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Further Mathematics

AI prompts for senior secondary learners.

📅 36-Week WAEC Study Guide for Further Mathematics →
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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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