701 prompts matching "Solving a quadratic that must be rearranged before factorising"
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Worked Example: Testing whether a binary operation is closed on a given set
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Spot My Mistake: Finding the inverse of an element under a binary operation
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Common Mistakes: A binary operation defined by arithmetic modulo n
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Worked Example: Collecting like surds in a single sum
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Worked Example: Simplifying an expression carrying both a negative and a fractional index
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Spot My Mistake: The power law of logarithms
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Worked Example: The discriminant, and what each of its three cases means
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Spot My Mistake: Forming a new equation whose roots are the reciprocals of the original
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Common Mistakes: Symmetric functions when the three roots of a cubic are involved
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Worked Example: Evaluating a polynomial by substitution
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Spot My Mistake: The factor theorem for a divisor of the form ax minus b
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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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Show All Working: Three roots in arithmetic progression in a cubic
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Common Mistakes: Three roots in geometric progression in a cubic
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Common Mistakes: The range of values of x for which an expression stays positive
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Show All Working: Arrangements of the letters of a given word
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Common Mistakes: Arrangements restricted at the first or the last place
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Show All Working: Counting the handshakes, or the lines joining n points
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Worked Example: The identities for one plus tan squared and one plus cot squared
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