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Further Mathematics

AI prompts for senior secondary learners.

📅 36-Week WAEC Study Guide for Further Mathematics →
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1,043 prompts matching "Deriving the arithmetic series sum formula"

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Solve the trigonometric equation cos^2(x) - sin^2(x) = 0.5, for 0 <= x <= 360

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Worked example: find the gradient of y = x^3 - 4x at the point where x = 2

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Worked example: find the stationary points of y = x^3 - 3x^2 - 9x + 5 and classify each one

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Worked example: find the equation of the tangent to y = x^2 - 5x + 6 at the point where x = 1

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Worked example: find the modulus and argument of 3+4i

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Worked example: solve x^2+4x+13=0 giving the roots as complex numbers

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Worked example: find the determinant of [[5,2],[3,4]]

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Worked example: find the inverse of [[2,1],[5,3]]

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Worked example: use matrices to solve the simultaneous equations 2x+y=8 and x-y=1

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Worked example: expand (x+2)^5 fully using the binomial theorem

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Worked example: find the term in x^3 in the expansion of (2x-1)^6

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Worked example: find the coefficient of x^4 in the expansion of (1+3x)^7

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Worked example: use the binomial expansion to estimate (2.01)^5 to 4 decimal places

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Worked example: construct the truth table for (p AND q) OR (NOT p)

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Worked example: construct the truth table for NOT(p OR q) and compare it to (NOT p) AND (NOT q)

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Worked example: determine whether the argument 'if p then q; p; therefore q' is valid using a truth table

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Worked example: write the converse, inverse and contrapositive of 'if a number is even, then it is divisible by 2'

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Worked example: determine whether p IMPLIES q is logically equivalent to (NOT p) OR q

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Real-life application of completing the square

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Real-life application of the remainder theorem

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