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136 Cards in this Set
- Front
- Back
- 3rd side (hint)
Integers
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Whole numbers on the number line
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Consecutive Integers
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Listed in order of increasing value without any integers missing in between them, such as:
• 0, 1, 2, 3, 4, 5 • -6, -5, -4, -3, -2, -1, 0 |
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Zero
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It is an integer, but it is neither positive nor negative (but it is even)
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All Prime Numbers Less Than 30
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2, 3, 5, 7, 11, 17, 19, 23, 29
There’s no such thing as a negative prime number or a prime fraction |
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Absolute Value
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The absolute value of a number is equal to its distance from 0 on the number line
The absolute value of any number is always positive ALSO: if ıxı = 4, then the value of of x is either 4 or -4. |
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An integer is divisible by 2 if...
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if its units digit is divisible by 2.
598,447,896 is divisible by 2 because the units digit, 6, is divisible by 2 |
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An integer is divisible by 3 if...
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if the sum of its digits is divisible by 3.
2,145 is divisible by 3 because 2+1+4+5 = 12, and 12 is divisible by 3!! |
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An integer is divisible by 4 if...
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if its last two digits form a number that’s divisible by 4
712 is divisible by 4 because 12 is divisible by 4!!! |
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An integer is divisible by 5 if..
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if its units digit is either 0 or 5
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An integer is divisible by 6 if...
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its divisible by both 2 and 3
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An integer is divisible by 9 if...
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the sum of its digit is divisible by 9
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An integer is divisible by 12 if...
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If the integer is divisible by both 6 and 8
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Factors
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A number a is a factor of another number b if b can be divided by a without leaving a remainder.
For example, 1, 2, 3, 4, 5, 6, and 12 are all factors of 12 |
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.2 = 20% = What Fraction?
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.2 = 20% = 1/5
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.4 = 40% = What Fraction?
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.4 = 40% = 2/5
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.6 = 60% = What Fraction?
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.6 = 60% = 3/5
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.8 = 80% = What Fraction?
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.8 = 80% = 4/5
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1/5 = What Decimal? What Percentage?
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.2 = 20% = 1/5
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2/5 = What Decimal? What Percentage?
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.4 = 40% = 2/5
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3/5 = What Decimal? What Percentage?
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.6 = 60% = 3/5
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4/5 = What Decimal? What Percentage?
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.8 = 80% = 4/5
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Percent Change Formula
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(Difference/Original) x 100
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How to Multiply Exponents
2^2 X 2^4 = ? |
Add the exponents
2^2 + 2 ^4 = 2^6 This doesn't work for adding exponents, but won't be asked to do that. |
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Dividing Exponents
2^6 / 2^2 = ? |
Subtract the exponents
2^6 / 2^2 = 2^6-2 = 2^4 |
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A negative exponent should be rewritten as ....
3^-2 = ? |
1/(3^2) => 1/9
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Raising a number greater than 1 to a power greater than 1 results in a BIGGER or SMALLER number?
2^2 = ? |
Raising a number greater than 1 to a power greater than 1 results in a BIGGER number
2^2 = 4 |
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Raising a fraction between 0 and 1 to a power greater than 1 results in a BIGGER or SMALLER number?
(1/2) ^2 = ? |
Raising a fraction between 0 and 1 to a power greater than 1 results in a SMALLER number
(1/2) ^2 = 1/4 |
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A negative number raised to an EVEN power becomes POSITIVE or NEGATIVE?
(-2)^2 = ? |
A negative number raised to an even power becomes POSITIVE
(-2)^2 = (-2)(-2) = 4 |
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A negative number raised to an ODD power remains POSITIVE or NEGATIVE?
(-2)^3 = ? |
A negative number raised to an ODD power remains NEGATIVE
(-2)^3 = (-2)(-2)(-2) = -8 |
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A number raised to a negative power is equal to...?
2^-2 = ? |
A number raised to a negative power is equal to 1 over the number raised to the positive number power.
2^-2 = 1/(2^2) = 1/4 |
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A number raised to the 0 power is what?
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A number raised to the 0 power is 1, no matter what the number is
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A number raised to the first power is what?
