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Algebra 2 Regents Exam Review
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Gravity
Terms in this set (110)
sequence
a set of numbers in a pattern
a₁
1st term
recursive formula
terms of a sequence are found by performing operations on previous terms
explicit formula
terms of a sequence are found by using the term's position
"d" in the arithmetic sequence formula
common difference
(the difference between any two consecutive terms)
"r" in the geometric sequence formula
common ratio
(the ratio between any two consecutive terms)
geometric sequence
a sequence in which each term is found by multiplying to get the next term
arithmetic sequence
a sequence in which each term is found by adding to get the next term
series
the sum of the terms of a sequence
asymptote
A line that a graph approaches but doesn't intersect.
domain
set of all inputs or x-values
range
set of all outputs or y-values
product law of logarithms
log (mn) = log m + log n
quotient law of logarithms
log (m/n) = log m - log n
power law of logarithms
log m^p = p * log m
base for LOG
10
base for LN
e
compound interest formula
continuous compound interest formula
equation of the unit circle
x² + y² =1
sin(θ) on the unit circle is the ___ -coordinate
y
cos(θ) on the unit circle is the ___-coordinate
x
reference angle
the acute angle formed by the terminal side and the closest x-axis.
positive angles are drawn...
counter-clockwise
negative angles are drawn ...
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
Quadrant I and II
cos(θ) is positive when θ lies in
Quadrant I and IV
tan(θ) is positive when θ lies in
Quadrant I and III
csc(θ) is the reciprocal of ___.
sine
sec(θ) is the reciprocal of ___.
cosine
cot(θ) is is the reciprocal of ___.
tangent
graph of y = sin x
graph of y = cos x
graph of y = tan x
"parent" Pythagorean identity in trig
sin²θ + cos²θ = 1
period
how long (distance) it takes to complete one cycle of the trig function.
formula for the period of a trig graph
P = (2π)/frequency
frequency
the number of cycles of the curve in 2π radians
amplitude
the distance the sinusoidal function rises and falls above and below its midline
midline
the horizontal line that lies midway between the minimum and maximum of a sinusoidal function.
sinusoidal function
Any graph primarily comprised of either the sine or cosine function
sin(π)
0
cos(2π)
1
sin(3π/2)
-1
tan(π/2)
undefined
Complex Fraction
fractions (major) that have other fractions (minor) within their numerators and/or denominators
Extraneous Solutions
Solutions that are introduced by various algebraic techniques that for one reason or another are not valid solutions of the original equations.
imaginary unit
complex number
y = f(x) + k
translate up k units
y = f(x) - k
translate down k units
y = f(x + k)
translate left k units
y = f(x - k)
translate right k units
y = -f(x)
Reflection over the x-axis
y = f(-x)
Reflection over the y-axis
If f(-x) = f(x) then the function is ...
even
If f(-x) = -f(x) then the function is ...
odd
Even functions are symmetric to the ...
y-axis
Odd functions are symmetric to the ...
origin
y = k f(x)
Vertical dilation of scale factor k
y = f(kx)
Horizontal dilation of scale factor k
Parabola
Graph of a Quadratic Function
Root / x-intercept / zero
Solution to the equation f(x) = 0.
Factor (the verb)
To rewrite a quantity as an equivalent product
Complete Factoring
Factoring an expression until it cannot be factored anymore.
Vertex Form of a parabola
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
Locus Definition of a Parabola
Collection of all points equidistant from a fixed point (focus) and a fixed line (directrix).
Equation of a Parabola using the Directrix & Focus
y = a(x - h)² + k, where(h, k) is the vertex
Average Rate of Change
Slope
Inverses Function Notation
f⁻¹(x)
No Solution
∅ or { }
Degree of a polynomial
Highest power of a polynomial
The degree of a polynomial function gives...
The maximum number of roots a polynomial function can have.
Factor and Zero: If (x - 3) is a factor, then ______________ is a zero.
x = 3
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 zero.
Quotient Remainder Form
q(x) is the quotient, r is the remainder, and (x - a) is the divisor
Function
A rule that assigns exactly one output for each input.
Domain
Set of inputs
Range
Set of outputs
Inverse Functions
Functions that literally "undo" one another. Created by switching the x and y.
A function is increasing when...
as x increases, y increases.
A function is decreasing when ...
as x increases, y decreases.
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.
x-intercept
when y = 0
known as roots or zeros
y-intercept
when x = 0
what "express in simplest form" means
no ( ) and all like terms combined
Expression
A mathematical sentence without an equal sign
phase shift
the horizontal translation of a sinusoidal function
Vertex
the turning point of a function
Minimum/maximum
the lowest/highest point of a function
whole numbers
the number set: 0, 1, 2, 3, ...
formula to determine if two events are independent is ___.
P(A and B) = P(A)*P(B)
quotient
to divide or the answer to a division problem
algebraically
to solve using algebraic techniques (in other words, not guessing & checking or graphing)
margin of error
2 * standard deviation
95 % confidence interval
center ± margin of error
end behavior
the behavior of a function to the far right and far left (rise/fall) - determined by the leading term of the function
integers
the set of positive and negative whole numbers
rational numbers
the set of integers and fractions
irrational numbers
the set of numbers when expressed as a decimal neither repeat nor terminate
real numbers
the set of all rational and irrational numbers
imaginary numbers
non-real numbers written with negative radicands or in terms of the imaginary unit, i
sum
to add or the answer to an addition problem
difference
to subtract or the answer to a subtraction problem
product
to multiply or the answer to a multiplication problem
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