Math Flashcards
Integer
Positive or negative whole number. No fractions or decimals
Prime
Whole number greater than 1 that can only be evenly divided by 1 or itself
Composite #
whole number greater than 1 that has more than 2 factors
Rational number
includes al integers, decimals, and fractions. Any terminating or repeating number is a rational number
Irrational
can’t be written as decimals because number of decimal places is infinite. Ex) pi
Thousands
1000
Thousandths
0.001
Prime factor
Also a prime number. Ex) prime factor of 12 are 2 and 3
Greatest common factor
largest number that’s a factor of 2 or more numbers
Least common multiple
smallest number that a multiple of two or more numbers. Ex) LCM for 3 and 5 is 15
a^1
a
1^n
1
a^n * a^m
a^(n+m)
a^n/a^m
a^(n-m)
(a^n)^m
a^(n*m)
(a*b)^n
(a/b)^n
a^n * b^n
a^n / b^n
a^-n
1/(a^n)
if a = sqrt(b)
a*a=b
Perfect square
a number that has an integer for its square root
ex)1, 4, 9, 16, 25…
undefined fraction
has denominator of zero
proper fraction
have denominator that’s greater than numerator
Percentage Equation
P = w*%
Part = whole * percentage
decimals to fractions
0.24 = 0.24/1 *(100/100) = 24/100 = 6/25
rational
number is rational if it can be represented by a fraction a/b where a and b are integers and b doesn’t equal zero
constant of proportionality
K = y/x
y=kx
unit rate
expresses quantity of one thing in terms of one unit of another. Denominator of unit rate is ALWAYS 1
ex) you travel 30 miles every 2 hours
unit rate = 15 mi/1 hour
slope
m=(y2-y1)/(x2-x1) or rise/run
where x1 cannot equal x2
positive = upward slope
negative = downward slope
single variable linear expression
sum of a single variable term and a constant
ex) 2w+7
Ax+By=C
slope = -A/B ; y intercept is C/B
y=mx+b
m=slope ; b is y intercept
point-slope
y-y1=m(x-x1)
m=slope
(x1,y1) = point
(y-y1)/(x-x1) = (y2-y)/(x2-x1)
(x,y) = are points
x-x1 + y/y1 = 1 ; (x,0) is point of line intersecting x-axis
(0,y) is point where line intersects y axis
Inequalities
if you multiply or divide both sides of the inequality by a negative number, the inequality is flipped
(x,y)
(abscisssa, ordinate)
parallel lines
2 or more lines with equivalent slopes
perpendicular lines
2 or more lines with negative reciprocals (a/b + -b/a)
precision
how reliable and repeatable a measurement is
accuracy
how close data is to correct data
note: data can be precise without it being accurate
approximate error
amount of error in a physical measurement; measurement ± approx error
max possible error
half the magnitude of the smallest unit used in the measurement
ex) max possible error for 1 cm is ± 0.5 cm
rounding numbers
make sure all numbers are rounded to the same level
ex) cannot round one number to the nearest thousand and the other to the nearest hundred. Both must be one or the other
giga
one billion
1,000,000,000
mega
one million
1,000,000
kilo
one thousand
1000
deci
one tenth
0.1
centi
one hundreth
0.01
milli
one thousandth
0.001
micro
one millionth
0.000001
1000µg
microgram
1mg
1000mg
milligram
1g
1000g
gram
1kg
1000kg
kilogram
1 metric ton
1000µm
micrometer
1mm
1000mm
millimeter
1m
100 cm
centimeter
1m
1000m
meter
1km
1000mL
milliliter
1L
1in
2.54 cm
12in = 1 foot
0.305 m
3ft = 1 yard
0.914 m
5280ft = 1 mile
1.609 km
4840 sq yd = 1acre
0.405 hectares
640 acres = 1square mile
2.590 km
8 fluid drams = 1 fluid oz
29.57 mL
8 fl oz = 1 cup
0.237 mL
16 fl oz = 1 pint
0.473 L
2 pt = 1 quart
0.946 L
4qts = 1 gallon
3.785 L
1 fl drams = 1 teaspoon
5 mL
4 fl drams = 1 tablespoon
16 mL
0.271 drams = 1 cubic centimeter
1mL
16 drams = 1 ounce
28.35 g
16 oz = 1 pound
453.6 g
2000 pounds = 1 ton
907.2 kg
°F to °C
°C = 5/9 * (°F − 32)
