Questions and Answers
What is the average rate of change?
What are negative exponents?
What is the relationship between radicals and fractional exponents?
Imaginary roots touch the x-axis.
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What are the conjugates of x-1?
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The powers of i are: $i=$, $i^2=$, $i^3=$, $i^4=$
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What is the formula for half-life?
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What is exponential regression?
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What does compounded continuously mean?
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What is the Compounded Interest Formula for more than once a year?
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What is the Percent Change Formula?
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What percentage corresponds to 1 standard deviation?
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What percentage corresponds to 2 standard deviations?
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What percentage corresponds to 3 standard deviations?
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What does 'astc' represent in trigonometry?
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What is the tangent function in terms of sine and cosine?
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What are Pythagorean identities?
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What are reference angles?
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What is the reciprocal of cos?
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What is the reciprocal of sin?
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What is the reciprocal of tan?
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What are Trigonometric graphs?
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What is the Unit Circle?
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What are radical equations?
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What are log rules?
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What does log to exponent mean?
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What defines an even function?
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What defines an odd function?
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What is the recursive formula?
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What is the explicit formula?
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What defines an arithmetic sequence?
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What defines a geometric sequence?
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What is sigma notation?
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What is P(AUB)?
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What is P(A|B)?
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What is an independence test?
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What does mutually exclusive mean?
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What is the Remainder Theorem?
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What is interval notation?
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What is the formula for directrix and focus?
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What is the equation of a circle?
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What is domain in mathematics?
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What is range in mathematics?
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How do you convert radians to degrees?
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How do you convert degrees to radians?
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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.
