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41 Cards in this Set

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determine combined % increase
use 100 and solve
find original whole before % increase or decrease
divide new number by percentage that it is:
after decreasing 5%, x=57,000
what is the original number?
.95% = 57,000
57,000/.95=60,000
simple interest
I=PRT
rate is decimal
time is in years

(12,000.00)x(.06)x(9/12)
compound interest
final balance = principal x (1 + interest rate / C) <(time)(C)>
where C is the number of times compounded annually

(10,000.00)x(1+.08/2)<(1)(2)>
digits
logic and trial / error?
+AB
+AB
CDC
weighted averages
don't just average averages, give appropriate weight:

avg A=30 avg B=24. 2 x B as A
therefore, AVG= 1A=2B/3(terms)
new average after number is added (or deleted)
use the sum of the terms of the old average:
average of 4 terms is 80
new term is 100
4x80=320+100=420 420/5=84
use original and new average to determine what has been changed
use sums:
number added = (new sum) - (original sum)
number deleted = (original sum) - (new sum)
average rate
average A per B = Total A/Total B
average speed = total dist/time
work problem
1/r + 1/s = 1/t:
takes joe 4 hours, pete 2x as long
1/4+1/8=1/t
2/8+1/8=1/t
3/8=1/t
t=8/3
combined ratio
mulitply one or both by terms necessary to match:
a/b=7:3 b/c=2:5 what is a/c
7:3x2 = 14:6 2:5 = 6/15
a/c = 14/15
dilution or mixture
straightforward:
5lbs of A @ 1.00 w/ 2lbs. of B @ 2.40, what is mixed cost / lb?
(1.00)(5)+(2.40)(2)=9.80
9.80/7 = 1.40

balanced:
# of liters of 10% added to 2 liters of 50% to create 15%?
(diff. btwn weak+strong)x(amt of weak) = (% diff. btwn strong+desired)x(amt. of strong)
n(15-10)=2(50-15)
n(5)=2(35)
n=70/5
14
group problem w/ both/neither
group 1 + group 2 + neith - both = total:
of 120, 65=A, 51=B, 53=neither; how many both?
65+57+53-both=120
169-both=120
both=49
group problem w/ either/or
use grid:
fill in information until info is obtained
factorials
if n is an integer greater than 1, then n factorial, denoted by n!, is defined as the product of all the integers from 1 to n:

2! = 2x1 = 2
3! = 3x2x1 = 6
4! = 4x3x2x1 = 24
etc.
permutations
use factorials:
# of arrangements for 7 books on a shelf = 7!

for order or arrangement of smaller group from larger group:
n!/(n-k)!
where n = # in larger group
and k = # in smaller group
combination
smaller group from larger group, order is not important:
n!/k!(n-k)!
where n = # in larger group
and k = # you're choosing
probabilities
when all outcomes are equally likely:
probability = # of desired outcomes / number of possible outcomes
NOTE: see book
standard deviation
a measure of how much numbers deviate from the mean. greater spread = higher deviation
multiply / divide powers
add or subtract the exponents:

x<a> x x<b> = x<a+b>

2<3> x 2<4> = 2<7>

x<c>/x<d> = x<c-d>

5<6>/5<2> = 5<4>
raise a power to a power to an exponent
multiply the exponents:

(x<a>)<b> = x<ab>

(3<4>)<5> = 3<20>
powers w/ base of 0 and powers w/ an exponent of 0
0 raised to any nonzero exponent = 0

any nonzero number raised to the exponent 0 = 1

0 raised to 0 is undefined
negative powers
number raised to the exponent -x is the reciprocal of that number raised to the exponent x:

5<-3> = 1/5<3> =

1/5x5x5 = 1/125
fractional powers
fractional exponents relate to roots:

x<1/2> = sq. rt. x or (^x)

x<1/3> = cube rt. x or (3^x)

x<2/3> = cube rt. x<2> or (3^x<2>)
cube roots
number that when multiplied by itself 3 times = the number being cubed
add, subtract, multiply, divide roots
add subtract: only when parts inside the root symbol are identical:

(^2)+3(^2)=4(^2)

multiply divide: deal with inside ^ and outside ^ separately

(2^3)(7^5)=

(2x7)(^3x5)=

14^15

10^21/5^3 =
10/5^21/3 =
2^7
simplify a radical
look for perfect squares
^48 = ^16x^3 = 4^3
^180 = ^36 x ^5 = 6^5
quadratic equations
manipulate into ___ = 0 form, factor the left side and break the quadratic into 2 simple equations:

x<2>+6=5x

x<2>-5x+5=0

(x-2)(x-3)=0

x-2=0 or x-3=0

x=2or3

x<2>=9

x=3or-3
multiple equations
combine:
5x-2y=-9 and 3y-4x=6, what is the value of x+y?
1x+1y=-3
x+y=-3
sequence problems
use operation
what is the difference in the 4th and 5th term in sequence 0,4,18 where the nth term is n<2>(n-1)?

n5th = 5<2>(5-1) =

25(4) = 100

n4th = 4<2>(4-1) =

16(3) = 48

100-48=52
function problem
algebraic expression of 1 variable is defined as function f or g:
min value of function f(x)= x<2>-1
use lowest numbers:
f(1)=1<2>-1=0
f(0)=0<2>-1=-1
graphs of functions
plug in obvious points on graph and plug into answer equations, eliminating answers that don't work
linear equations
y=mx+b, where m=the slope of line rise/run and b=the y-intercept:
y=-3/4x+3
or
3x+4y=12
find x and y intercepts
value of line where it intersects x or y respectively
max and min lengths for a triangle
if n = the lengths of 2 sides of the triangle, the 3rd side is between the positive difference and the sum:

length of one side is 7 and the other side is 3.
3rd side is greater than 7-3=4 and less that the sum 7+3=10
angles for a polygon
sum of interior angles in a polygon with n sides: (n-2) x 180

degree measure of one angle: (n-2)x180/n
length of an arc
fraction of circles circumference:
length of arc = n/360x2piR
area of a sector (of a circle)
think of the sector as a fraction of the circle's area:
n/360xpir<2>
dimensions of an inscribed or circumscribed figure
use the geometric parameters of the objects (circle, square, etc.)
volume of a rectangular solid
wxhxl
volume of a sphere
4/3 pi r <3>