1,293 prompts matching "Proving a surd statement is true or false"
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Worked Example: Finding one over alpha plus one over beta
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Common Mistakes: Symmetric functions when the three roots of a cubic are involved
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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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Explain Back: Finding an unknown coefficient given that a stated factor divides the polynomial
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Common Mistakes: Adding, subtracting and multiplying two polynomials
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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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Common Mistakes: Three roots in geometric progression in a cubic
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Worked Example: Solving a quadratic inequality by sketching the parabola
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Practice: Solving an inequality with the unknown in the denominator
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Spot My Mistake: Showing the solution of an inequality on a number line
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Worked Example: The number of arrangements of n different objects in a row
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Spot My Mistake: Arrangements in which two particular objects must be kept apart
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Worked Example: The difference between a permutation and a combination
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Spot My Mistake: The identity that n choose r equals n choose n minus r
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Common Mistakes: Selections in which at least one of a kind must appear
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Final Revision: Combinations used with the addition and multiplication principles
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Worked Example: The identities for one plus tan squared and one plus cot squared
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Quiz: The compound angle formula for sine of A plus B
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