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Algebra 2 Regents Review Live
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Gravity
Terms in this set (159)
Sequence
an ordered list of numbers
Formally defined as a function that has as its domain the set of positive integers
f(1) or a₁
1st term
previous term
recursive formulas
terms of a sequence are found by performing operations on previous terms
d
common difference
(the difference between a term and the previous term)
r
common ratio
(the quotient of a term and the previous term)
Explicit Arithmetic Sequence Formula
Explicit Geometric Sequence Formula
Summation (Series) Notation
Series
the sum of the terms of a sequence
Arithmetic Series Formula
Geometric Series Formula
Horizontal Asymptote
A horizontal line the graph approaches
Domain
set of all inputs
x's
Range
set of all outputs
y's
Basic Form of an Exponential Function
where a is the y-intercept and b is the base (multiplier)
(2xy⁴)(x²y²) =
2x³y⁶
x⁸÷x⁵ =
x³
4⁻² =
1/4² = 1/16
(x³)⁵ =
x¹⁵
(2xy²)³ =
8x³y⁶
vertical asymptote
A vertical line the graph approaches (formed when a function is undefined)
Quotient Log Law
Power Log Law
Exponential Function Graph
Logarithmic Function Graph
Inverse Functions
Switch the x and y then
Solve for y
Common Log
base 10
y = log(x)
Natural Log
base e
y = ln(x)
Compound Interest Formula
Continuous Compound Interest Formula
Equation of Unit Cirlce
x² + y² =1
center (0, 0)
radius = 1
Reference Angle
The positive acute angle formed by the terminal ray and the x-axis.
Coterminal Angles
Any two angles drawn in standard position that share a terminal ray.
Positive angles are drawn in which direction?
counter-clockwise
Negative angles are drawn in which direction?
clockwise
Angle drawn in Standard Position
vertex is at the origin and its initial ray points along the positive x-axis.
sin(θ) is positive when θ lies in which quadrants?
Quadrant I and II
cos(θ) is positive when θ lies in which quadrants?
Quadrant I and IV
tan(θ) is positive when θ lies in which quadrants?
Quadrant I and III
csc(θ) is ____________'s reciprocal
sine
sec(θ) is ____________'s reciprocal
cosine
cot(θ) is _____________'s reciprocal
tangent
tan(θ) =
parent sine graph
parent cosine graph
The Pythagorean Identity
Period
minimum distance along the x-axis for the cycle to repeat
Frequency
B (how many cycles in 2π radians)
Amplitude
|A| (distance the sinusoidal model rises and falls above and below its midline)
Midline
C (average y-value in a trig graph)
Maximum of a trig function
midline + amplitude
Minimum of a trig function
midline - amplitude
even function
symmetric about the y-axis
cos(π/3)
½
cos(π/4)
√2/2
Undefined Fraction
when the denominator of a fraction is 0
Division of opposites= -1
Division of Rational Expressions
multiplying the first fraction by the reciprocal of the second fraction (keep-change-flip)
Adding/Subtracting Rational Expressions
find a common denominator - make new fractions - add/subtract the numerators - keep the denominator - reduce if needed
Solving a Proportion
when 2 fractions are equal to each other; cross multiply
LCD
least common denominator (the lowest common multiple, LCM, of all the denominators)
Graph of a Square Root Function
Extraneous Solutions
Solutions that don't work in the original equations, therefore are rejected.
Symbol that indicates No Solution
∅ or { }
Conjugates
(a + b)(a - b)
Complex Number
If b²-4ac < 0, ____________________ roots
Imaginary
If b²-4ac = 0, then...
Equal, Rational Roots
If b²-4ac > 0 and a perfect square, then...
Unequal, Real, Rational Roots
If b²-4ac > 0 and a non-perfect square, then...
Real, Irrational Roots
y = f(x) + k
Vertical shift up k units
y = f(x) - k
Vertical shift down k units
y = f(x + k)
Horizontal shift left k units
y = f(x - k)
Horizontal shift right k units
y = -f(x)
Reflection over the x-axis
y = f(-x)
Reflection over the y-axis
The graph of the parent function y = x²
Leading Coefficient
In f(x)=ax²+bx+c, the a is referred to as the ...
Equation of the Axis of Symmetry
Root / x-intercept / zero
Soluiton to the equation f(x) = 0.
Zero Product Law
If the product of multiple factors is equal to zero then at least one of the factors must be zero.
Solving a System of Equations Graphically
Find the points of intersection /
You are solving for both x and y
Vertex Form of a Quadratic
y = a(x - h)² + k
(h, k) is the vertex
Equation of a Circle in Center-Radius Form
(x - h)² + (y - k)² = r²
(h, k) is the center
r is the radius
Definition of a Parabola
Collection of all points equidistant from a fixed point (focus) and a fixed line (directrix).
