Algebra 2 Regents Flashcards

Study Notes

Parabolas

Focus/directrix relationship defined by the equation ( y = -\frac{1}{4}p(x-h)^2+k ).

Factoring Techniques

Sum of Cubes (SOAP): Factored form of ( x^3 + y^3 ) is ( (x+y)(x^2 - xy + y^2) ).
Difference of Cubes (SOAP): Factored form of ( x^3 - y^3 ) is ( (x-y)(x^2 + xy + y^2) ).

Financial Mathematics

Compound Interest Formula: ( A = P(1 + \frac{r}{n})^{nt} ) calculates the amount accrued over time with interest compounded ( n ) times per year.
Continuous Compounding: The formula ( A = Pe^{rt} ) computes the accrued amount when interest is compounded continuously.

Exponential Growth and Decay

Half-Life and Doubling Time: Expressed as ( Y = a(1/2)^{t/n} ), indicates how a quantity decreases or increases over time.

Trigonometric Identities

Pythagorean Identity: The equation ( 3\sin^2\theta + \cos^2\theta = 1 ) is essential in verifying relationships between sine and cosine functions.

Rate of Change

Average Rate of Change Formula: Given by ( \frac{y_2 - y_1}{x_2 - x_1} ), this formula helps determine how a function changes between two points.

Probability Concepts

Conditional Probability: The probability of event A given B is calculated as ( P(A|B) = \frac{P(A \text{ and } B)}{P(B)} ).
Probability of OR: Summation for independent events is defined by ( P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) ).
Conditional Independence Test: Indicates that probabilities are independent through ( P(A|B) = P(A) ).
Multiplication Rule for Independence: States ( P(A \text{ and } B) = P(A) \times P(B) ) for independent events.

Statistical Concepts

Margin of Error Formula: Calculated as ( 2SD ), represents the range of uncertainty in the estimate.
Period/Frequency Relation: Given by ( PB = 2\pi ), relates the period to the frequency in oscillatory systems.

Description

This quiz consists of flashcards covering key concepts from Algebra 2, specifically tailored for the Regents exam. Topics include focus/directrix, SOAP factoring, compound interest formulas, and more. Test your understanding and improve your preparation for the exam with these essential definitions and formulas.