##### GRE MATH
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#### Complete List of Terms and Definitions for GRE MATH

Terms Definitions
3/4 0.75
75%
1
729
1
√5 2.2
2¹⁰ 1024
8
b²bⁿ b²⁺ⁿ
15² 225
9
permutation N!
complementary angles two angles are complementary if their measures sum to 90
complementary angles 32
5/6 63 1/3%
3/5 = ?% 60%
ODD + EVEN= ODD
pythagorean triplets (2) 3:4:5 (leg:3 leg:4 hypotenuse:5) and 5:12:13
pythagorean triplets (2) 40
Even Divisible by 2
Find the percent: 1/6 16²/₃%
Area of a parallelogram bh
12 inches = 1 foot
even# + even# = even#
to simplify a radical... factor out the perfect squares and move them to the front of the radical sign. For example, the square root of 50 = 5 square root 2
Fractions within Fractions Rewrite horizontally
Complete the triangle: 4x, 5x... 3x
how you divide exponents subtract em
define: diameter of a circle diameter: a line segment that connects two points on the circumference of a circle and passes through the center
define: diameter of a circle 52
zero is even or odd? even
Distance Problems Distance = rate x time
average formula (sum) ÷ (number of terms)
5% as a decimal and fraction 0.05 and 1/20
5% as a decimal and fraction 9
area of a square area = (side)(side)
supplement angle X + Y = 180
Compare 5/7 and 9/11 Quick Tip: Cross-multiply! 5x11>9x7
To subtract decimal numbers... ...Line up the decimals
Percent Increase/Decrease Equations % increase/decrease = (change/original amount) x 100%
When MULTIPLYING same numbers with different powers... add exponents
what happens when an exponent is negative? Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
what happens when an exponent is negative? 23
An integer is divisible by 4 if... ...if its last two digits are a multiple of 4 4,716/4 = 1179
An integer is divisible by 4 if... 4
fractions get smaller as... ...their denominator gets bigger
quart = 2 pints = 1/4 gallon

volume unit
For a given perimeter, the rectangle with the largest area is... A square
for the probability of one thing AND another thing happening __ the probability fractions multiply
Dividing Decimals move decimals point in the divisor (outside #) until the # is a whole number, move the decimals point the same # of places in the dividend (inside #)
Equation: Probability  (# possible outcomes that satisfy the condition) DIVIDED BY (# total possible outcomes)
supplementary angles two angles are supplementary if their measures sum to 180
supplementary angles 31
how do you find the greatest common factor the find the greatest common factor, break down both numbers into their prime factorization and take all the prime factors they have in common. the GCM of 36 and 48 is 12
how do you find the greatest common factor 69
Reducing Fractions Divide numerator and denominator by factors common to both
Reducing Fractions Ex. 16/20 divided by 4 = 4/5
Multiply & Divide Roots To multiply/divide roots deal with what's inside the √ and outside the √ separately.
(2√3) (7√5) = (2x7) (√3x√5) = 14√15
10√21 ÷ 5√3 = (10/5) (√21/√3) = 2√7
Every non-prime > 1 can be written as a product of... Primes
isosceles right triangle sides x/x/x * sq rt of 2
Sum of the 3 exterior angles of a triangle = ? 360°
To change a percent to a number divide by 100
percent increase (or decrease) amount of increase/original whole X 100
percent increase (or decrease) 16
when a negative number is raised to an odd power, the result is... ...negative
2
(X+Y)
2 2
X + 2XY + Y
2
(X+Y)
2 2 2
(X+Y) = X + 2XY + Y
What is a function? y=f(x)=2x+3, to every number x, the number 2x+3 is assigned.
