737 prompts matching "Structured question: polynomial with a given remainder pattern"
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Show All Working: Solving a simple logarithmic equation
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Common Mistakes: Rejecting a root that makes a logarithm undefined
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Worked Example: Converting a logarithm to base ten so that tables can be used
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Practice: The relation between log a of b and log b of a
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Explain Back: A logarithmic equation written in two different bases
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Common Mistakes: A logarithmic equation that becomes a quadratic
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Worked Example: Writing out the terms of a sequence from its nth term
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Practice: Finding the nth term of a quadratic sequence
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Common Mistakes: The Fibonacci sequence and the rule behind it
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Worked Example: Finding the common difference of an arithmetic progression
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Worked Example: The alternative sum formula that uses the last term
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Explain Back: Finding the first term from the sum and the common difference
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Common Mistakes: Proving the sum formula by pairing the terms
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Worked Example: Finding the common ratio of a geometric progression
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Common Mistakes: Inserting a geometric mean between two numbers
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Worked Example: Which form of the sum formula to use when r is less than one
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Show All Working: The sum to infinity of a geometric progression, and when it exists
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Common Mistakes: A bouncing ball problem, and the total distance travelled
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Worked Example: Adding or subtracting the same number on both sides
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Practice: Reversing the sign when multiplying by a negative number
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