Indices and index equations

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ITEM	TYPE	NUMBER
Harder problems with indices	Workout	24 slides
Indices and index equations	Library	12 questions

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SAMPLE FROM THE WORKOUT

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SLIDE 1 - SUMMARY

SLIDE 2 - QUESTION 1

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SAMPLE FROM THE LIBRARY

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QUESTION [difficulty 0.2]

SOLUTION

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DEPENDENCIES

		318: Algebraic products

		324: Indices and index equations

		1837: Logarithms

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CONCEPTS

ITEM

LEV.

Consolidation and summary of rules for indices

780.1

Index equation

781.4

Method: write to the same base and equate indices

781.4

Surds to indices, simplifying denominators

781.7

Simplifying denominators with surds

782.1

Expansions of expressions with rational indices

782.4

RAW CONTENT OF THE WORKOUT

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Harder Indices SLIDE 1 Definition of an index RULES Multiplication Division Negative Index Zero Index Exponent of exponent Rational Index SLIDE 2 Using the integer 2, write examples that will help to explain and justify each of the rules Multiplication Division Negative Index Zero Index Exponent of exponent Rational Index SLIDE 3 Using the integer 2, write out examples that will help to explain and justify each of the rules Multiplication Division Negative Index Zero Index Exponent of exponent Rational Index SLIDE 4 Definition of an index From memory, state all the rules for indices RULES Multiplication Division Negative Index Zero Index Exponent of exponent Rational Index SLIDE 5 Definition of an index RULES Multiplication Division Negative Index Zero Index Exponent of exponent Rational Index SLIDE 6 Evaluate ? ? ? ? SLIDE 7 ? ? ? ? SLIDE 8 Evaluate ? ? ? ? SLIDE 9 ? ? ? ? SLIDE 10 Simplify ? ? ? ? SLIDE 11 ? ? ? ? SLIDE 12 ? Write as a product of its prime factors. ? Express in the form , stating y in terms of x. ? Express in the form , stating y and z in terms of x. SLIDE 13 ? ? ? SLIDE 14 Index equation Solve Solution It is possible to just �spot� the answer. Since , . Method Write 16 as a number to the base 2. Equate the indices If two numbers to the same base are equal, then their indices must also be equal. SLIDE 15 Solve ? ? ? ? SLIDE 16 ? ? ? ? SLIDE 17 Write in the form where p and q are constants. SLIDE 18 Write in the form where p and q are constants. Solution SLIDE 19 Simplify , by writing without a denominator. SLIDE 20 Simplify , by writing without a denominator. Solution SLIDE 21 Write in the form where p and q are constants. SLIDE 22 Write in the form where p and q are constants. Solution SLIDE 23 Write in the form , where A, B and C are constants, and evaluate SLIDE 24 Write in the form , where A, B and C are constants, and evaluate Solution