Rules to Remember Flashcards
Percent Change Formula
[(Amount of change)/(Starting Amount)] * 100
How do you find aggregate change?
Multiply the respective multipliers. ex: (1.40)(0.70)(1.20)
Don’t assume x is…
…an integer unless specified.
(even)+(even)=
even
(odd)+(odd)=
even
(even)+(odd)=
odd
(even) * (even)=
even
(odd) * (odd)=
odd
(even) * (odd)=
even
2 is the only…
…even prime number.
If zero is an option…
…then it is forbidden to divide by a variable.
A^2-B^2 is equal to…
(A+B)(A-B)
(A+B)^2 is equal to…
A^2 + 2AB + B^2
(A-B)^2 is equal to…
A^2 - 2AB + B^2
Add/Subtracting any number/variable or dividing by a positive to both sides of an inequality…
…leaves the inequality true.
Exponentiation distributes over…
…multiplication but not addition.
Multiplying exponents…
…add together.
Dividing exponents…
…subtract from one another.
Raising a power to a power…
…multiplies the powers together.
3^3
27
4^3
64
5^3
125
Average Velocity of a Trip
(Total distance) / (Total time)
Given the mean, sum of items =
= (Average) * (# of items)
If all entries of the list are equal then the standard deviation…
…is zero.
If all entries have a number added or subtracted the SD…
…doesn’t change.
If you multiply a list by a constant the SD…
…the SD is also multiplied by that constant.
If all entries are the same distance away from the mean, the distance is…
… the standard deviation.
Inclusive Counting Formula (ex: from a to b)
Number of entries = (a - b) + 1
Sum - Inclusive counting
= (sum of each pair) * (# of pairs)
Inclusive counting sum works for…
…consecutive integers, consecutive multiples of any integer, and any sequence in which each new term is the previous term plus a constant.
Do not assume lines are…
…perfectly perpendicular or parallel.
The sum of two sides of a triangle must…
…be longer than the third.
Other names for an isosceles triangle are…
…the 45-45-90 triangle and the rad2:1:1 triangle.
Other names for a half equilateral triangle are…
…the 30-60-90 triangle and the 1:rad3:2 triangle.
Circumference of a Circle
c = pi * d
c = 2 * pi * r
Area of a Circle
A = pi * r^2
Fundamental Counting Principle
If a category has P alternatives and Q alternatives, with no overlap, P*Q equals the number of possible combinations.
Permutation vs. Combination
In a permutation order matters; in a combination order does NOT matter.
Permutation Formula
of permutations of n objects = n!
Combination Formula
of combinations = [n! / r! * (n - r)!]
In the combination formula…
…“n” is the larger collection and “r” is the number of elements selected.
“Disjoint” events are…
…mutually exclusive.
Mutually exclusive or disjoint events formula
P(A or B) = P(A) + P(B)
Non-disjoint events formula
P(A or B) = P(A) + P(B) - P(A and B)
Independent events formula
P(A and B) = P(A) x P(B)
P(A or not A) =
1
P(not A) =
1 - P(A)
The negation or opposite of “at least 1” is…
…none.
P(at least one success) =
1 - P(no successes)
Interquartile Range (IQR)
Between Q1 and Q3
Histogram is a representation of the…
…distribution of a single qualitative variable.
It’s impossible to calculate the mean from a…
…histogram.
Population between one SD of the mean equals…
…68%.
Population between two SDs of the mean equals…
…95%.
Population between three SDs of the mean equals…
…99.7%.
For quantitative comparison questions know that…
…dividing by anything other than a positive is forbidden.