Ex: F(10)=2(10)+3 = 23
.083 and 8 1/3% 1/12 as a fraction and a percent
What are the Pythagorean Triplets? Right triangles with sides 3,4,5 (6,8,10, or 9,12,15) and 5,12,13 and 7,24,25 and 9,40,41 and 11,60,61
If a number is divisble by 3 then the sum of its digits is divisible by? 3
how do you use a ratio to find a number? example: in a group of 18 people, the ratio of men to women is 1:2. How many women are there? if the parts add up to the whole, a part-to-part ratio can be turned into 2 part-to-whole ratios by putting each number in the original ratio over the sum of the numbers. if the ratio of men to women is 1 to 2, then the men-to-people ratio is 1/ 1+ 2 = 1/3. And the women-to-peeps ratio is 2/1+2 = 2/3. 2/3 of the 18 are women, or 12.
how do you use a ratio to find a number? example: in a group of 18 people, the ratio of men to women is 1:2. How many women are there? 86
Properties of 0 1) only # that is neither +/-
2) a multiple of every integer
3) is an even #
4) a/0 = undefined
5. 0/a = 0
Multiple Event Probability where individual events can have different types of outcomes 1. Find total number of possible outcomes (find total for each individual event and multiply those together)
2. Find number of desired outcomes
When you have a number with a power raised to a power... multiply the exponents
A number is divisible by 4 if its _____ digit(s) is divisible by... last two, 4
Negative + Positive = keep the sign of the larger number and subtract
ex:
(-6) + 3 = -3 9 + (-12) = -3
(-5) + 7 = 2 4 + (-2) = 4
# is divisible by 6 if... it is divisible by 2 and 3
What is the formula for the area of an equilateral triangle with side s? A = (s²√3)/4
rule of proportion for triangles In every triangle, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle
volume of a rectangular solid volume rectangle = length x width x height
volume of a rectangular solid 50
define: cylinder and give the formula for volume cylinder: a solid whose horizontal cross section is a circle. The volume of a cylinder = (pi)(r^2)(h)
The Slope of a Line 1) a horizontal line = 0
2) a vertical line = undefined
3) a line that goes up from left to right = +
4) a line that goes down from left to right = -
If one quantity increase as a second decreases... ...Multiply them to get a constant
What is the Pythagorean Theorem? In a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the hypotenuse: a²+b²=c²
to divide powers with the same base... subtract the exponents and keep the base the same

4^5/4^2 = 4^3
Solve this inequality: 3-(x/₄) ≥ 2 Solve the same as you would solve an equation EXCEPT: if the inequality is multiplied/divided by a negative #, the direction of the inequality changes!
-(x/4) ≥ 2-3
-x ≥(-1)(4) =-4 (then divide by (-1) & swap inequality**)
= x≤4
m+n = -b if m and n are solutions to x² + bx + c = 0, then
Original Average & New Average (to figure out what was deleted or added) number added = (new sum) - (original sum)
number deleted = (original sum) - (new sum)
raising a fraction between zero and 1 to a power... ...yields a smaller result
(1/2)^2 = 1/4
What is true about the area of similar triangles? *ratio of the lengths of their corresponding sides = k, then the ratio of their areas = k²
Ex: Each side of triangle B is 2x the length of the corresponding side of triangle A. So triangle B must have 2², or 4x area of A
For n numbers in an arithmetic sequence... If n is odd, the average of the numbers is the middle term
If n is even, the average is the average of the 2 middle terms
If a=bc, which of the following is equal to b/c?
A) a/bc B) ab/b C) a/c D) a/c²
Pick three easy numbers to plug in: a=6, b=2, c=3
So, b/c=2/3. Then test the answers to see which one gives you 2/3.
Only choice D works.
An integer is divisible by 9 if... ...if its digits sum to a multiple of 9

6,930...6+9+3+0=18, which is a multiple of 9
The price of an antique is reduced by 20% and then this price is reduced by 10%. If the antique originally cost \$200, what is its final price? 1) 20% = X/\$200, X = \$40
2) \$200-\$40=\$160
3) 10% = X/\$160, X=\$16
4) \$160-\$16 = **\$144**
A building has 2/5 of its floors below ground. What is the ratio of the # of floors above ground to the # below ground? Pick Numbers! Pick a value for the total # of floors, one that is divisible by 2 and 5. Let's pick 10.
