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Indices and index equations |
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CONTENTS |
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| Harder problems with indices |
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Workout |
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24 slides |
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| Indices and index equations |
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Library |
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12 questions |
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The workout comprises a series of sides that guide you systematically through the topic concept by concept, skill by skill. The slides may be used with or without the support of a tutor. The methodology is based on problem-solving that advances in logical succession by concept and difficulty. The student is presented with a problem or series of questions, and the next slide presents the fully-worked solution. To use the material you must sign-in or create an account.
blacksacademy.net comprises a complete course in mathematics with resources that are comprehensive.
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SAMPLE FROM THE WORKOUT |
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SLIDE 1 - SUMMARY |
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SLIDE 2 - QUESTION 1 |
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SAMPLE FROM THE LIBRARY |
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QUESTION [difficulty 0.2] |
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SOLUTION |
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DEPENDENCIES |
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CONCEPTS |
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LEV. |
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Consolidation and summary of rules for indices
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780.1 |
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Index equation
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781.4 |
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Method: write to the same base and equate indices
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781.4 |
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Surds to indices, simplifying denominators
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781.7 |
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Simplifying denominators with surds
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782.1 |
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Expansions of expressions with rational indices
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782.4 |
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RAW CONTENT OF THE WORKOUT |
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| What is provided here is the raw text of the workout. Most of the information is contained in the image files, which are not included with this text. The text may appear deceptively short. (The content overall of blacksacademy.net is vast.) Any in-line questions appear as a question mark [?]. This text is provided only as an indication of the overall quantity of material contained in the chapter. To use the material you must sign-in or create an account. |
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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
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SLIDE 7
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SLIDE 8
Evaluate
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SLIDE 9
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SLIDE 10
Simplify
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SLIDE 11
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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
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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
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SLIDE 16
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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
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