755 prompts matching "Learn: The parabola y squared equals 4ax, with its focus and directrix"
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Practice: Testing a set for closure under multiplication
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Show All Working: Showing a set is not closed by a single counter-example
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Common Mistakes: Closure on a set of three elements under a stated rule
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Worked Example: Testing a*b against b*a for a given rule
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Explain Back: What it means for an operation to be associative
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Show All Working: An operation that is associative but not commutative
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Practice: Multiplication distributing over addition in ordinary arithmetic
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Explain Back: Showing distributivity fails by a counter-example
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Show All Working: Using distributivity to simplify an expression
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Common Mistakes: Distributivity on a set of three elements
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Practice: Why an identity element must work from both sides
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Explain Back: What an inverse element is
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Worked Example: Rewriting a negative index as a fraction
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Common Mistakes: Writing a root as a fractional index before simplifying
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Worked Example: Solving an indicial equation where one side must be factorised first
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Show All Working: A word problem that leads to an indicial equation
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Common Mistakes: An indicial equation solved by substitution
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Worked Example: Writing an index statement as a logarithm
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Practice: Evaluating log to base 2 of 8
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Common Mistakes: Reading a logarithm from a table
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