2/5 x 10 = 4 floors below ground & 6 above. Therefore, the ratio is 6:4 or 3:2
what is the average rate equation? Average A per B = total A / total B Average speed = total distance/total time
what is the average rate equation? 88
What is the Absolute Value of a number? It is the number of units a number is away from 0 on a number line.
the length of any side of a triangle is... less than the sum of the other 2 sides AND greater than the difference of the other 2 sides
If ³/₅ of the pets in a store are dogs, and ¼ of the other pets are cats, what fraction of the pets is neither cats nor dogs? 1) Choose a total # of pets, lets say 20.
2) Then ³/₅ of 20 =12, so there are 12 dogs.
3) Of the remaining 8 pets, 2 (¼ of 8) are cats.
4) So 6 pets are neither dogs nor cats: 6/20=3/10
6/8 0.75
75%
√2 1.41
125
4
12² 144
11² 121
a²-b² (a-b)(a+b)
64
18² 342
12³ 1728
Circumference [C] πd
1/3 33 1/3%
4/5 = ?% 80%
Volume of rectangle= (L)(W)(H)
to divide radicals... ...divide the two numbers in question and then put them under a single radical
x^2 - y^2 = (x+y)(x-y)
Find the fraction: 37.5% 3/8
Volume of a Cylinder πr²h
area of a rhombus (½)(d₁)(d₂)
Find the percent: 1/3 33¹/₃%
even# x odd# = even#
2 2
X - Y
(x+y)(x-y)
2 2
X - Y
2 2
X - Y = (X+Y)(X-Y)
Is zero positive or negative? No
how you multiply exponents add em
how do you divide fractions? to divide fractions, invert the second one and multiply
how do you divide fractions? 74
circumscribed circle vong tron ngoai tiep
Area of a trapezoid ½(b₁ + b₂)h
Integer Whole numbers and their opposits. {...-3,-2,-1,0,1,2,3...} These are rational numbers. Negative, positive, include 0 (neither negative or positive)
20% as a decimal and fraction 0.2 and 1/5
20% as a decimal and fraction 11
percent formula PART/WHOLE x 100 = PERCENT
pound = 16 ounce = 0.454 kg
Compound Interest Rate Formula A=P (1+ (r/n))^nt
A-Final Amount
P-Principle
r-rate of interest expressed as a decimal
n-# times compounded annually
1/11 and 9 1/11 .09 and a percent
CHORD a straight line connecting two points on a circle... can never be longer than the diameter
Area of triangle A = 1/2 * bh
An integer is divisible by 6 if... ...if it divisible by 2 and 3
An integer is divisible by 6 if... 6
define: rectangle a quadrilateral with four right angles. Opposite sides are equal.
Multiple The infinite set of numbers when multiplying the number by other whole numbers
Each diagonal divides a square into two... 45-45-90 Triangles
(x + y)^2 = x^2 + 2xy + y^2)
In any triangle... *longest side is opposite largest angle
*shortest side is opposite smallest angle
*sides w/same length are opposite (=) angles
*sum of lengths of any 2 sides is > 3rd length
which is bigger: 8/3 or the square root of 7? to figure this out, square both sides. They compare 64/9 to 7 (or 63/9)...64/9 (or 8/3) is a little bigger
which is bigger: 8/3 or the square root of 7? 63
16 2/3 % as a decimal and fraction 0.16666 and 1/6
16 2/3 % as a decimal and fraction 14
perimeter of a rectangle perimeter = 2(length + width)
factor A factor is a whole number that divides evenly into another whole number. A factor can also be called a divisor.
Prime Numbers Numbers that can only divide evenly by 1 or themselves
Area of a square, in terms of its diagonal ½d²
what happens to a negative number raised to an even power it gets positive
Simple Interest Rate Formula
ex: If \$12,000 is invested at 6 percent simple annual interest, how much interest is earned after 9 months?
