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Further Mathematics

AI prompts for senior secondary learners.

📅 36-Week WAEC Study Guide for Further Mathematics →
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1,019 prompts matching "A set closed under one operation but not another"

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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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Quiz: Finding alpha cubed plus beta cubed

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Spot My Mistake: Forming an equation whose roots are alpha squared and beta squared

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WAEC Prep: Forming an equation whose roots are alpha over beta and beta over alpha

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Show All Working: Finding a coefficient given a stated relation between the roots

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Common Mistakes: Symmetric functions when the three roots of a cubic are involved

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Final Revision: Checking a symmetric-function answer by solving the equation outright

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Quiz: The factor theorem, and testing whether x minus a is a factor

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Spot My Mistake: The factor theorem for a divisor of the form ax minus b

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WAEC Prep: Sketching a cubic from its factorised form

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Show All Working: Solving a cubic equation by factorisation

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Common Mistakes: Adding, subtracting and multiplying two polynomials

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Final Revision: The zeros of a polynomial and where its graph cuts the x-axis

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Quiz: The product of the roots of a cubic

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Spot My Mistake: The relations between roots and coefficients for a quartic

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Show All Working: Three roots in arithmetic progression in a cubic

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Common Mistakes: Three roots in geometric progression in a cubic

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Final Revision: Checking that the roots found satisfy the original equation

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Quiz: Solving a quadratic inequality using a sign table

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