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Further Mathematics

AI prompts for senior secondary learners.

📅 36-Week WAEC Study Guide for Further Mathematics →
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1,331 prompts matching "An element with no inverse under a given operation"

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Practice: Converting between index form and logarithm form

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Show All Working: Solving a logarithmic equation and rejecting the invalid root

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Common Mistakes: Solving an exponential equation using logarithms

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

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Practice: Finding alpha minus beta from the sum and the product

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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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Common Mistakes: Arrangements restricted at the first or the last place

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Worked Example: The difference between a permutation and a combination

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

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

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Worked Example: Solving cos x equals a negative value, and finding both solutions

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Worked Example: The shape, period and range of the cosine curve

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Common Mistakes: The angle between two lines found from their gradients

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Show All Working: The intersection of a circle and a straight line

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Common Mistakes: The condition for a line to be a tangent to a circle

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