Interest = Prt
P-principle
r-interest rate expressed as a decimal
t-time in years
12,000(.06)(9/12) = \$540
Percent and fractinal equivalents?10%20%30%40%50%60%70%80%90%100%12 1/2%25%37 1/2%62 1/2%75%87 1/2%16 2/3%33 1/3%66 2/3%83 1/3% 10%= 1/1020%= 2/5 1/530%= 3/1040%= 4/10 2/550%= 5/10 4/8 2/4 3/6 1/260%= 6/10 3/570%= 7/1080%= 8/10 4/590%= 9/10100%= 10/10 112 1/2%= 1/825%= 2/8 1/437 1/2%= 3/862 1/2%= 5/875%= 6/8 3/487 1/2%= 7/816 2/3%= 1/633 1/3%= 2/6 1/366 2/3%= 4/6 2/383 1/3%= 5/6
33 1/3% as a decimal and fraction .3333 and 1/3
33 1/3% as a decimal and fraction 12
vertical angles two angles that are not adjacent to each other are opposite, or vertical, and are equal in measure
Integers Whole numbers (-6, -2, 0, 1, 3, 7)
Not fractions
Consecutive Integers - listed in order with none missing
Integers Ex. 148
Sum of all 3 angles in a triangle = ? 180°
What is the largest chord that can be drawn in a circle? The diameter
Properties of Zero For every positive integer n: 0ⁿ = 0
What are the formulas for the surface area of a rectangular solid and the surface area of a cube? Rectangular solid: A=2(lω+lh+hω)
Cube: A=6e²
A number is divisble 9 if the sum of its digits is divisble by what number? 9
how do you use the average to find the sum? example: the average of 10 numbers is 50. What is the sum of the 10 numbers? sum = average x number of terms if the average of 10 numbers is 50, then they add up to 10 x 50, or 500
how do you use the average to find the sum? example: the average of 10 numbers is 50. What is the sum of the 10 numbers? 81
How to solve quadratic equations? Set equation equal to zero, ax²+bx+c = 0
Solve, using one of two methods:
1) Factor and then solve
2) Use the quadratic formula: x=[-b±(√(b²-4ac)]/2a
*You will end up with two answers*
Anything raised to the zero power = ? 1
Ex: 4⁰ = 1
# is divisible by 5 if... it ends in 5 or 0
Formula for avg. rate? avg= total of a/total of bex. avg miles per hr= total miles/hours
A number is divisible by 9 if the ____ of its digits is divisible by... sum, 9
If "a" is inversely proportional to "b" and b=5 when a=3, what is the value of "b" when a=10? By definition, "a" is inversely proportional to "b" if the product "ab" is a constant.
1) 3x5 = 15, the constant is 15
2) 10 x b =10b
3) 10b=15
**b=³/₅**
What are the formulas for the volumes of a rectangular solid and the volume of a cube? Rectangular solid: V=lwh
Cube: V=e³ (e=edge)
A number is divisble by 6 if it is divisble by what two numbers? 2 or 3
perimeter of a triangle the sum of the lengths of all three sides
perimeter of a triangle 35
area of a sector area of a sector: a slice of pie,
n/360(pi)(r^2)
If an experiment is done 2 (or more) times, the probability that the 1st even will occur and then a second event will occur is... The product of the probabilities
Permutation Equation **Figure out how many possible outcomes to arrange elements sequentially nPk =n! /(n-k)!
n= (# in the larger group)
k= (# you're arranging)
distance formula, used to define the distance between two points: distance formula = square root of (x1-x2)^2+(y1-y2)^2
For any numbers a and b, with a≠b, a♥b=(a+b)/(a-b); What is 25♥15? = 25+15/25-15 = 40/10 = 4
If 0 < x < 1 then 1/x > x. In fact, 1/x > 1.
