755 prompts matching "using the factor theorem to factorise a cubic"
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Final Revision: Deciding whether a given rule really is a binary operation
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Worked Example: Testing the even numbers for closure under addition
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Quiz: Testing the odd numbers for closure under addition
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Explain Back: Testing the integers for closure under division
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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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Explain Back: What it means for an operation to be associative
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Common Mistakes: Subtraction as an example of neither law
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Worked Example: Testing whether star distributes over plus
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Final Revision: Why distributivity links two operations rather than one
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Worked Example: Finding the identity element from a rule such as a*b = a + b - 3
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Quiz: Finding the identity element from an operation table
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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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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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Quiz: The law for dividing powers of the same base
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Practice: A fractional index with numerator one, read as a root
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Explain Back: A fractional index with a numerator above one
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Explain Back: An indicial equation with the unknown in the exponent on both sides
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