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Further Mathematics

AI prompts for senior secondary learners.

📅 36-Week WAEC Study Guide for Further Mathematics →
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754 prompts matching "Structured question: arrangements with a restriction"

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Worked Example: The division algorithm for polynomials

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Practice: A division that leaves no remainder

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Explain Back: A division that leaves a constant remainder

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Show All Working: Synthetic division as a shorter route

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Common Mistakes: The degree of the quotient and of the remainder

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Worked Example: The remainder on dividing by x minus 3

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Practice: The remainder on dividing by 2x minus 1

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Explain Back: Finding a coefficient when the remainder is given

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Show All Working: A remainder of nought, and what it means

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Common Mistakes: The remainder theorem applied to a quartic

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Worked Example: Testing a list of candidates to find a factor

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Practice: Showing that x plus 3 is a factor of a given polynomial

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Explain Back: Finding a coefficient so that a stated expression is a factor

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Show All Working: What the factor theorem says about the roots

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Common Mistakes: Using the factor theorem before dividing

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Worked Example: Factorising a cubic into a linear and a quadratic factor

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Practice: Factorising a quartic as the product of two quadratics

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Common Mistakes: Factorising fully, and knowing when to stop

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Worked Example: How many roots a cubic equation has

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Show All Working: Solving a cubic that must first be rearranged

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