Math Stuff Flashcards
Simple interest
V=P(1+rt/100)
Compound interest
V=P(1+r/(100n))^(nt)
Summation
Sum(x,i=1,n)=n(n+1)/2
Sum(x,i=a,b)=(b-a+1)(b+a)/2
Sum(S[i],i=a,b)=(b-a+1)(S[b]+S[a])/2
S is sequence of evenly spaced number form similar to S[i]=c+k(i-1), c is initial number S[1] and k and the spacing number, ex 1, 3, 5 c is 1 and k is 2
equation also works for when start at 0 or negative
Factor
1 and itself and also negative
Prime number
Not 1
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Odd even
e+-o=o e+-e=e o+-o=e e×e=e e×o=e o×o=o o/o=o e/e=e||o
Least common multiple
30,75=150
2,3,5;3,5,5=2,3,5,5
Union of prime factor
Greatest common divisor (factor)
30,75=15
2,3,5;3,5,5=3,5
Intersect of prime factor
Power of 2
0 1 1 2 2 4 3 8 4 16 5 32 6 64 7 128 8 256 9 512 10 1024
Polynomial terms
4xy^2+5 Term=2 Coefficient=4 Constant=5 Degree=1+2=3
Perpendicular slope
a/b -> -b/a
Graph symmetry
X axis: a,b -> a,-b
Y axis: a,b -> -a,b
Origin: a,b -> -a,-b
Line of symmetry y=x: a,b -> b,a
Reciprocal
a/b -> b/a
a -> 1/a
Circle graph
(x-a)^2+(y-b)^2=r^2
Center a,b
Radius r
Congruent line segment
Line segment with equal length
Angles name
Vertical angle = opposite angle = angle on opposite side of intersection
Congruent angle = angle with equal measure
Polygon, regular angle and interior angle
Interior angle = 180*(#sides-2) Pentagon = 5, 108, 540 Hexagon = 6, 120, 720 Heptagon = 7, 128.57, 900 Octagon = 8, 135, 1080 Nonagon = 9, 140, 1260 Decagon = 10, 144, 1440
Triangle name
Equilateral = 3 congruent side, 60 degree Isosceles = 2 congruent side, 2 same angle
Common right triangle
45, 45, 90 = 1, 1, root(2) 30, 60, 90 = 1, root(3), 2 60, 60, 60 = 1, 1, 1 3, 4, 5 5, 12, 13 8, 15, 17 7, 24 ,25
Congruent polygon ex triangle
Similar polygon ex triangle
Can match same length and angle
Same shape or angle but different size
Trapezoid area
(1/2)(base1+base2)height
Chord
Any line joining 2 points in circle
Central angle
Measure of arc
Sector
Angle with vertex at center of circle
Measure if central angle
Regious boud by arc and 2 radii (radius)
Inscribe
Circumscribe
All vertices lie on container
Contain all vertices in its parameter, or side tangent to circle
If one side of triangle inscribe in circle is diameter, it is right triangle
Cylinder
2 basrs and lateral surface
Volume = pi r^2 h
Area = 2pi r^2+2pi r h
Sector
Part of circle graph
Quartile
Start at median and half the top and bottom half
2 4 4 5 7 7 7 7 7 7 7 8 9 9 9 9 2 4 4 5 Q1 7 7 7 7 Q2 7 7 7 8 Q3 9 9 9 9 Q1 = (5 + 7)/2 Q2 = median = 74 in quartile 1 Q3 = (8+9)/2 = 8.5
2 4 4 [5] 7 7 7 [7] 7 7 7 [8] 9 9 9
Q1 = 5
Q2 = 7
Q3 = 8
Range
Interquartile range
Biggest - smallest
Q3 - Q1
Standard deviation or population standard deviation
Sample standard deviation
Sqrt(sum((x-avg)^2)/count)
Sqrt(sum((x-avg)^2)/(count-1))
Standardization
For each ((x-avg)/std)
Same as finding how many standard deviation away from average
Ex avg 32.5, std 7.1
48 is (48-32.5)/7.1 = 2.2 standard value or 2.2 std away from avg
Mutually exclusive, disjoint
No element in common Event cannot occur at same time |A∩B| = 0 |A∪B| = |A| + |B| P(A and B) = 0 P(A or B) = P(A) + P(B)
A∩B
A∪B
P(A and B)
P(A or B)
Intersect
Union
|A∪B| = |A| + |B| - |A∩B|
P(A or B) = P(A) + P(B) - P(A and B)
Combination
Permutation
C(n,k)=n!/((n-k)!k!)
P(n,k)=n!/(n-k)!
Sample space
Event
All possible set of outcomes
Particular set of outcome
Independent
Occurrence of one does not affect the other
P(A and B) = P(A)P(B) != 0
Can’t be both mutually exclusive and independent
Mean of random variable
expected value
Average of distribution
Uniform distribution
probability distributed uniformly over all possible outcome
All outcome equally likely
Normal distribution
Mean, median, mode nearly equal Fairly symmetrical about mean About 2/3 data (0.68) within 1 std Almost all data (0.96) within 2 std 2% 14% 34% 34% 14% 2% 0.1% 2.1% 13.6% 34.1% 34.1% 13.6% 2.1% 0.1%
Normal distribution shape
Less std, less spread, narrower and taller graph, data more concentrated
Different center, different mean
Area under probability graph
Equals 1
Sum of all probabilities = 1
Standard normal distribution
Normal distribution mean 0, std 1
Do standardization, for each subtract mean and divide std
Percentage wording
x is what percent more than y : 100(x-y)/y
x is what percent less than y : 100(y-x)/y
what is percent increase from y to x : 100(x-y)/y
what is percent decrease from y to x : 100(y-x)/y
x is what percent of y : 100(x/y)
Evenly spaced set
average equals median\
ex set of S[n] = k*n+c
Percentile
Portion of a group that score below some number
ex. 50 is 32 percentile means 32% less than 50 and 68% more than or equal to 50
Combination with repetition
(total # item)!/((group 1)!(group 2)!…)
ex # ways rearrange MISSISSIPPI -> 1 M, 4 I, 4 S, 2 P ->
11!/(1!4!4!*2!)
Central and inscribed angle
Central angle’s vertex is center of circle.
Inscribed angle’s vertex is on circle’s parameter.
If central and inscribed angle share same arc, inscribed angle is half the central angle.
The inscribed angle has angle x, inscribed in a circle is half of the central angle (2x) that produce the same arc on the circle.
Angle is 90 only if one of the side is diameter.
x as many A as B
A = xB
remainder
x/y remainder z
y > z