°C to °F
°F = (9/5)*°C+ 32
Polygon
closed, 2D
vertex = point at which 2 sides of polygon intersect
number of sides = number of vertices
Perimeter of triangle
Area
P= a+b+c
A=(1/2)bh
Perimeter of trapezoid
Area
P= a+b1+c+b2
A = (1/2)h*(b1+b2)
Perimeter of parallelogram
Area
P =2(a+b)
A=bh
Perimeter of rectangle
Area
P=2l+2w
A=lw
Perimeter of rhombus
Area
P= 2sqrt[(d1)^2+(d2)^2]
A=(d1*d2)/2
Perimeter of square
Area
P=4s
A=s^2
Circles
radius of circle are equal. Circles that have same centre but not same olength of radi are concentric
Circumference of circle
Area
C=2πr
A=πr^2
Volume of prism
v=Bh
Volume of rectangular prism
v=lwh
Volume of cube
v=s^3
Volume of sphere
(4/3)πr^3
Volume of cylinder
v=πr^2h
Volume of pyramid
v=(1/3)Bh
Volume of cone
V=(1/3)bh
mean
(sum of data)/(quantity of data)
make sure all data is in the same units
median
middle number of data
if data has even number of data, take two middle most data points and divide by 2
mode
number that appears the most
range
difference b/w greatest and lowest value
units of data must all be the same
standard deviation
larger standard deviation results in greater variance of the data from the mean
if mean is to the right of the median, data is positive skewed
if mean is to the left of the median, data is negative skewed
no skw = perfect bell curve
unimodal distribution
single peak
bimodal distribution
2 peaks
uniform distribution
no peaks or variation
event
any situation that produces a result
ex) flipping a coin
compound event
involves 2 or more independent events
ex) rolling dice and taking the sum
desired outcome
meets particular set of criteria
ex) roll of 1 or 2 if we want to roll a number less than three
independent event
2 or more events whose outcomes do not affect one another
ex) 2 coins tossed at the same time
dependent events
2 or more events whose outcomes affect one or another
ex) 2 cards drawn consecutively from the same deck
certain outcome
probability of outcome is 100% or 1
impossible outcome
probability of outcome is 0% or 0
mutually exclusive outcomes
2 or more consecutively outcomes whose criteria can’t all be satisfied in a single event
ex) coin coming up heads and tails on same toss of single coin
Random variable
all possible outcomes of a single event which may be discrete or continuous
Theoretical probability = likelihood of an outcome occurring
P(A)= (# of acceptable outcomes)/(# of possible outcomes)
total number of acceptable outcomes must be less than or equal to the total number of possible outcomes
if the two are equal then P(A) = 1
ex) there are 20 marbles and 5 are red. What is theoretical probability of selecting a red marble?
P(A) = 5/20 = 1/4 = 25%
sample space
total set of all possible results of a test
event is portion of sample space
distribution = function that assigns a real number probability from zero to one to each outcome
ex) probability of drawing a specific face card from a probability of drawing any face card (12 face cards in deck): 1/52 = 0.19
probability of drawing any face card: 12(0.019) = 0.228
mutually exclusive
2 events that have common outcomes
addition rule for probability
P(A or B) = [P(A) + P(B)] - [P (A&B)]
conditional probability
probability that event A will occur given that event B has occurred
Multiplication rule for probability
P(A&B) = P(A) * P(B)
where P(A&B) is the probability of 2 independent events occurring where A is one event and B is the other
The probability that at least one outcome of the element will occur
P(at least one event occurring) = 1 - P(no outcomes occurring)
relative frequency table
shows proportions of each unique value compared to the entire set
given as percentages