In a 30⋅30⋅90 triangle: if you know the length of the longer leg... To find shorter leg: divide by √3 ⋅ To find the hypotenuse: multiply the length of the shorter leg by 2
how do you find the least common multiple? to find the least common multiple, check out the multiples of the larger number until you find one that's also a multiple of the smaller. LCM of 12 and 15 is 60
how do you find the least common multiple? 68
How do you find the average (mean) of a group of numbers? Average = sum of values/number of values
If two sides of a triangle are equal, then... ...The two opposing angles must be equal
How to find the average of consecutive #s Take the average of the largest and smallest # in the set. (i.e. for the set of consecutive #s 5....172 would be (172+5)/(2)= 88.5)
An integer is divisible by 3 if... ...if its digits sum to a multiple of 3

6,930 is a multiple of 3 because 6+9+3+0=18 which is a multiple of 3
What is true about the slop of perpendicular lines? The slop of one line is the negative reciprocal of the slope of the other line.
In a classroom of 30 students, the ratio of the boys in the class to students in the class is 2:5. How many boys? Multiply the ratio by the total = 2 boys/5 students x 30 students = 12 boys
how do you determine the mode of a group of numbers? the mode is the number that appears the most often. If two numbers appear equally often, they are both the modes. the mode of 12, 15, 23, 40, and 40 is 40 b/c it appears more often.
how do you determine the mode of a group of numbers? 85
John travels 30 miles in 2 hrs and then 60 miles in 3 hrs. What is his average speed in miles/hr? Average A per B = Total A/Total B
= (30+60)miles/(2+3)hrs = 18mph
What is the formula for the area of a triangle? A = ½ base x height
base-any side of the triangle
height-the altitude drawn to the base from the opposite vertex
4/8 0.5
50%
7/8 0.875
87.5%
216
10³ 1000
14² 196
2^3(2^4)= 2^7
5⁴ 625
81
√3 1.7
36
root(1)= 1
1^2 is 1
even
NEGATIVE =
Positive
even
NEGATIVE =
even
NEGATIVE = Positive
Complementary angles = 90°
area of sector= (x/360)pie(r^2)
combined time (AxB)/ (A+B)
Find the fraction: 66²/₃% 2/3
Find the fraction: 30% 3/10
1/3 = ?% 33 1/3%
5,280 feet = 1 mile
Find the fraction: 87.5% 7/8
Find the percent: 1/20 5%
odd
NEGATIVE =
Negative
odd
NEGATIVE =
odd
NEGATIVE = negative
Area of an equilateral triangle (s²√3)/4
hypotenuse longest side of the triangle
how do you multiply fractions? to multiply fractions, multiply the numerators and multiply the denominators
how do you multiply fractions? 73
Negative x Positive =
Positive x Negative =
Negative
a²+b²+c²=d² formula for diagonal of a cube
mile = 1760 yards ~ 1609 meters
Similar triangles... 1) Corresponding angles are equal
2) Lengths of corresponding sides are in proportion
Measures of Interior Angles ((n-2) 180) / n
Probability of an event that cannot occur is? 0
Isosceles triangle have two equal? sides and angles
x^2 ± 2xy + y^2 = (x ± y)^2
A multiple is... ...The integer values formed by multiplying that number
for the probability of one thing OR another happening __ the probability fractions together add
Probability Equation # of desired outcomes/# of total possible outcomes
to multiple powers (or raise a power to a power) multiply the exponents 7^2(^3) = 7^6
to multiple powers (or raise a power to a power) 19
right triangles triangles with one interior angle of 90. The hypotenuse lies opposite the right angle. The other two sides are legs. leg^2 + leg^2 = hypotenuse^2
The first 4 positive multiples of 8 are 8, 16, 24 and 32. The first positive multiple of any number is itself. prime
Multiplying Decimals Multiply the #s and then move the decimal point the total # of places in the answer
Subtraction Rules If exactly one of the endpoints is included, subtract (time)
If neither endpoint is included, subtract and subtract 1
for ratios do a ratio chart with ratio numbers on top ___ numbers on bottom and ___ by in between real/multiply
What are the formulas for the diameter, circumference, and area of a circle of radius r? D=2r
C=πd or 2πr
A=πr²
adjacent angles angles that are adjacent (next to each other) are supplementary because they lie along a straight line
