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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