878 prompts matching "Structured question: circle with a diameter given by two endpoints"
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Worked Example: The product of the roots as c over a
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Explain Back: Finding a missing coefficient from a stated sum of roots
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Common Mistakes: Roots that are reciprocals of one another
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Worked Example: The identity linking alpha squared plus beta squared to the sum and product
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Practice: The value of alpha to the fourth plus beta to the fourth
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Explain Back: The value of alpha minus beta, all squared
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Common Mistakes: A symmetric function needing the sum and product twice over
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Worked Example: Substituting into the quadratic and tidying up
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Practice: Finding the matching value of the second unknown
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Explain Back: Writing the answers as ordered pairs
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Common Mistakes: A word problem giving one linear and one quadratic equation
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Worked Example: The discriminant used as the test for intersection
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Practice: The condition for the line to be a tangent
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Explain Back: The condition for the line never to meet the curve
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Worked Example: The degree of a polynomial in one variable
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Practice: Polynomial notation such as P of x
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Worked Example: The division algorithm for polynomials
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Practice: A division that leaves no remainder
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Explain Back: A division that leaves a constant remainder
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Common Mistakes: The degree of the quotient and of the remainder
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