Questions and Answers
What is the formula for direct variation?
What is the formula for inverse variation?
What does joint variation represent?
What is the constant of proportionality in variation equations?
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What is the value of i^2?
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What is the value of i^3?
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What is the value of i^4?
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If you have a large exponent on i, divide by four and the whole number equals ____.
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What is the 68-95-99.7 rule used for?
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What is the first step to factoring according to the provided content?
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What is the formula for a logarithmic graph?
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What is the formula for an absolute value graph?
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What is the formula for an exponential graph?
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What is the formula for a square root graph?
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What is the formula for a cubic graph?
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What is the formula for a cube root graph?
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In the equation y = a(x-h) + k, what does a represent?
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In the equation y = a(x-h) + k, what does h represent?
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In the equation y = a(x-h) + k, what does k represent?
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Study Notes
Direct Variation
- Represented by the equation y = kx, indicating a linear relationship where y varies directly with x.
Inverse Variation
- Expressed as y = k/x or xy = k, showing that as one variable increases, the other decreases.
Joint Variation
- Defined by the equation y = kxz, indicating that y varies directly with both x and z simultaneously.
Constant of Proportionality
- Denoted by k, it is the constant factor that relates two proportional quantities.
Imaginary Unit (i) Power Properties
- i^2 equals -1, establishing the basis for complex numbers.
- i^3 equals i, continuing the cyclical pattern of powers of i.
- i^4 equals 1, completing the cycle back to one.
Reducing Large Exponents of i
- To simplify large exponents of i, divide the exponent by four:
- Resulting values:
- Remainder 0 = 1
- Remainder 1 = i
- Remainder 2 = -1
- Remainder 3 = -i
- Resulting values:
68-95-99.7 Rule
- Also known as the empirical rule, it indicates that in a normal distribution:
- Approximately 68% of values lie within one standard deviation of the mean.
- About 95% within two standard deviations.
- Roughly 99.7% within three standard deviations.
First Step to Factoring
- The greatest common factor (GCF) should always be identified first to simplify expressions before further factoring.
Graph Types
- Logarithmic graph: y = logx, illustrating the relationship between the logarithm of x and y.
- Absolute value graph: y = |x|, presenting a V-shaped graph showing distance from the origin.
- Exponential graph: y = 2^x, demonstrating exponential growth.
- Square root graph: y = √x, showing a gradual increase starting from the origin.
- Cubic graph: y = x^3, representing a curve that passes through the origin with changing concavity.
- Cube root graph: y = ^3√x, illustrating the gradual increase of y relative to x, including negative values.
General Form of a Line
- The equation y = a(x - h) + k describes a linear function, where:
- a > 1 indicates a steeper slope (skinny graph).
- h represents the horizontal shift, affecting where the graph intersects the x-axis.
- k represents the vertical shift, affecting where the graph intersects the y-axis.
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Description
Test your knowledge of key concepts in Algebra II with these flashcards. Covering topics like direct and inverse variation, the constant of proportionality, and the properties of imaginary numbers, this quiz is essential for mastering the material. Perfect for students preparing for the Algebra II SOL exam.
