Math Flashcards
Integers
positive, negative, and zero whole numbers
integer zero even or odd
neither or even
even+even=
even
odd+odd=
even
odd+even=
odd
evenXeven=
even
oddXodd=
odd
oddXeven=
even
to find the least positive integer divisible by a number
- eliminate smaller numbers (if one of the numbers is 4, eliminate 2)
- multiply them all together and check to see if thats the lowest possible
when you divide any positive integer by three
the remainder must be less than or equal to 2
prime number
number whose only factors are 1 and itself
union of sets
all the numbers from both in one, duplicates not repeated
intersection of sets
one the numbers that are repeated in both sets
combinations problems (how many combinations of this are possible)
multiply the number of choices from each section together
permutations and combinations
combinations that are limited after every round. ex. theres a four letter password but no letter can be used more than once. so do 26x25x24x23. order doesn’t matter.
there are 12 students in a class, 2 will be chosen, how many different pairs? 12X11 then divide by 2 since they can be chosen 2 different ways
difference of two squares a^2-b^2
(a+b)(a-b)
when an exponent is raised to a second exponent like (n^3)^6
multiply them
working with “unsolvable” equations
if an equation is unsolvable, factor it and plug in the value given
inversely proportional word problem
a=k/b, plug in numbers you know to find k, plug in the rest to find your answer
a car traveling at an average rate of blank can make the trip in blank, how much longer would it be going at this rate
use distance formula
complementary angles
two angles whose measures have a sum of 90degrees
30 60 90 triangles legs
short leg=x
long leg=xroot3
hypotenuse=2x
45 45 90 triangle legs
equal legs=x
hypotenuse= xroot2
3-4-5 triangles
- the sides have a ration of 3:4:5
- short leg=3x
- other leg=4x
- hypotenuse=5x
- so if x=2 then the leg lengths are 6, 8, and 10
congruent triangles
same size and shape
similar triangles
same angles, different size but ratio of sides are the same
two triangles are similar if
- two pairs of corresponding angles each have the same measure
- one pair of corresponding angles has the same measure, and the pairs of corresponding sides that form those angles have lengths that are in the same ratio
the sum of any two sides of a triangle
is greater than the length of the third side
parallelogram
- slanted rectangle
- equal opposite angles
rectangles
type of parallelogram
squares
type of rectangle
square sliced in half
two 45-45-90 triangles
area of a triangle
(1/2) bh
area of a parallelogram
length times height
regular polygon
a polygon whose sides all have the same length and whose angles all have the same measure
angles in a polygon
180(n-2)
arc
- piece of circle with rounded edge (like pie piece)
- number of degrees in the arc equals the number of degrees in the angle formed by the two radii at the center of the circle called the central angle
- aka curved angle in degrees equals the degree
tangent
line that touches circumference at one point, straight
circumference equation
2pir or pid
area of a circle
pir^2
volume of a prism
height times area of its base
volume of a right circular cylinder
V=pir^2h
distance formula
d= square root (X2-X1)^2+(Y2-Y1)^2 distance= rate x time
Point of symmetry
- point of rotation
- doest change the point or the shape
weighted average
the average of two or more groups that do not all have the same number of members.
(#x members)+(#x members) over the total number of people
ex. 15 members had an average score of 500, the remaining 10 had an average of 550.
(500X15)+(550X10) over 25= 520
average of algebraic expressions
average/arithmetic mean of 3x+1 and x-3 is just (3x+1)+(x-3) over 2
using averages to find missing numbers
- sum of a list of values over number of values on the list=average
- average X number of values = sum of values
- once you ring the sum of the second set of values, subtract it from the sum of the first
independent probability
the outcome of either event has no effect on the other. multiply the probably of each event together to get total probability
