Questions and Answers
What is the simplified expression of log---?
Match the following functions to their definitions:
Inverse Variation Function = y = k/x Direct Variation Function = y = kx
In combinations, repetition is allowed.
False
In permutations, order does not matter.
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What is the probability that a person was NOT born in this month?
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What is the probability of selecting a blue crayon from a bag containing 5 blue, 3 yellow, and 7 orange crayons?
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What does Independent Events refer to?
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What is the standard deviation graph representation?
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What is the mean?
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What is the mode?
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What is the median?
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What is the range?
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The equation of a circle is ___?
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What is the inverse of SIN 0 = 0.75?
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How do you determine if a relation is a function?
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How do you determine by composition if two functions are inverses?
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What does the expression 45 45 90 represent?
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Match the trigonometric functions to their reciprocals:
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What is the land distance of a plane represented as?
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How do you convert positive angles?
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How do you convert negative angles?
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What is the conversion from radians to degrees?
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What is the conversion from degrees to radians?
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What does HAND TECHNIQUE represent?
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Sin and Cos are always above 2.
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What does 'circle thing' refer to in trigonometry?
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Good luck on this test is not important.
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Study Notes
Logarithmic and Exponential Functions
- Logarithmic form: ( x = \log_b y ), where ( b^x = y ).
- Example: ( 3 = \log_5 125 ) as ( 125 = 5^3 ).
Variations
- Inverse Variation: ( y = \frac{k}{x} ), where ( k ) is a constant.
- Direct Variation: ( y = kx ), indicating a linear relationship.
Combinations and Permutations
- Combination: Order does not matter, and repetition is not allowed.
- Permutation: Order matters, and repetition is not allowed.
Probability
- Probability of not being born this month: ( \frac{11}{12} ).
- Probability of selecting a blue crayon from a bag of 15 (5 blue, 3 yellow, 7 orange): ( \frac{5}{15} = \frac{1}{3} ).
Statistics
- Independent Events: One event's occurrence does not affect the other.
- Mean: Average value found by summing all values and dividing by count.
- Mode: Most frequently occurring value in a data set.
- Median: Middle value when data is ordered.
- Range: Difference between highest and lowest values.
Circle Equations
- Standard circle equation: ( r^2 = (x - h)^2 + (y - k)^2 ).
Trigonometric Functions
- ( \sin 0 = 0.75 ) leads to ( \sin^{-1} (0.75) \approx 48.6^\circ ).
- Convert between radians and degrees: ( 180/\pi ) for radians to degrees and ( \pi/180 ) for degrees to radians.
Angle Measurement
- Positive angles: Add ( 360^\circ ); Negative angles: Subtract ( 360^\circ ).
- Circle technique helps visualize and calculate angles.
Radian Values
- Hand technique for common angles: ( 90^\circ ) (π/2), ( 60^\circ ) (π/3), ( 45^\circ ) (π/4), ( 30^\circ ) (π/6), and ( 0^\circ ).
Inverse Relations
- A relation's inverse is a function if it passes the horizontal line test.
- Verify inverses via composition: ( f(g(x)) = x ) confirms they are inverses.
Special Triangles
- 45-45-90 triangle: Sides are ( x, x, x\sqrt{2} ).
Trigonometric Ratios
- The cosecant (csc), secant (sec), and cotangent (cot) functions are the reciprocals of sine, cosine, and tangent, respectively.
Final Encouragement
- Best of luck on the exam! ❤️❤️❤️❤️❤️❤️
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Description
Test your understanding of logarithmic, exponential functions, and basic probability concepts. This quiz covers inverse and direct variations, combinations, permutations, and statistical measures. Perfect for students looking to reinforce their Algebra skills.
