Studied by 2 peoplethe product of any two numbers is...
the product of their GCF and LCM
squares are...
nonnegative
quotient x divisor + remainder = ...
dividend
(a+b)^n does not equal...
a^n+b^n
a^n has...
n factors
(a+b)² = ...
a²+b²+2ab
ab² = ...
a²b²
(1/a)² = ...
1/a²
(a/b)² = ...
a²/b²
(-a)² is always ...
nonnegative
-a² is always ...
nonpositive
any number raised to the exponent of 1 equals ...
the original number
in general, (-a)^3 = ...
-a^3
when it is easier to count what you don't want, it is called ...
complementary counting
(a^m)^n = ...
a^mn
if a does not equal 0, a^0 = ...
a^0 = 1
a^-n = ...
1/a^n
to find the number of factors from prime factorization ...
add one to each exponent, then multiply.
if sqrt(a) > sqrt(b), then ...
a > b
a denominator with a radical is ...
NOT accepted
sqrt(a) x sqrt(b) =
sqrt(ab)
sqrt(a) / sqrt(b)
sqrt(a/b)
distance = ...
rate x time
in sets, set R is ...
real numbers
in sets, set Z is ...
integers
in sets, set Q is ...
rational numbers
in sets, set N is ...
natural numbers
sum of natural numbers from 1 to n is ...
(n(n+1))/2
y = k/x
inverse variation
y = kx
direct variation
when |x| < y, the solution is :
-y<x<y
if a linear equation is in standard form, the slope is ...
-A/B
switch the inequality sign when ...
multiplying by negatives
absolute values are always ...
positive or 0
(y+x)(y-x) = ...
y²-x²
in Ax+By=C, A>...
0
when multiplying two integers and one is even, ...
halve the even number and double the other number
when multiplying a number by any power of 2, ...
double the other number for each power of 2
when multiplying by 9, ...
round up the 9 to 10, solve, then subtract the original number
when multiplying a two digit number by 11, ...
add the two digits together and place their sum in the middle
any point (x,y) reflected over the x-axis appears as ...
(x,-y)
any point (x,y) reflected over y=x appears as ...
(y,x)
any point (x,y) when reflected over the y-axis appears as...
(-x,y)
(x,y) rotated 90 degrees (-270 degrees) is ...
(-y,x)
(x,y) rotated 180 degrees is ...
(-x,-y)
(x,y) rotated 270 degrees (-90 degrees) is ...
(y,-x)
expected value is ...
the probability x the number of repetitions
if there are m ways to do one thing and n ways to do another ...
there are mn ways of doing both.
if there are m ways to do one thing or n ways to do another ...
there are m+n ways of doing one or the other
if the order does not matter, it is a ...
combination
if the order does matter, it is a ...
permutation
if p, then q. the converse is ...
if q, then p
if p, then q. the inverse is ...
if not p, then not q
if p, then q. the contrapositive is ...
if not q, then not p
if the original statement is true, the contrapositive is always ...
true
in networks, the sum of the degrees of all vertices is equal to...
twice the number of edges, making it even
a graph with a Euler trail must have either ...
0 or 2 vertices of odd degree
the order of a graph is ...
the number of vertices
the size of a graph is ...
the number of edges
Note
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