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Senior Secondary

Further Mathematics

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695 prompts matching "Roots that are reciprocals of one another"

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Final Revision: Why brackets matter when an operation is not associative

Act as my SS1 Further Mathematics tutor at the end of the term. Give me a rapid recap of w

Show All Working: Using distributivity to simplify an expression

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Show All Working: An element with no inverse under a given operation

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Common Mistakes: Checking an inverse by working the operation both ways

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Final Revision: Identity and inverse together, and what they give the set

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Show All Working: Simplifying an expression with letters and indices

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Common Mistakes: Why the index laws need the bases to match

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Final Revision: Evaluating a numerical expression using the index laws

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Common Mistakes: An indicial equation solved by substitution

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Final Revision: Checking an indicial solution by substitution

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Show All Working: The common logarithm, to base ten

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Common Mistakes: Reading a logarithm from a table

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Show All Working: Solving a simple logarithmic equation

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Final Revision: Proving a logarithmic identity from the laws

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Show All Working: Comparing logarithms given in different bases

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Common Mistakes: The Fibonacci sequence and the rule behind it

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Final Revision: Describing a sequence in words and then in symbols

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Show All Working: Deciding whether a number belongs to a given arithmetic progression

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Common Mistakes: An arithmetic progression with a negative common difference

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Final Revision: Inserting an arithmetic mean between two numbers

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