Algebra 2 Regents Formulas Flashcards

Questions and Answers

What is the formula for Slope (average rate of change)?

m = (y2 - y1) / (x2 - x1)

What is the equation of a circle?

(x - h)^2 + (y - k)^2 = r^2

When a and b are independent, what is the formula for probability?

P(A) x P(B) = P(A n B)

What is the formula for Conditional Probability?

P(A|B) = P(A u B) / P(B) Signup and view all the answers

What is the formula for Either/Or Probability?

P(A or B) = P(A) + P(B) - P(A n B) Signup and view all the answers

What is the formula for And Probability?

P(A n B) = P(A) x P(B|A) Signup and view all the answers

What is the formula for Margin of Error (#1)?

z(√(p(1 - p) / n)) Signup and view all the answers

What is the formula for Margin of Error (#2)?

2 x S.D. Signup and view all the answers

What is the formula for a 95% Confidence Interval?

mean +/- 2 x S.D. Signup and view all the answers

What is the formula for Interest?

A = P(1 +/- r)^t Signup and view all the answers

What is the formula for Compounded Interest?

A = P(1 + r/n)^(nt) Signup and view all the answers

What is the formula for Continuously Compounded Interest?

A = Pe^(rt) Signup and view all the answers

What is the formula for a Parabola?

y = (1/4)p(x - h)^2 + k Signup and view all the answers

What is the first Pythagorean Identity?

sin^2 + cos^2 = 1 Signup and view all the answers

What is the second Pythagorean Identity?

1 + tan^2 = sec^2 Signup and view all the answers

What is the third Pythagorean Identity?

1 + cot^2 = csc^2 Signup and view all the answers

What is the general formula for a Trig Function?

y = Asin/cos(bx) + c Signup and view all the answers

What is the formula for a General Trig Function?

y = Asin/cos(bx - h) + k Signup and view all the answers

What is the formula for Maximum in trigonometric functions?

C + A Signup and view all the answers

What is the formula for Minimum in trigonometric functions?

C - A Signup and view all the answers

What is the formula for the Period of a function?

P = 2π/B Signup and view all the answers

What is the Reciprocal of Sine?

Csc = 1/sin Signup and view all the answers

What is the Reciprocal of Cosine?

Sec = 1/cos Signup and view all the answers

What is the Reciprocal of Tangent?

Cot = 1/tan Signup and view all the answers

What is the Recursive Formula for a Geometric Sequence?

A_n = A_(n-1) * r Signup and view all the answers

What is the Recursive Formula for an Arithmetic Sequence?

A_n = A_(n-1) + d Signup and view all the answers

What is the Reference Angle for an angle greater than 180 degrees?

Angle - 180 degrees Signup and view all the answers

What is the definition of a Coterminal Angle?

Continuously subtract angle by 360 degrees until it's less than 360 degrees. Signup and view all the answers

What is Newton's Law of Cooling formula?

T = Ta + (To - Ta)e^(-kt) Signup and view all the answers

What does Summation refer to in sequences?

Top: Number of terms; Bottom: Beginning term; d_n + b Signup and view all the answers

What is the formula for the Sum of an Arithmetic Sequence?

S_n = n(a_1 + a_n)/2 Signup and view all the answers

Study Notes

Slope and Rates of Change

Formula for average rate of change: ( m = \frac{y_2 - y_1}{x_2 - x_1} )

Circle Geometry

Standard equation of a circle: ( (x - h)^2 + (y - k)^2 = r^2 )

Probability Concepts

Independent Events: Probability of both events A and B occurring is given by ( P(A) \times P(B) = P(A \cap B) )
Conditional Probability: Calculated as ( P(A|B) = \frac{P(A \cup B)}{P(B)} )
Either/Or Probability: Applies when considering the probability of either event A or event B: ( P(A \text{ or } B) = P(A) + P(B) - P(A \cap B) )
And Probability: For dependent events: ( P(A \cap B) = P(A) \times P(B|A) )

Statistical Measures

Margin of Error: Can be calculated as ( z \left(\sqrt{\frac{p(1-p)}{n}}\right) ) or as ( 2 \times S.D. )
95% Confidence Interval: Derived from the mean as ( \text{mean} \pm 2 \times S.D. )

Financial Mathematics

Interest Calculation: General formula is ( A = P(1 \pm r)^t )
Compounded Interest: Formula for compounded interest is ( A = P(1 + \frac{r}{n})^{nt} )
Continuously Compounded Interest: Expressed as ( A = Pe^{rt} )

Quadratics and Parabolas

Parabola vertex form: ( y = \frac{1}{4p}(x - h)^2 + k )

Trigonometric Identities

Pythagorean Identities:
- ( \sin^2 + \cos^2 = 1 )
- ( 1 + \tan^2 = \sec^2 )
- ( 1 + \cot^2 = \csc^2 )
Trig Functions: General form is ( y = A \sin(\text{or } \cos)(bx) + c )
General Trig Function: ( y = A \sin(\text{or } \cos)(bx - h) + k )

Trigonometric Values

Maximum and Minimum Values:
- Maximum of a trigonometric function: ( C + A )
- Minimum of a trigonometric function: ( C - A )
Period of Trigonometric Functions: Given by ( P = \frac{2\pi}{B} )

Reciprocal Trigonometric Functions

Sine, cosine, and tangent reciprocal relationships:
- Cosecant: ( \csc = \frac{1}{\sin} )
- Secant: ( \sec = \frac{1}{\cos} )
- Cotangent: ( \cot = \frac{1}{\tan} )

Sequences

Recursive Formula for Geometric Sequence: ( A_n = A_{n-1} \times r )
Recursive Formula for Arithmetic Sequence: ( A_n = A_{n-1} + d )

Angles

Reference Angle: Calculated based on quadrants:
- ( \text{Angle} - 180^\circ ) in second quadrant
- Remains the same if less than ( 90^\circ )
- For third and fourth quadrants, ( \text{Angle} - 360^\circ )
Coterminal Angle: Found by continuously subtracting ( 360^\circ ) until under ( 90^\circ )

Newton's Law of Cooling

Formula: ( T = T_a + (T_o - T_a)e^{-kt} )

Summation Notation

Summation is expressed with terms labeled:
- Top: Number of terms
- Bottom: Starting term
- General form: ( dn + b )

Sum of Arithmetic Sequence

Calculated using: ( S_n = n \left(\frac{a_1 + a_n}{2}\right) )

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your understanding of key Algebra 2 formulas that are not included on the reference sheet. This quiz covers essential concepts such as slope, circle equations, and probability definitions. Perfect for students preparing for the Algebra 2 Regents exam!