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A number raised to the first power is ALWAYS the number itself.
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0 raised to the 0 power is what?
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Undefined
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√1 =
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√1 = 1
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√2 =
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√2 = 1.4
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√3 =
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√3 = 1.7
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√4 =
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√4 = 2
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Associative Law for Multiplication
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(ab)(cd) = a(bcd)
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4 X (5X8) = (4X5) X 8 = 5 X (8X4)
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Distributive Law
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a(b + c) = ab + ac
a(b - c) = ab - ac |
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Associative Law for Addition
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(a + b) + (c + d) = a + (b + c + d)
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4 + (5+8) = (4+5) + 8 = 5 + (4+8)
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12 X 4
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48
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12 X 3
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36
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12 X 5
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60
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12 X 8
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96
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12 X 9
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108
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12 X 7
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84
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12 X 11
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132
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12 X 12
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144
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12 X 10
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120
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12 X 6
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72
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12 X 13
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156
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Distributive Law:
a(b + c) = |
ab + ac
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Distributive Law:
ab + ac |
a(b + c)
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Distributive Law:
a(b - c) = |
ab - ac
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Distributive Law:
ab - ac = |
a(b - c)
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Factoring:
xy + xz = |
x(y + z)
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Unfactoring:
x(y + z) = |
xy + xz
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1.4⌃2 = √?
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√2
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1.7⌃2 = √?
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√3
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Unfactor:
5(x + y) |
5x + 5y
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Factor:
5x + 5y |
5(x + y)
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Factor:
8⁷ - 8⁶ |
8⁶(8ⁱ - 1)
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Good Plug In Numbers for Percentage Problems:
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10, 100
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Good Plug In Numbers for Minutes or Seconds Problems
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30,120
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How to solve "Must Be" problems
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1. Plug in numbers
2. Eliminate answer choices 3 Plug in different numbers |
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What numbers to use when Plugging In to Quant Comp questions
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First use "normal numbers"
Then use "weird" numbers (zero, 1, negatives, fractions, or big numbers) to disprove your first answer. If different numbers give you different answers, you've proved answer is D |
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When Plugging In answer choices, which answer choice should you start with
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The one in the middle
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When is answer D eliminated with Quant Comp questions?
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When the question contains only numbers.
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Dividing Fractions:
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Dividing Fractions: Multiply the first fraction by the reciprocal of second fraction
*Cross Reduce before you multiply |
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⅔ ÷ ⅘
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2/3 ÷ 4/5 =
2/3 X 5/4 =Then Cross-Reduce 1/3 X 5 /2 = 5/6 |
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Bowtie
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Multiply denominators together to get the new denominator, and multiply diagonally up to get the new numerators
2/3 - 3/4 = 8/3 -9/4 = 8/12 - 9/12 = -1/12 |
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When to Bowtie
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When adding or subtracting fractions with different denominators
When comparing fractions with different denominators |
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1/5 = x%
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20%
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1/4 = x%
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25%
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4/5 = x%
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80%
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2/5 = x%
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40%
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3/5 = x%
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60%
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2x⁴ X 2x⁵
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2x⁹
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When do you use weird numbers?
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Second round of Pluggin In on quant comps
(0, 1, negatives, fractions, or really big numbers) |
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Whenever the answer choices are far apart in value you can...
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ESTIMATE/BALLPARK
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Whenever you see the word APPROXIMATELY in a question you can...
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Ballpark!/Estimate!
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Formula for Averages:
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Total
______ # of things |
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RANGE
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Difference between highest and lowest numbers in your set
(2, 6, 13, 3, 15, 4, 9) range: 15-2, or 13 |
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STANDARD DEVIATION
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How much the numbers in a set vary from the mean of the set
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A large standard deviation means...
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the numbers in the set are spread far from the mean
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A small standard means the values in the set are...
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clustered closely around the average
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RATE
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Distance or Amount
_________________ Time X Rate |
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Ratio Table
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Part Part Total
Ratio Multiply by Real |
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PROBABILITY
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Number of possible outcomes that satisfy the condition
_________________________ Number of total possible outcomes |
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To find the probability of a series of events in a row
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Multiply the probabilities of the individual events
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To find the probability of either one event OR another event happening
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Add the probabilities
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The probability of an event happening and the probability of an event NOT happening....
