Math Stuff

Question 1

Simple interest

Answer 1

V=P(1+rt/100)

Question 2

Compound interest

Answer 2

V=P(1+r/(100n))^(nt)

Question 3

Summation

Answer 3

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

Question 4

Factor

Answer 4

1 and itself and also negative

Question 5

Prime number

Answer 5

Not 1

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Question 6

Odd even

Answer 6

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

Question 7

Least common multiple

Answer 7

30,75=150
2,3,5;3,5,5=2,3,5,5
Union of prime factor

Question 8

Greatest common divisor (factor)

Answer 8

30,75=15
2,3,5;3,5,5=3,5
Intersect of prime factor

Question 9

Power of 2

Answer 9

0   1
1   2
2   4
3   8
4   16
5   32
6   64
7   128
8   256
9   512
10 1024

Question 10

Polynomial terms

Answer 10

4xy^2+5
Term=2
Coefficient=4
Constant=5
Degree=1+2=3

Question 11

Perpendicular slope

Answer 11

a/b -> -b/a

Question 12

Graph symmetry

Answer 12

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

Question 13

Reciprocal

Answer 13

a/b -> b/a

a -> 1/a

Question 14

Circle graph

Answer 14

(x-a)^2+(y-b)^2=r^2
Center a,b
Radius r

Question 15

Congruent line segment

Answer 15

Line segment with equal length

Question 16

Angles name

Answer 16

Vertical angle = opposite angle = angle on opposite side of intersection
Congruent angle = angle with equal measure

Question 17

Polygon, regular angle and interior angle

Answer 17

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

Question 18

Triangle name

Answer 18

Equilateral = 3 congruent side, 60 degree
Isosceles = 2 congruent side, 2 same angle

Question 19

Common right triangle

Answer 19

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

Question 20

Congruent polygon ex triangle

Similar polygon ex triangle

Answer 20

Can match same length and angle

Same shape or angle but different size

Question 21

Trapezoid area

Answer 21

(1/2)(base1+base2)height

Question 22

Chord

Answer 22

Any line joining 2 points in circle

Question 23

Central angle
Measure of arc
Sector

Answer 23

Angle with vertex at center of circle
Measure if central angle
Regious boud by arc and 2 radii (radius)

Question 24

Inscribe

Circumscribe

Answer 24

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

Question 25

Cylinder

Answer 25

2 basrs and lateral surface Volume = pi r^2 h Area = 2pi r^2+2pi r h

Question 26

Sector

Answer 26

Part of circle graph

Question 27

Quartile

Answer 27

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

Question 28

Range | Interquartile range

Answer 28

Biggest - smallest | Q3 - Q1

Question 29

Standard deviation or population standard deviation | Sample standard deviation

Answer 29

Sqrt(sum((x-avg)^2)/count) | Sqrt(sum((x-avg)^2)/(count-1))

Question 30

Standardization

Answer 30

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

Question 31

Mutually exclusive, disjoint

Answer 31

``` 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) ```

Question 32

A∩B A∪B P(A and B) P(A or B)

Answer 32

Intersect Union |A∪B| = |A| + |B| - |A∩B| P(A or B) = P(A) + P(B) - P(A and B)

Question 33

Combination | Permutation

Answer 33

C(n,k)=n!/((n-k)!k!) | P(n,k)=n!/(n-k)!

Question 34

Sample space | Event

Answer 34

All possible set of outcomes | Particular set of outcome

Question 35

Independent

Answer 35

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

Question 36

Mean of random variable | expected value

Answer 36

Average of distribution

Question 37

Uniform distribution

Answer 37

probability distributed uniformly over all possible outcome | All outcome equally likely

Question 38

Normal distribution

Answer 38

``` 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% ```

Question 39

Normal distribution shape

Answer 39

Less std, less spread, narrower and taller graph, data more concentrated Different center, different mean

Question 40

Area under probability graph

Answer 40

Equals 1 | Sum of all probabilities = 1

Question 41

Standard normal distribution

Answer 41

Normal distribution mean 0, std 1 | Do standardization, for each subtract mean and divide std

Question 42

Percentage wording

Answer 42

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)

Question 43

Evenly spaced set

Answer 43

average equals median\ | ex set of S[n] = k*n+c

Question 44

Percentile

Answer 44

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

Question 45

Combination with repetition

Answer 45

(total # item)!/((group 1)!(group 2)!...) ex # ways rearrange MISSISSIPPI -> 1 M, 4 I, 4 S, 2 P -> 11!/(1!*4!*4!*2!)

Question 46

Central and inscribed angle

Answer 46

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.

Question 47

x as many A as B

Answer 47

A = xB

Question 48

remainder

Answer 48

x/y remainder z | y > z