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Algebra
Algebra 1 Regents Review
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Terms in this set (67)
rational number
a number that can be written as a fraction
irrational number
a number that cannot be written as a fraction
commutative property
numbers can be added or multiplied in any way and the answer stays the same
associative property
the way in which numbers are grouped does not change their sum or product
addition property of equality
if you add the same number to each side of an equation, the two sides remain equal
multiplication property of equality
when both sides of an equation are multiplied by the same number, the remaining expressions are still equal
distributive property
to multiply a sum by a number, multiply each addend by the number outside the parentheses
pythagorean theorem
a²+b²=c²/(leg)²+(leg)²=(hypotenuse)²
square roots
multiplying a number by itself
scientific notation
a mathematical method of writing numbers using powers of ten/example:(4.2 x 10²)
standard form
highest degree (exponent of a variable) is written first
gcf
greatest common factor (24 and 18 = 6)
difference of two squares
9x² - 1 = (3x + 1)(3x - 1)
split the middle
2x²-x-3 = 2x²+2x-3x-3
when multiplying or dividing both sides by a negative you...
switch the inequality symbol
closed circle
≤ or ≥
open circle
< or >
shade above
≥ or >
shade below
≤ or <
literal equations
an equation involving two or more variables
when solving word problems use...
l: let statement
e: equation
s: solution
s: sentence
linear regression
y=mx+b
parallel lines
same slope
perpendicular lines
negative (opposite) reciprocal slope
system of equations
a set of two or more equations containing the same variables
quadratic regression
y=ax²+bx+c
axis of symmetry
x=-b/2a
parabola
the graph of a quadratic function
when a is negative (quadratic)
opens downward
when a is positive
opens upward
y-intercept
the y-coordinate of a point where a graph crosses the y-axis
x-intercept
the x-coordinate of a point where a graph crosses the x-axis
absolute value equation
y=IxI
vertex of a parabola (turning point)
the highest or lowest point on the graph
minimum of a parabola
maximum of a parabola
vertex form
y=a(x-h)²+k
quadratic formula
x = -b ± √(b² - 4ac)/2a
exponential regression
ab^x
compounded interest
y=p(1+r)^t
function
a relationship that assigns exactly one output value to one input value.
interval notation
(4,9]
set builder
{xI4<x≤9}
piece-wise
absolute value
domain
the set of x values of a function.
range
the set of y values of a function.
slope
the steepness of a line on a graph
average rate of change
change in y/change in x
mean
average
median
the middle score in a distribution; half the scores are above it and half are below it
mode
the value that occurs most frequently in a given data set
range (central tendency)
maximum-minimum
first quartile
the median of the lower half of the data set
third quartile
the median of the upper half of a data set
interquartile range
the difference between the upper and lower quartiles
box and whisker plot
scatter plot
line of best fit
a line that is very close to most of the data points in a scatter plot
correlation coefficient (r=?)
a statistical index of the relationship between two things (from -1 to +1)
correlation of determination
r² value
standard deviation
a computed measure of how much scores vary around the mean score
residual plot
a scatterplot of the residuals against the explanatory variable
exponential graph
linear graph
quadratic graph
dot plot
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