1,202 prompts matching "Why a conditional and its contrapositive are equivalent"
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Quiz: Multiplying two surds and simplifying the result
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Worked Example: Simplifying an expression carrying both a negative and a fractional index
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Practice: Converting between index form and logarithm form
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Explain Back: The laws of logarithms for a product and for a quotient
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Show All Working: Solving a logarithmic equation and rejecting the invalid root
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Explain Back: The range of values of k for which the roots are real
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Practice: Finding alpha minus beta from the sum and the product
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Explain Back: Finding alpha squared beta plus alpha beta squared
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Quiz: The factor theorem, and testing whether x minus a is a factor
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Common Mistakes: Adding, subtracting and multiplying two polynomials
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Explain Back: Forming a cubic equation whose three roots are given
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Spot My Mistake: The relations between roots and coefficients for a quartic
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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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Final Revision: Combinations used with the addition and multiplication principles
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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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Quiz: Solving tan x equals a given value, and the period of the tangent
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Worked Example: The shape, period and range of the cosine curve
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Final Revision: The graphs of y equals sec x, cosec x and cot x
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