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Must add up to 1
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Factorial
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That number times every positive whole number smaller than itself, down to 1
6 = 6 X 5 X 4 X 3 X 2 X 1= 720 |
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Symbol for a Factorial
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!
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0!
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1
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When factorials show up in GRE...
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Look for a shortcut like canceling or factoring
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12!
___ 11! |
12 X 11 X 10 X 9 X 8 X 7 6 X 5 X 4 X 3 X 2 X 1
_________________________ 11 X 10 X 9 X 8 X 7 6 X 5 X 4 X 3 X 2 X 1 12!/11! = 12 |
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4!
___ 2! |
4 X 3 X 2 X 1
___________ 2 X 1 4!/2! = 12 |
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Permutation
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Arrangement of things in a particular order
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To solve a permutation
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Figure out how many slots you have, write down number of options for each slot, and then multiply
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Combination
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A group, and the order of elements within the group doesn't matter
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To solve a combination
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Figure out how many slots you have, fill in the slots like a permutation, then divide by the factorial of the number of slots
*denominator will always cancel out completely |
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Given events A and B, the probability of events A AND B=
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(Probability of A) x (Probability of B)
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Given events A and B, the probability of events A OR B =
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(Probability of A) + (Probability of B)
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Given event A: Probability that A happens + Probability that A does NOT happen =
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1
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Unfactor:
x^2 - y^2 |
(x + y)(x - y)
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Factor:
(x + y)(x - y) |
X^2 - y^2
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Unfactor:
X^2 + 2xy + y^2 |
(x + y)(x + y)
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Factor:
(x + y)(x + y) |
X^2 + 2xy + y^2
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Unfactor:
(x - y)^2 |
x^2 - 2xy + y^2
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Factor:
x^2 - 2xy + y^2 |
(x - y)^2
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When two lines intersect, four angles are formed; what is the sum of these angles?
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360 degrees
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The three angles inside a triangle add up to...
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180 degrees
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The four angles inside any four sided figure add up to...
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360 degrees
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When two parallel lines are intersected by a third line, all the big angles are...
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Equal
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When two parallel lines are intersected by a third line, all the small angles are...
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Equal
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When two parallel lines are intersected by a third line, the sum of any big and any small angle is always...
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180 degrees
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Degrees of a right triangle
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30, 30, 60
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Degrees of an equilateral triangle
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60, 60, 60
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Isosceles Triangles
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40, 70,70
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The length of any side of a triangle must be ___________ than the sum of the other two sides and ________ than the difference between the other two sides.
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The length of any side of a triangle must be LESS than the sum of the other two sides and LARGER than the difference between the other two sides.
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Area of a Triangle
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Height multiplied by the base, divided by 2
A = (1/2)BH |
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Pythagorean Theorem
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a^2 + b^2 = c^2
Only works with right angles |
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Degrees of Isosceles Right Triangle
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45, 45, 90
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The ratio between the length of sides in a _______ (degrees) triangle is constant.
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30, 60, 90
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If you know the length of any sides in a ______ (degrees) triangle, you find the length of any of the others
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If you know the length of any sides in a 30, 60, 90 triangle, you find the length of any of the others
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In an isosceles right triangle, the two non-hypotenuse sides are...
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Equal
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In an isosceles right triangle, the length of each short leg is x, then the length of the hypotenuse is...
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x√2
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Circumference of a Circle
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∏d
2∏r |
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Area of a Circle
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πr^2
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Slope
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y = mx + b
x and y are points on the line b stands for the y-intercept |
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Slope
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rise/run
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Volume
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LWH
length x width x height |
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Volume of Circular Cylinder
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∏r^2h
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Finding the Length of a Diagonal Line inside a Three Dimensional Rectangular Box
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a^2 + b^2 + c^2 = d^2
a, b, c = dimensions of the figure |
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Surface Area of a Rectangular Box
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Sum of the areas of all its sides
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