1,334 prompts matching "An answer left in surd form after completing the square"
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Worked Example: The intersection of two overlapping sets
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Practice: The difference of two sets, A minus B
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Explain Back: The symmetric difference of two sets
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Common Mistakes: Showing that intersection distributes over union
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Worked Example: Testing whether a binary operation is closed on a given set
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Practice: Testing a binary operation for associativity
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Explain Back: Finding the identity element of a binary operation
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Common Mistakes: A binary operation defined by arithmetic modulo n
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Final Revision: Proving that root 2 is irrational
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Final Revision: Sketching the graph of a logarithmic function
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Learn: The sum and the product of the roots read from the coefficients
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Common Mistakes: Proving that a quadratic expression is positive for every real x
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Final Revision: Solving a disguised quadratic by substitution
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Worked Example: Finding one over alpha plus one over beta
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Explain Back: Finding alpha squared beta plus alpha beta squared
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Common Mistakes: Symmetric functions when the three roots of a cubic are involved
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Worked Example: Evaluating a polynomial by substitution
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Practice: Factorising a cubic completely once one factor is known
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Practice: Finding the third root of a cubic when two are known
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Common Mistakes: Three roots in geometric progression in a cubic
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