define: quadrilateral a four sided polygon where the four interior angles add up to 36, regardless of the quadrilateral's shape
0.25 = 1/4 = 25% 0.333 = 1/3 = 33 1/3%
0.25 = 1/4 = 25% 0.4 = 2/5 = 40%
* Zero times any number equals zero. * Zero is an even integer. * Zero is neither positive nor negative. * Zero divided by any number is zero. * Any number raised to the zero power is equal to 1. product & quotient
Geometric Sequence = ? Gn= G₁r ⁿ⁻¹ (the ratio between one term and the next is constant, not the actual difference. Ex: 3, 9, 27, 81)
Diagonal of a Box d² = l² + w² + h²
how a pizza can be ordered with 3 diff toppings form a choice of 8 8x7x6/3X2X1
In a 45⋅45⋅90 right triangle, solve for the legs by... dividing the hypotenuse by √2
Difference between Permutation and Combination? Permutation- Order is Relevant (1st, 2nd, 3rd place finalists; pictures on wall)Combination- Order is NOT Relevant (5 of 8 pizza toppings)
A number is divisible by 3 if the _____ of its digits is divisible by... sum, 3
Properties of a rectangle *The measure of each angle = 90°
*The diagonals are congruent
To divide decimal numbers... ...Move the decimal until it is all the way to the right of the divisor. Then move it that many places to the right in the dividend.
Consider the sequence 1,4,2,8,5,7,1,4,2,8,5,7...what is the 500th term of the sequence? When a group of k numbers repeats itself, to find the nth number, divide n by k and take the remainder r. The rth term and the nth term are always the same. So n=500, & k=6 (6 #s repeat)
*500/6 = 83.3
*Ignore the decimal, the quotient is 83, since 83x6=498, the remainder is 500-498=2
*The 500th term = 2nd term (rth term) = 4
common percent and fraction equivalents1/20=1/10=1/8=1/6=1/5=1/4=1/3=1/2= 1/20= 5%1/10= 10%1/8= 12 1/2%1/6= 16 2/3%1/5= 20%1/4= 25%1/3= 33 1/3%1/2= 50%
to solve for larger fractions with unlike parts... cross multiply keeping numerators of the same side OR find a common numerator or denominator
The total deviation above the average is equal to... ...the total deviation below the average
in FRACTIONS with the SAME DENOMINATOR... the larger numerator is the larger fraction
To multiply and divide roots? Solve for both the outside then inside radicals
What is the counting principle? If two jobs need to be completed and there are m ways to do the first job and n ways to do the second job, then there are m x n ways to do one job followed by the other.
The degree measure of an arc equals... ...the degree measure of the angle that intercepts it
If 2 students are chosen at random from a class with 5 girls and 5 boys, what's the probability that both students chosen will be girls? *Probability that the 1st student chosen will be a girl = 5/10
*Probability that the 2nd student chosen will be a girl = 4/9
*Probability that both students chosen will be girls = 1/2 x 4/9 = 2/9
How do you divide two exponents w/ the same base? 4^4 / 4^2 Subtract the exponents. ex= 4^2
to multiple powers with the same base... add the exponents and keep the base

7^3 x 7^5 = 7^8
The answer is D (not enough information provided) if.... you have 2 variables and neither is proven to be positive
If a class of 10 boys & 15 girls took a test & the average grade of the boys was 80, and for the girls was 90, what was the class average? Calculate the weighted averages!
(10x80) + (15x90) / (10+15) = 86
*b/c the class is 40% boys & 60% girls, calculate the average as: (.4x80)+(.6x90)= 86
a negative number raised to an odd power... ...yields a negative result (-1)^57 = -1
a negative number raised to an odd power... 21
a negative number raised to an even power... ...yields a positive result (-1)^2 = 1
How do you count consecutive integers? ex: How many integers are there from 73 through 419, inclusive? The number of integers from A to B inclusive is B-A+1.
ab = xy when x is the GCD of a and b and y is the LCM of a and b
How do you slove for negative exponents?ex. 2^-3 change the base to a fraction over 1 and put the exponent in the bottom part of the fraction. ex- 1/2^3
The quotient is the result of division. For example, if you divide 60 by 12, the quotient is 5.
