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- value = principal (1+rate*time/100)! Simple
- value = principal (1+rate/100n)to exponent n*time in years!
Compound, where N is number of times /year compounded
slope of a line
(y2 - y1) / (x2 - x1)
- If a is positive, the parabola opens upward and the vertex is its lowest point. If a is negative, the parabola opens downward and the vertex is the highest point.
square root function graphs
area of a trapezoid
A = 1/2 (b1 + b2 )(h)
- half the product of the sum of the lengths of the two parallel sides b1 and b2 and the corresponding height h
length of an arc
arc / circumference = angle / 360
area of a sector
area sector / area circle = angle / 360
surface area of a cone
volume of cone
SA = (pi x r x S ) + pi (rsquared) = area of funnel + area of base
where S is hypotenuse / length of cone side
vol = pi * rsquared (h)
vol of pyramid (square base)
v = 1/3 (b squared) (h) where b is length of a base side
or 1/3 (base area) (h) for rectangular
volume of sphere
area of sphere
area of ellipse
- v = 4/3 (pi) (rcubed)
- a = 4 (pi) (rsquared)
area ellipse = (pi) (a) (b) where a and b are the two radii, short and long.. essentially (pi) (rsquared) except the (r) is not identical
part / whole
Change in percent = delta / base
[(Original - new) / original ] *100
FOR ALL QUESTIOSN THAT SAY NORMAL DISTRIBUTION OR STANDARD DEVIATION:
YOU WILL NEVER NEED TO CALCULATE IT
Instead, draw a curve and fill in percentages:
Must know the mean! or cant solve. If not given, cant solve.
Match average to center line (mean), also median and mode have to be center line
And find out from the numbers given, what the actual standard deviation numbers are (i.e x, 2x) are from that median number
- Sample or population std dev:
for a sample! otherwise its /n not /(n-1)
- where n is number of elements in data set
- x is each element
- bar-x is the mean
so its the sum of the square of each element's deviation from the mean (to make it positive), divided by one less than the numbers in the set, all quantity squarerooted
for a random experiment with a finite number of possible outcomes, if each outcome is equally likely to occur, then the probability that an event E occurs is defined by the ratio
- P(E) =
- [the number of outcomes in the event (E)] / [the number of possible outcomes in the experiment]
relative risk (probability comparison)
If there are two possible adverse events A and B, with probabilities PA and PB respectively,
- then the relative risk is the ratio PA/PB
- Probability is a value between 0 and 1.
odds of an event
- PA/(1 – PA)
- If event A has probability PA of happening, then
the odds it happens is PA/(1 – PA)
probability it DOESNT happen
1 – p.
(because probabilities sum to 1)
if the probability something happens is p,
then the probability it doesn’t happen is
1 – p.
quartiles and median
MUST LIST ALL ELEMENTS IN ORDER BEFORE CHOOSING MEDIAN!
Q2 = M, median
- Q1 = median of bottom half
- Q3 = median of top half
So: Quartile 1 = L to Q1
Quart2 = Q1 to M
Quart 3 = M to Q3
Quart 4 = Q3 to G
list of numbers that appear most frequently in a list
Range is inclusive!
The range of the numbers in a group of data is the difference between the greatest number G in the data and the least number L in the data;
that is, For example, given the list 11, 10, 5, 13, 21,
the range of the numbers is 21 - 5 = 16
range (max element - min element) of Q3 - Q1
(range Q3) - (range Q1)
the number of permutations of n objects taken k at a time; that is, the number of ways to select and order k objects out of n objects
and the k objects will be placed in order from 1st to kth
where n! is n(factorial) or n(n-1)(n-2)(n-3)...
rules of exponents
x-a = 1/xa
xa / xb = xa-b
(xa)(ya) = (xy)a
(x/y)a = xa / ya
(xa)b = xab
rule of inequalities
when multiplying both sides by a NEGATIVE FACTOR -- you have to flip the > / < !
because the negative reverses the equality from > to < or from < to >
first and second and third rule of difficult or frightening problems
1) mark and go on, do not wait more than 1 minute
2) reread several times, copy carefully, and use clean scratch paper; mark and go on if stuck again
3) if you are tempted to write an algebra formula (and for all mult choice) plug in the answers STARTING WITH C FIRST< INSTEAD!
One and only one of the values is right, and has been given to you, try them all, and if you start with the median value it can eliminate the next two or first two as well along with it
a is what percent of b?
of, times, product ( )
what x, k, whatever
so a = x/100(b)
(difference /original) x 100
WATCH FOR PERCENTAGE INCREASE OR DECREASE! DONT HURRY!
If increase, original (i.e. base) is SMALLER of the two numbers, if DECRASE, BASE (divisor) is BIGGER of the two numbers
find the total: 2:1 means 3 total parts
Ratio box: fill it out! Use the real total given in the problem, and figure out the ration of the total of elements to that number
- ie 11:9:3:2 = 25 total parts
- Problem asks for ratios in 20lbs of mix
20/25 = 4/5 so thats the multiple: multiply whichever part (say, 11) times 4/5 to get the fraction of that part in the whole!!!! :D
- Real (i.e.the Y quantity in "if a:b:c:d in X quantity, what is proportion of c in Y quantity)
- / Total (ie the X quantity above) = Ratio multiplier for all
How to crack proportion problems!
they always give you 3 values and ask for a 4th value:
if 1 hour call is 7.20, how much is a 10 minute call?
