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41 Cards in this Set
 Front
 Back
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(1510)=2(5015) 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+53both=120 169both=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!/(nk)! where n = # in larger group and k = # in smaller group 

combination

smaller group from larger group, order is not important:
n!/k!(nk)! 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<cd> 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 (x2)(x3)=0 x2=0 or x3=0 x=2or3 x<2>=9 x=3or3 

multiple equations

combine:
5x2y=9 and 3y4x=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>(n1)? n5th = 5<2>(51) = 25(4) = 100 n4th = 4<2>(41) = 16(3) = 48 10048=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 yintercept:
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 73=4 and less that the sum 7+3=10 

angles for a polygon

sum of interior angles in a polygon with n sides: (n2) x 180
degree measure of one angle: (n2)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>
