Algebra I
what does the graph of an inverse variation look like?
(a) curve
what do you call a pairing of two sets of numbers, where for every number in the first set there is exactly one in the second set?
(a) function
how can you represent a function? (3 ways)
(a) table (a) formula (a) graph
What do you call the number which tells you how many times to multiply a number by itself, for example 10^4 = 10 · 10 · 10 · 10
(an) exponent
what do you get when you divide a number by 0?
(it is) illegal
what is the result you get when you subtract one number from another called?
(the) difference
what is the point at which the x and y axes intersect called?
(the) origin
what do you call the result of multiplying two or more numbers together?
(the) product
what do you call the result when you divide one number by another?
(the) quotient
In a function, is it ok to have repeats in the first set or the second set?
(the) second (set)
what is the result of adding two or more numbers called?
(the) sum
write -8 as a monomial
-8x⁰
every number except 0 is a monomial with degree ____
0
what is the slope of a horizontal line?
0
What do you get when you divide 0 by any number?
0 (This is legal. You can have 1 fifth, 2 fifths, etc., including 0 fifths.)
write 0 as a monomial
0x¹
what number can by multiplied by any number without changing that number?
1
what number can you divide any number by without changing that number?
1
x⁰= ?
1
x⁻ⁿ = ?
1/xⁿ
what is the opposite of -5?
5
in slope-intercept form (y=ax+b), which is the slope?
a
what do you call an expression of the form axⁿ where a is any number and n is a positive integer?
a monomial
what does the graph of an exponential function look like?
a smooth curve
what the form of scientific notation?
a x 10ⁿ
what is the distributive rule over addition, using a, b, and c?
a(b+c)=ab + ac
in Newton's second law, what directly varies with net force ________?
acceleration
the answer you get when you _____ two or more number is the sum
add
multiplication can be understood as repeated ______________?
addition
a polynomial is an expression showing the ____ or ______ of two or more monomials
addition subtraction
what does the symbol ≈ mean?
approximately equal
what is the standard form of a linear equation?
ax + by = c
in slope-intercept form (y=ax+b), which is the intercept? Which intercept?
b is the y-intercept
The definition of quotient: If a/b=c, it is the number that can be multiplied ____________.
by b to get a.
what is a rational number?
can be written as the quotient of two integers
how do you choose between two numbers that are equal approximations of another number (i.e. 2 or 3 could both be an approximation of 2.5)
choose the one farther from 0
in a monomial axⁿ, what do you call the a?
coefficient
what do you call an integer larger than 1 that CAN be written as the product of smaller positive integers?
composite
what is the equation relating distance, rate, and time
d=rt
in a monomial axⁿ, what do you call the n?
degree
A ______________ is a special case of a linear function.
direct variation
the answer you get when you _____ two numbers is the quotient
divide
what division problem is simply NOT DONE, doesn't make sense, is "illegal", not defined?
dividing by 0
in the table for an inverse variation, as the x numbers go up, the y numbers go ______
down
in the table for a linear function y=ax+b, where x is 0, then 1, then 2, etc. how does a appear?
it is the difference between the y's
in the table for a linear function y=ax+b, where x is 0, then 1, then 2, etc. how does b appear?
it is the y when x is 0 (the y-intercept)
what is the distance between a number an 0 on the number line called?
its absolute value
in Newton's second law, what inversely varies with net force ________?
mass
the answer you get when you ________ two or more numbers together is the product
multiply
in the form for scientific notation a x 10ⁿ, what can you say about n?
must be an integer
in the form for scientific notation a x 10ⁿ, what can you say about a?
must be at least 1 and less than 10
if a line goes down from left to right, what can you say about the slope?
negative
the product or quotient of a positive and a negative number is...
negative
what is in the set of integers that is NOT in the set of counting numbers?
negative integers and 0
the sum of a number and its ___________ is 0
opposite
how do you write a solution to an equation with two variables?
ordered pairs
what do you call an expression showing the addition or subtraction of two or more monomials?
polynomial
what kind of thing grows exponentially?
populations, interest....
if a line goes up from left to right, what can you say about the slope?
positive
the product or quotient of two negative numbers is
positive
in a monomial axⁿ, the n must be a _____ ______
positive integer
what do you call an integer larger than 1 that CANNOT be written as the product of smaller positive integers?
prime
what are the four regions of a coordinate graph called?
quadrants
how do you find the slope of a line?
rise over run
what is this form of a linear equation called? y = ax + b
slope-intercept form
what is this form of a linear equation called? ax + by = c
standard form
the answer you get when you _____ two numbers is the difference
subtract
the degree of a polynomial is the degree of its highest-degree ______
term
what do you call the monomials of a polynomial?
terms
when two simultaneous equations are equivalent, what does that mean and how does it look on a graph?
they have infinite solutions and are the same line
when two simultaneous equations are inconsistent, what does that mean and how does it look on a graph?
they have no solutions and are parallel on a graph
what is the slope of a vertical line?
undefined
in the table for an direct variation, as the x numbers go up, the y numbers go ______
up (too)
x to the a over x to the b = ?
x to the a - b
x to the a times x to the b = ?
x to the a plus b
x to the a to the b = ?
x to the ab
(x + y)² =
x² + 2xy + y²
(x - y)² =
x² - 2xy + y²
(x + y)(x - y)
x² - y²
(x/y)ⁿ = ?
xⁿ/yⁿ
(xy)ⁿ=?
xⁿyⁿ
what is the form of an exponential function?
y = abⁿ
what is the slope-intercept form of an equation?
y = ax + b
what is the form of the formula for an inverse variation?
y=a/x
what is the form of the formula for a direct variation?
y=ax
what is the form of the formula for a linear function?
y=ax+b
are all integers whole numbers?
yes
is 0 a monomial?
yes