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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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Final revision: my three hardest Further Maths topics

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Learn: Simplifying a surd by extracting the largest perfect square

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Worked Example: Collecting like surds in a single sum

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Explain Back: Rationalising a denominator of the form a plus root b using the conjugate

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Learn: The multiplication and division laws of indices used together

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Worked Example: Simplifying an expression carrying both a negative and a fractional index

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Explain Back: The laws of logarithms for a product and for a quotient

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Learn: The sum and the product of the roots read from the coefficients

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Worked Example: The discriminant, and what each of its three cases means

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Explain Back: The range of values of k for which the roots are real

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Learn: Finding alpha squared plus beta squared from the sum and product

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Explain Back: Finding alpha squared beta plus alpha beta squared

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Learn: The degree of a polynomial and its leading coefficient

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Worked Example: Evaluating a polynomial by substitution

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Explain Back: Finding an unknown coefficient given that a stated factor divides the polynomial

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Learn: The sum of the roots of a cubic read from its coefficients

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Worked Example: The sum of the products of the roots of a cubic taken two at a time

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

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Learn: Solving a linear inequality, and reversing the sign on dividing by a negative

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Worked Example: Solving a quadratic inequality by sketching the parabola

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