GRE Kaplan Math L3
Terms
undefined, object
copy deck
- determine combined % increase
- use 100 and solve
- find original whole before % increase or decrease
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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
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I=PRT
rate is decimal
time is in years
(12,000.00)x(.06)x(9/12) - compound interest
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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
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logic and trial / error?
+AB
+AB
CDC - weighted averages
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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)
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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
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use sums:
number added = (new sum) - (original sum)
number deleted = (original sum) - (new sum) - average rate
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average A per B = Total A/Total B
average speed = total dist/time - work problem
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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
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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 - group problem w/ both/neither
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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
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use grid:
fill in information until info is obtained - factorials
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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
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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
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smaller group from larger group, order is not important:
n!/k!(n-k)!
where n = # in larger group
and k = # you're choosing - probabilities
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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
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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
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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
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0 raised to any nonzero exponent = 0
any nonzero number raised to the exponent 0 = 1
0 raised to 0 is undefined - negative powers
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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
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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
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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
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look for perfect squares
^48 = ^16x^3 = 4^3
^180 = ^36 x ^5 = 6^5 - quadratic equations
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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
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combine:
5x-2y=-9 and 3y-4x=6, what is the value of x+y?
1x+1y=-3
x+y=-3 - sequence problems
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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
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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
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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
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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
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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
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fraction of circles circumference:
length of arc = n/360x2piR - area of a sector (of a circle)
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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>