Average Rate of Change
Slope
Slope-Intercept Form of a Line
Point-Slope Form of a Line
Graph of an Absolute Value Function
Cubic Polynomial Function
Degree 3, tails in opposite directions
Degree of a polynomial
Highest power of a polynomial
Odd Functions
Have Point Symmetry centered at the origin
Quartic Polynomial Function
Degree 4, tails in the same direction
Relationship between degree of a polynomial and roots
The degree is the maximum number of roots a polynomial function can have.
Factor and Roots: If (x - 3) is a factor, then ______________ is a root.
x = 3
Factor and Roots: If (2x + 1) is a factor, then ______________ is a root.
x = -1/2
Identity
An equation that is true for all values of the replacement variable or variables.
Let p(x) be a polynomial function
and p(8)=0, then ...
(x - 8) is a factor and x = 8 is a root.
Odd degree polynomial when the leading coefficient is negative.
Odd degree polynomial when the leading coefficient is positive.
End Behavior
Even degree polynomial when the leading coefficient is negative.
Even degree polynomial when the leading coefficient is positive
End Behavior
Remainder Theorem
When the polynomial p(x) is divided by the linear factor (x - a) or (bx - a), then the remainder will always be p(a) or p(a/b).
Let p(x) be a polynomial function
and p(-2)=12, then ...
When p(x) is divided by (x + 2), the remainder will be 12.
Let p(x) be a polynomial function
and p(2)=12, then ...
When p(x) is divided by (x - 2), the remainder will be 12.
Quotient Remainder Form
q(x) is the quotient, r is the remainder, and (x - a) is the divisor
Let p(x) be a polynomial function
and p(2/3)=0, then ...
(3x - 2) is a factor and x = 2/3 is a root
Function
A rule that assigns exactly one output for each input.
Composition of Functions
The output of one function becomes the input to another function. Notation f(g(x)) or (f ₀ g)(x)
One-to-One Functions
Both original and inverse are functions, passes VLT and HLT.
A function is increasing when...
the y-values are going up.
A function is decreasing when ...
the y-values are going down.
A function is positive when...
the y-values are positive (above the x-axis)
A function is negative when...
the y-values are negative (below the x-axis)
Vertical Line Test
A line test used to determine if a relation is a function.
Horizontal Line Test
A line test used to determine if an inverse is a function.
x-intercept
Occurs when y = 0
known as roots or zeros
y-intercept
Occurs when x = 0
Relative Max and Mins
high and low points on a graph and/or endpoints
Absolute Max and Mins
the highest and lowest point on a graph
In the unit circle, sinθ =
The y value
In the unit circle, cosθ =
The x value
In the unit circle, tanθ =
y / x or sinθ/cosθ
Two Events are Independent if...
P(A|B) = P(A) OR P(A∩B) = P(A) x P(B)
P(A∪B) is equivalent to
P(A) + P(B) - P(A∩B)
95% Confidence Interval
Mean ± 2 Standard Deviations
Margin of Error
The number which represents 2 Standard Deviations
What does the 'p' value represent in the following equation? y = 1/4p(x-h)²+k
The distance between the focus and vertex
What does (h, k) represent in the following equation? y = 1/4p(x-h)²+k
The vertex
Directrix
The line underneath or above a parabola
Focus
The point inside the parabola
The vertex of a parabola is located
Directly between the focus and directrix
Converting from Radians to Degrees
Multiply by 180/π
Converting from Degrees to Radians
Multiply by π/180
Discriminant Formula
b²-4ac
√-1 =
i
i² =
-1
i³ =
- i
i⁴ =
1
Factors are always represented by
( x ± #)
What is the first method of factoring you should always look for?
GCF
What is the only time your calculator will not be in degree mode?
When graphing sine or cosine!
sin graph starts at the
midline
cos graph starts at the
max/min
BP=
2π
log₂(x)=y
2^y=x
3
Σ=i(i+1)
i=1
20
P(A|B)
P(A and B)/P(B)
In a normal distribution, approximately what percentage lies within one standard deviation?
68
P(A or B)=
P(A)+P(B)-P(A and B)
In a normal distribution, approximately what percent lies within 2 standard deviations?
95
Percentile that occurs at the value one standard deviation above the mean
84
Percentile that occurs at the value one standard deviation below the mean.
16
Percentile that occurs at the mean
50
Equation of the x-axis
y=0
Equation of the y-axis
x=0
Calculation for the standard deviation of a sample
Product Log Law
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