1,333 prompts matching "Arranging r of n objects in a line"
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Final Revision: Solving a disguised quadratic by substitution
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Worked Example: Finding one over alpha plus one over beta
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Final Revision: Checking a symmetric-function answer by solving the equation outright
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Worked Example: Evaluating a polynomial by substitution
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Common Mistakes: Adding, subtracting and multiplying two polynomials
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Learn: The sum of the roots of a cubic read from its coefficients
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Quiz: The product of the roots of a cubic
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Common Mistakes: Three roots in geometric progression in a cubic
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Final Revision: Checking that the roots found satisfy the original equation
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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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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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Final Revision: Combinations used with the addition and multiplication principles
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Final Revision: Proving an identity by working on one side only
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Worked Example: Solving cos x equals a negative value, and finding both solutions
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Final Revision: Losing solutions by dividing through by cos x
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Common Mistakes: Sketching two trigonometric curves on the same axes to find where they meet
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Worked Example: The midpoint formula applied to a given segment
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Practice: The equation of a circle on a given diameter
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