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?
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What is the formula for Either/Or Probability?
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What is the formula for And Probability?
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What is the formula for Margin of Error (#1)?
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What is the formula for Margin of Error (#2)?
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What is the formula for a 95% Confidence Interval?
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What is the formula for Interest?
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What is the formula for Compounded Interest?
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What is the formula for Continuously Compounded Interest?
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What is the formula for a Parabola?
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What is the first Pythagorean Identity?
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What is the second Pythagorean Identity?
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What is the third Pythagorean Identity?
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What is the general formula for a Trig Function?
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What is the formula for a General Trig Function?
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What is the formula for Maximum in trigonometric functions?
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What is the formula for Minimum in trigonometric functions?
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What is the formula for the Period of a function?
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What is the Reciprocal of Sine?
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What is the Reciprocal of Cosine?
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What is the Reciprocal of Tangent?
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What is the Recursive Formula for a Geometric Sequence?
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What is the Recursive Formula for an Arithmetic Sequence?
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What is the Reference Angle for an angle greater than 180 degrees?
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What is the definition of a Coterminal Angle?
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What is Newton's Law of Cooling formula?
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What does Summation refer to in sequences?
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What is the formula for the Sum of an Arithmetic Sequence?
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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) )
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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!