An inscribed angle will always make an arc that is... twice the size of the degree of the inscribed angle
How do you convert a percent to a fraction? Put the given percent over 100, remove the percent symbol (%) and simplify if needed.
Distributive Law A (B + C) = AB + AC

A (B - C) = AB - AC
What is the formula for the volume of a cylinder? V=πr²h, where r is the radius of the circular base and h is the height
How to find the sum of a group of numbers Sum of values = average value x number of values
The sum of 3 consecutive integers is less than 75, what is the greatest possible value of the smallest one? n + (n+1) + (n+2) < 75
3n + 3 < 75
3n < 72
n < 24
*The most n can be is 23*
12/5 2.4
240%
1/2 0.5
50%
1⁴ 1
49
19² 361
25² 625
22² 484
64
root(4)= 2
0! = 1
define: slope change in y/change in x
define: slope 61
a(b+c) = ab +ac
Acute angles = <90°
1/3 as percent: 33.33333%
inch = 2.54 cm
Find the fraction: 83¹/₃% 5/6
45.1 x 0.3 = 13.53
Measures of Exterior Angles 360/n
4 quarts = 1 gallon
Find the fraction: 12.5% 1/8
Area of a rectangle? l*w
vertical angleopposite angle goc doi
1.73 approximate value of radical 3
Area of a circle? a= pie*r^2
Circumference of a circle πd OR 2πr
how do you compare decimal fractions? the simplest way to compare decimal fractions is to add zeros after the last digit to the right of the decimal point in each decimal fraction until all the decimal fractions you're comparing have the same number of digits
how do you compare decimal fractions? 76
Decimal to % Move decimal point two places to the right
Decimal to % Ex. .45 = 45%
percentage formula [(part) ÷ (whole)] × 100
or
(is/of) = (%/100)
Simplify a Radical Look for perfect squares (4,9,16,25,36...) inside the √. Factor them out and "unsquare" them.
ex. √48= √16 x √3 = 4√3
ex2. √72= √(36x2) = √36 x √2 = 6√2
even number plus even number equals even number
A triangle inscribed in a semicircle such that one side of the triangle coincides with the diameter of the semicircle is a ______? Right triangle
In any polygon, the sum of the exterior angles, taking one at each vertex, is... 360
to divide by a fraction invert it and multiply
area of trapezoid (formula 2) A= (s1+s2)/2 * h
how do you determine the average of consecutive numbers? example: what is the average of all the integers from 13 through 77 inclusive to find the average of evenly spaced numbers, just average the smallest and largest. the average of all the intefers from 13 through 77 is 13 + 77 / 2 = 90/2 = 45
how do you determine the average of consecutive numbers? example: what is the average of all the integers from 13 through 77 inclusive 83
area of a rectangle area = length x width
Factoring and Unfactoring Rewriting xy+xz as x(y+z) = factoring

Rewriting x(y+z) as xy+xz = unfactoring
Factoring and Unfactoring If you can factor or unfactor on the GRE, do it
Inscribed shapes are... inside another shape and all the vertices touch the edge of the outside shape
What's important about vertical angles? They have the same measure
distance (traveling) formula DIRT --> distance is rate ∗ time
Distance = Rate × Time
define: parallelogram a parallelogram has two pairs of equal sides. Opposite angles are equal. Consecutive angles add up to 180
define: parallelogram 44
volume of a cube volume of a cube = (edge)^3
(+) (+) =
(-) (-) =
(+) (-) =
+
+
-
(+) (+) =
(-) (-) =
(+) (-) =
(+) (+) = +
(-) (-) = +
(+) (-) = -
Negative - Negative = Negative + Positive
keep the sign of the larger number and subtract
(-7) - (-5) = -7 + 5= -2
(-5) - (-7) = -5 + 7 = 2
What is the formula for the distance b/w two points? (√(x₂-x₁)² + (y₂-y₁)²)
If a < b, the percent increase from a to b is always ___ than the percent decrease going from b to a Greater
Add & Subtract Roots You can add/subtract roots only when the parts inside the radical are identical.
