755 prompts matching "The dot product worked out from components"
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Common Mistakes: Rationalising a denominator of the form root a over root b
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Final Revision: Expressing a rationalised answer in the form a root b over c
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Spot My Mistake: Simplifying the denominator once the conjugate has been used
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Show All Working: A conjugate where the surd term comes first
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Common Mistakes: Rationalising when both terms of the denominator are surds
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Final Revision: Deciding whether a given rule really is a binary operation
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Final Revision: Why closure is checked before any other property
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Common Mistakes: Subtraction as an example of neither law
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Final Revision: Why distributivity links two operations rather than one
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Spot My Mistake: Finding the inverse of a given element
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Common Mistakes: Checking an inverse by working the operation both ways
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Final Revision: Identity and inverse together, and what they give the set
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Spot My Mistake: The law for a quotient raised to a power
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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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Show All Working: Simplifying an expression that mixes the index types
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Spot My Mistake: The logarithm of the base itself
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Show All Working: The common logarithm, to base ten
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Final Revision: The characteristic and the mantissa of a logarithm
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Spot My Mistake: Evaluating an expression using the laws of logarithms
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