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Further Mathematics

AI prompts for senior secondary learners.

📅 36-Week WAEC Study Guide for Further Mathematics →
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1,333 prompts matching "A binary operation defined on the integers"

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

Act as my WAEC Further Mathematics coach in the last week before the paper. I am in SS 3.

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

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

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

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

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Spot My Mistake: Showing the solution of an inequality on a number line

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

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Final Revision: The region of the plane satisfying a set of linear inequalities

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

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Final Revision: Counting the number plates or codes that can be formed under a rule

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Worked Example: The difference between a permutation and a combination

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WAEC Prep: Pascal's triangle and the combination numbers in it

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Final Revision: Combinations used with the addition and multiplication principles

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Learn: The Pythagorean identity, sin squared plus cos squared equals one

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

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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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Practice: Solving an equation of the form sin of 2x equals a given value

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Common Mistakes: Giving the general solution of a trigonometric equation

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Explain Back: The effect of b in y equals sin bx on the period

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