887 prompts matching "Multi-part index exam question with a real context"
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Practice: Working through a quadratic by completing the square, step by step
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Common Mistakes: Checking a completed square by expanding it again
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Practice: Giving the roots correct to two decimal places
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Common Mistakes: A sign error in the formula, and how to catch it
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Practice: Forming an equation from a given sum and product
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Common Mistakes: Roots that are reciprocals of one another
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Practice: The value of alpha to the fourth plus beta to the fourth
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Common Mistakes: A symmetric function needing the sum and product twice over
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Practice: Finding the matching value of the second unknown
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Common Mistakes: A word problem giving one linear and one quadratic equation
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Practice: The condition for the line to be a tangent
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Practice: Polynomial notation such as P of x
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Practice: A division that leaves no remainder
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Common Mistakes: The degree of the quotient and of the remainder
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Practice: The remainder on dividing by 2x minus 1
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Common Mistakes: The remainder theorem applied to a quartic
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Practice: Showing that x plus 3 is a factor of a given polynomial
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Common Mistakes: Using the factor theorem before dividing
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Practice: Factorising a quartic as the product of two quadratics
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Common Mistakes: Factorising fully, and knowing when to stop
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