413 prompts matching "Learn: What makes two surds similar"
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Explain back: completing the square when the coefficient of x squared is not one
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Worked Example: Factorising a quadratic whose leading coefficient is not one
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Explain Back: The zero product rule, and why it works
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Common Mistakes: Writing down the roots once the brackets are found
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Worked Example: Halving the coefficient of x and squaring it
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Common Mistakes: Checking a completed square by expanding it again
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Worked Example: Substituting a, b and c into the quadratic formula correctly
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Common Mistakes: A sign error in the formula, and how to catch it
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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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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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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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Explain Back: The condition for the line never to meet the curve
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Common Mistakes: A line and a curve meeting once without the line being a tangent
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