Podcast
Questions and Answers
What is the average rate of change?
What is the average rate of change?
What are negative exponents?
What are negative exponents?
What is the relationship between radicals and fractional exponents?
What is the relationship between radicals and fractional exponents?
Imaginary roots touch the x-axis.
Imaginary roots touch the x-axis.
What are the conjugates of x-1?
What are the conjugates of x-1?
The powers of i are: $i=$, $i^2=$, $i^3=$, $i^4=$
The powers of i are: $i=$, $i^2=$, $i^3=$, $i^4=$
What is the formula for half-life?
What is the formula for half-life?
What is exponential regression?
What is exponential regression?
What does compounded continuously mean?
What does compounded continuously mean?
What is the Compounded Interest Formula for more than once a year?
What is the Compounded Interest Formula for more than once a year?
What is the Percent Change Formula?
What is the Percent Change Formula?
What percentage corresponds to 1 standard deviation?
What percentage corresponds to 1 standard deviation?
What percentage corresponds to 2 standard deviations?
What percentage corresponds to 2 standard deviations?
What percentage corresponds to 3 standard deviations?
What percentage corresponds to 3 standard deviations?
What does 'astc' represent in trigonometry?
What does 'astc' represent in trigonometry?
What is the tangent function in terms of sine and cosine?
What is the tangent function in terms of sine and cosine?
What are Pythagorean identities?
What are Pythagorean identities?
What are reference angles?
What are reference angles?
What is the reciprocal of cos?
What is the reciprocal of cos?
What is the reciprocal of sin?
What is the reciprocal of sin?
What is the reciprocal of tan?
What is the reciprocal of tan?
What are Trigonometric graphs?
What are Trigonometric graphs?
What is the Unit Circle?
What is the Unit Circle?
What are radical equations?
What are radical equations?
What are log rules?
What are log rules?
What does log to exponent mean?
What does log to exponent mean?
What defines an even function?
What defines an even function?
What defines an odd function?
What defines an odd function?
What is the recursive formula?
What is the recursive formula?
What is the explicit formula?
What is the explicit formula?
What defines an arithmetic sequence?
What defines an arithmetic sequence?
What defines a geometric sequence?
What defines a geometric sequence?
What is sigma notation?
What is sigma notation?
What is P(AUB)?
What is P(AUB)?
What is P(A|B)?
What is P(A|B)?
What is an independence test?
What is an independence test?
What does mutually exclusive mean?
What does mutually exclusive mean?
What is the Remainder Theorem?
What is the Remainder Theorem?
What is interval notation?
What is interval notation?
What is the formula for directrix and focus?
What is the formula for directrix and focus?
What is the equation of a circle?
What is the equation of a circle?
What is domain in mathematics?
What is domain in mathematics?
What is range in mathematics?
What is range in mathematics?
How do you convert radians to degrees?
How do you convert radians to degrees?
How do you convert degrees to radians?
How do you convert degrees to radians?
Study Notes
Algebra Concepts and Definitions
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Average rate of change measures how much a quantity changes relative to another quantity over a specific interval.
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Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent.
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Radicals can be expressed as fractional exponents, where √a = a^(1/2).
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Imaginary roots do not intersect the x-axis on a graph, indicating solutions that are not real numbers.
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Conjugates of a binomial expression, such as x-1 and 1-x, are used to simplify expressions or rationalize denominators.
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Powers of i (the imaginary unit):
- i = i
- i² = -1
- i³ = -i
- i⁴ = 1
Formulas and Theorems
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Half-life formula describes the time required for a quantity to reduce to half its initial value.
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Exponential regression fits a statistical model to data exhibiting exponential growth or decay.
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Compounding continuously uses the formula A = Pe^(rt), where A is the amount, P is the principal, r is the rate, and t is time.
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Compounded Interest Formula for interest calculated more than once a year is A = P(1 + r/n)^(nt).
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Percent Change Formula calculates the change from an original value as (new value - old value) / old value × 100%.
Statistics and Probability
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For a normal distribution:
- 1 standard deviation captures approximately 68% of data values.
- 2 standard deviations capture roughly 95%.
- 3 standard deviations encompass around 99.7%.
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ASTC mnemonic helps remember which trigonometric functions are positive in each quadrant of the unit circle: All Students Take Calculus.
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Tangent can be represented as t = sin/cos.
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P(A ∪ B) represents the probability that event A or event B occurs, calculated as P(A) + P(B) - P(A ∩ B).
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P(A|B) denotes the conditional probability of A given B, expressed as P(A ∩ B) / P(B).
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Events are independent if P(A|B) = P(A) or P(A ∩ B) = P(A) × P(B).
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Mutually exclusive events cannot occur simultaneously.
Trigonometric and Geometric Concepts
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Pythagorean identities relate the squares of sine and cosine: sin²(x) + cos²(x) = 1.
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Reference angles are the smallest angle between the terminal side of an angle and the axis, always acute.
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Radicals in equations require isolation, squaring both sides, solving, and checking solutions for extraneous roots.
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Sigma notation summarizes the sum of a series, using the Greek letter sigma (Σ) and an expression for the summand.
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The Remainder Theorem states that when a polynomial f(x) is divided by (x-c), the remainder is f(c).
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Interval notation expresses ranges of numbers, typically written using parentheses ( ) for exclusions and brackets [ ] for inclusions.
Other Important Formulas
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The directrix and focus formula for parabolas:
- Upward/downward: (x-h)² = 4p(y-k)
- Sideways: 4p(x-h) = (y-k)
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The equation of a circle can be represented as (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.
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Domain refers to all possible input values for a function.
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Range represents all possible output values (y values) of a function.
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Conversion from radians to degrees uses the factor 180/π.
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Conversion from degrees to radians employs the factor π/180.
Studying That Suits You
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Description
Test your knowledge of essential Algebra 2 formulas with these flashcards! This quiz covers a variety of topics, including rates of change, exponents, imaginary roots, and more. Perfect for preparing for the Regents exam.
