1,301 prompts matching "An arithmetic progression with a negative common difference"
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Explain Back: The range of values of k for which the roots are real
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Common Mistakes: Proving that a quadratic expression is positive for every real x
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Practice: Finding alpha minus beta from the sum and the product
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Common Mistakes: Symmetric functions when the three roots of a cubic are involved
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Explain Back: Finding an unknown coefficient given that a stated factor divides the polynomial
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Explain Back: Solving an inequality that involves a modulus
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Show All Working: Solving a pair of simultaneous linear inequalities
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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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Explain Back: Arrangements in which two particular objects must stay together
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Show All Working: Arrangements of the letters of a given word
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Explain Back: Choosing a committee with a stated number from each of two groups
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Show All Working: Counting the handshakes, or the lines joining n points
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Common Mistakes: Selections in which at least one of a kind must appear
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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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Explain Back: The compound angle formula for tan of A plus B
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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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