$/min = $7.20/60 = x/10, find X
how to attack problems with "mean"s
First: Call all means "average
Second: Take the 2 numbers they give you and fill out a pie to find the third value
Third: Take the next two numbers they give you, and fill out a second pie to find the second missing value
- Fourth: Relate the found value in Pie1 to the found value in Pie2 as needed :D :D
- divide total by number = average
- divide total by average = number
- number x average = total
mean or average = total / # of things
mode of a range of numbers
the number that occurs MOST in that range
- use a rate pie!!
First rule of chart problem
- All ETS chart problems are designed to trick, or hide information. Not to communicate information like normal world charts.
- Look for the gotcha. Always find it and double check answer against the gotcha.
Top five math things to remember!
As soon as you feel choky / stuck / puzzled / like you have to guess!
1) Plug in values!!! Start with C and work up or down
2) Ball park!
3) Average pie, rate pie
4) Normal distribution CURVE, put in your 34/14/2s... OR LOOK FOR 50th PERCENTILE TO FIND A MEDIAN (add up % in order from bottom of scale until you pass 50)
5) Ratio box:
Enter the ratios and add them to get total number of parts.
Enter the total real number amount you are trying to get a portion of.
Find the multiplier that gives you the real number, if you multiply it by the number of parts. IE if total is 25 parts and real number is 20, then 25 x 4/5 = 20
- Now that real number (the real quantity amount youre getting a ratioed portion of) is now baked into your multiplier.
- Just multiply that quantity baked multiplier by whatever ratio is asked for out of the list, to get the total quantity for the part youre asked for.
Evil special triangles
30 60 90
zero is what kind of integer and digit?
zero is an even digit.
Thats some fucked up shit right there.
what is square root of 3?
Difference OVER ORIGINAL!! If they make it easy for you to subtract percentages.. the answer is what you get OVER THE ORIGINAL! not just a percentage delta!
For percent change, use your difference/original formula (because the change is “from" 2010, use that number as the original.
Yes: Be careful: the problem did not specify whether the change was an increase or a decrease. While Brownberry is projected to have the greatest percent increase in market share (41.3 – 24.2 = 17.1 and 17.1/24.2 is approximately 70%) Symbilian is projected to have the greatest percent decrease (26.8 – 1.8 = 25.0
BUT*** 25.0/26.6 is approximately 93%). Since 93% is a greater change, the answer is 93.
geometry trick questions
make sure if you have an inscribed figure, i.e. a triangle inside another.. that the DEFINE WHERE ALL POINTS ARE.. do not assume, because it *looks* equilateral inside, that it is, unless they tell you the value for the inside sides of the triangle :(
Dont assume W is a midpoint
probability of two events
(prob a )(prob b) ! their multiplicative total
percent change trick question
Answers: A, B, C, D, and GSince the questions asks when the increase was greater than 20%, start with 1978. Remember that you can estimate 20% by finding 10% (by dividing by 10) and then multiplying by 2. From 1976 to 1978, the total expenditures started at 21.6 and increased to 35.9. 20% of 21.6 is about (2.1 × 2) 4.2.
Since the total increase was 14.3, which is larger than 4.2, the increase from 1976 to 1978 was larger than 20%, and answer choice (A) is correct.
- For 1978 to 1980, 20% of the 1978 expenditures is about (3.5 × 2) 7. The increase in expenditures is 15.3, which is larger than 7, so the increase from 1978 to 1980 is greater than 20%, and answer (B) is correct.
- Keep checking 20% of each year's expenditures against the increase: 20% of 1980's expenditures is 10, but the increase is 11.2, so (C) is correct.
- 20% of 1982's expenditures is about 12.4, but the increase from 1982 to 1984 is 14.1, so (D) is correct.
- For (E), however, the increase (12.5) was smaller than 20% (7.6 × 2 = 15ish), so (E) is incorrect. (F) is also incorrect: The increase of 16.8 is smaller than 20% of 89, which is about 18.
- (G) is correct, because the 1988-1990 increase, of 22.5, is greater than 20% of the 1988 expenditures (20% of 105 is about 21).
- (H), however, is incorrect because the increase, of 19.4, is smaller than 20% of 128, which is about 26.
Essay strongest points
Length! 450 - 750 words issue, 4 + indented paragraphs; Arguement 350 - 600 words
issue vs arguement
issue is your opinion, and why! a quotation is given
arguement: a claim is given; analyze, critique, take apart their opinion. Do not present your own!!!
How to structure your writing time
Think - -brainstorm!
Issue: Look at both sides of the quote, and take a position pro or con.
Arguement: Look at the structure of the statement and its logic, and follow the instructions on how to critique that arguement
ORganize -- lay out your paragraph framework
Write last, fill in the blanks
four characteristics for essay
Supports with relevant examples
CLEARLY WELL ORGANIZED, dont overthink, over complicate or get lost in weeds
Superior facility with conventions of written English