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