643 prompts matching "Proving that a quadratic expression is positive for every real x"
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Show All Working: Checking a rationalised answer by decimal approximation
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Learn: What a binary operation actually is
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Learn: What closure means for a binary operation
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Show All Working: Showing a set is not closed by a single counter-example
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Learn: What it means for an operation to be commutative
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Worked Example: Testing whether star distributes over plus
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Learn: What an identity element is
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Learn: Why any non-zero number to the power nought is one
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Worked Example: Solving an indicial equation where one side must be factorised first
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Show All Working: A word problem that leads to an indicial equation
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Learn: The law for the logarithm of a product
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Learn: The change of base formula
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Worked Example: Converting a logarithm to base ten so that tables can be used
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Learn: What a sequence is, and what a term means
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Show All Working: Deciding whether a given number is a term of a sequence
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Learn: The formula for the sum of the first n terms of an arithmetic progression
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Learn: The formula for the sum of the first n terms of a geometric progression
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Show All Working: The sum to infinity of a geometric progression, and when it exists
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Worked Example: The critical values of a quadratic inequality
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Show All Working: The region satisfying two linear inequalities together
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