1,281 prompts matching "Index law shortcuts for mental exam questions"
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Common Mistakes: Proving that a quadratic expression is positive for every real x
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Worked Example: Finding one over alpha plus one over beta
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Spot My Mistake: Forming an equation whose roots are alpha squared and beta squared
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Worked Example: Evaluating a polynomial by substitution
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Spot My Mistake: The factor theorem for a divisor of the form ax minus b
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Worked Example: The sum of the products of the roots of a cubic taken two at a time
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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: Solving a quadratic inequality by sketching the parabola
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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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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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Quiz: The compound angle formula for sine of A plus B
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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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Spot My Mistake: The double angle formula for sine
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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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Worked Example: Solving cos x equals a negative value, and finding both solutions
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Practice: Solving an equation of the form sin of 2x equals a given value
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