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Further Mathematics

AI prompts for senior secondary learners.

📅 36-Week WAEC Study Guide for Further Mathematics →
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1,200 prompts matching "Structured question: composite function with a restricted domain"

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Explain Back: Forming a cubic equation whose three roots are given

I have just studied forming a cubic equation whose three roots are given in my SS3 Further

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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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Worked Example: Solving a quadratic inequality by sketching the parabola

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Explain Back: Solving an inequality that involves a modulus

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Show All Working: Solving a pair of simultaneous linear inequalities

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Common Mistakes: The range of values of x for which an expression stays positive

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Worked Example: The number of arrangements of n different objects in a row

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Practice: Arrangements when some of the objects are identical

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Explain Back: Arrangements in which two particular objects must stay together

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Show All Working: Arrangements of the letters of a given word

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Worked Example: The difference between a permutation and a combination

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Practice: Choosing a committee that must contain one particular person

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Show All Working: Counting the handshakes, or the lines joining n points

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Common Mistakes: Selections in which at least one of a kind must appear

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Worked Example: The identities for one plus tan squared and one plus cot squared

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Practice: The compound angle formula for cosine of A minus B

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Explain Back: The compound angle formula for tan of A plus B

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Show All Working: The half angle formulae and the t-substitution

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Common Mistakes: Expressing a cos x plus b sin x in the form R cos of x minus alpha

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