755 prompts matching "Why does completing the square work"
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Spot My Mistake: Rationalising and then cancelling a common factor
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Show All Working: Checking a rationalised answer by decimal approximation
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Practice: Rationalising a denominator of the form a plus root b over c minus root d
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Spot My Mistake: Simplifying the denominator once the conjugate has been used
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Learn: Solving an equation with a single square root term
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Worked Example: Squaring both sides safely when solving a surd equation
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Show All Working: Finding a and b when a plus b root 2 equals a given surd
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Show All Working: Evaluating a repeated operation such as a*(b*c)
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Show All Working: Showing a set is not closed by a single counter-example
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Worked Example: Testing a*b against b*a for a given rule
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Show All Working: An operation that is associative but not commutative
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Final Revision: Why brackets matter when an operation is not associative
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Show All Working: Using distributivity to simplify an expression
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Spot My Mistake: Finding the inverse of a given element
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Show All Working: An element with no inverse under a given operation
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Practice: The law for a power raised to another power
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Spot My Mistake: The law for a quotient raised to a power
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Show All Working: Simplifying an expression with letters and indices
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Worked Example: Rewriting a negative index as a fraction
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Worked Example: Solving an indicial equation where one side must be factorised first
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