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Common Mistakes: Rejecting a root that makes a logarithm undefined
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Final Revision: Proving a logarithmic identity from the laws
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Common Mistakes: A logarithmic equation that becomes a quadratic
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