√2 + 3√2 = 4√2
√2+√3 = cannot be combined!
√2-3√2 = 2√2
What is the sum of the measures of the n angles in a polygon with n sides? =(n-2)(180°)
30-60-90 right triangles the ratio of sides is always 1:root3:2 paired as follows...the side opposite the 30 degree angle is 1, etc.
30-60-90 right triangles 42
Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Digits Integers are composed of digits
.029 x 10³ (move decimal 3 places to the right) = 29
surface area sum of the areas of all its sides for a triangle
If a polygon has n sides, what is the sum of the measures of its n exterior angles, taking one angle at each vertex? = 360°
COMBINATIONS- keys to finding answers: 1. Like a permutation: multiply each 'slot's options with each other- THEN: 2.  divide by the factorial of the number of slots.ie, bring home three of five ice cream flavors. (5x4x3)/3!
Absolute value Distance away from 0 (always a positive number).
Absolute value Ex. Absolute value for -3 is 3, for 2 is 2, etc.
The PROBABILITY of an event = (# of desired outcomes)/ (# of possible outcomes)
square root of 3 divided by 4 multiplied by side² area of an equilateral triangle
In FRACTIONS with the SAME NUMERATOR... the smaller denominator is the larger fraction
A number is divisble by 5 if the last digit are what? 0 or 5
A number is divisible by 6 if it is divisible by... 2 and 3
Sides of a 30-60-90 triangle base= a, side= a times the square root of 3, hypotenuse= 2a
1) set it equal to "0"
2) factor it out
3) find values that make each factor = "0"
how you fix this: 2^-2? put a 1 over it: 1/2^2 then to 1/4
What is a factorial? n! The PRODUCT of all the integers from 1 to n. ex: 4!=4x3x2x1=24
ex2: 0!=1!=1.
A number is divisible by 4 when its last two digits are divisible by 4
3 steps to solve an ALGEBRAIC INEQUALITY: 1) multiply to get rid of fractions
3) multiply by -1 to get positive "x" which will change direction of inequality ( < to >)
To make a decimal percent a decimal number? move decimal to the right two places
How do you change a percent to a decimal? Remove the percent symbol and divide by 100 (move decimal 2 places to the left)
ex: 0.8% = .008
Given Events A & B: PROBABILITY of A OR B  Probability of A PLUS Probability of B
If the measures of the two acute angles of a right triangle are in the ratio of 5:13, what is the measure of the larger angle? 1) Let the measures of the 2 angles=5x & 13x
2) Remember the sum of all 3 angles = 180°
3) 5x+13x+90=180
4) x=5, so the larger acute angle is 13x5=65°
The measure of an exterior angle of a triangle is equal to... The sum of the two opposite interior angles
If a fair coin is tossed 4 times, what's the probability that at least 3 of the 4 tosses will come up heads? *2 possible outcomes/toss x 4 tosses = 16 possible outcomes
*5 possible desired outcomes
Probability = 5/16
How do you find the length of an arc of a circle? An arc is part of the circumference.
Length of the arc = (x/360°)(2πr), where x=the measure of the central angle
how do you find the median of a group of numbers? the median is the middle value in a group of numbers. If there's an even number of values, the median is halfway between the two middle values. median of 12, 15, 23, 40, and 40 is 23 b/c its the middle value. median of 12, 15, 23, and 40 is 19 b/c its halfway b/w the two middle values of 15 and 23
how do you find the median of a group of numbers? 84
what is the equation for a straight line? y = mx + b where, m = slope and b = y-intercept
what is the equation for a straight line? 62