GRE Math Flashcards by Tom Dethlefs

Greatest Common Factor

1) Divide by common mults
2) Multiply common mults
Use table

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Lowest Common Demoninator

1) Find GCF
2) Divide either number by GCF
3) Multiply other number by #2

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Quadratic Equation

ax^2+bx+c=0

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Quadratic Formula

x = [ -b ± √(b^2 - 4ac)} / 2a

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Pythagorean Formula

a^2 + b^2 = C^2

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Pythagorean Triples

3-4-5
5-12-13
7-24-25
8-15-17
9-40-41

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Special Right Triangles

45-45-90 :: x-x-x√2

30-60-90 :: x-x√3-2x

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Compound Interest

Final Balance = Principal * (1 + Rate/Periods)^Time*Periods

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Ratio

Ratio = of/to

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Multiples of 2

Last digit divisible by 2

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Multiples of 2

Digits add up to mult of 3

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Multiples of 4

Last two digits are mult of 4

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Multiples of 5

Last digit 0 or 5

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Multiples of 6

Divisible by 2 and 3

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Multiples of 9

Digits add to mult of 9

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Odd + Odd

Even

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Odd / Even Rules

O + E = O
O * O = O
O + O = E
E + E = E
E * E = E
O * E = E

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First 10 Prime Numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

1 not a prime number

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Prime Factorization

Branch and divide by primes

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Bigger or Smaller? (1/2)^2

Smaller 1/4

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Zeros? 10^6

6 zeros: 10^6 = 1,000,000

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Bigger or Smaller? (-2)^2

Bigger/positive 4

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Bigger or Smaller? (-2)^3

Smaller/negative -8

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Even base to any power? 8^5

Even 8^5 = 32,768

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Odd base to any power? 5^8

Odd 5^8 = 390,625

Mult exponents: 2^2 * 2^3

Add: 2^5

Divide exponents: 4^5 / 4^2

Subtract: 4^3

Raise exponents: (3^2)^4

Mult: 3^8

Fraction exponents: x^0.5

Radical: √x

Negative exponents: x^-3

Fraction: 1 / x^3

Diff exponent base: x^3 * y^3

Mult base: (x * y)^3

Mult radicals: 2√x * 3√y

Mult both: 6√(x*y)

Divide radicals: 12√15 / 2√5

Div both: 6√3

Mult fractions: 3/4 * 2/3

Mult numerator and denominator: 6/12 = 1/2

Div fractions: 4/9 / 4/3

Mult by reciprocal: 4/9 * 3/4 = 12/36 = 1/3

Greater fraction? 5/6 or 7/9

Cross mult: 5/6 or 7/9 :: 5*9 = 45 > 6*7 = 42

% Increase

Increase / Original x 100%

% Decrease

Decrease / Original x 100%

Part of whole by Percent

Part = Percent * Whole

Speed Formula

Speed = Dist / Time

Time Formula

Time = Dist / Speed

Distance Formula

Dist = Speed * Time

Avg A per B

Total A / Total B

Average Formula

Avg = Sum of Terms / # of Terms

Sum of Terms Formula

Sum of Terms = Avg * # of Terms

Wtd Avg Formula

A(wt1) + B(wt2) = wtd avg | [wts add to 1)

Missing Average

Sum of Terms + x = Avg * # of Terms

Avg of consecutive #s

is avg of small and large

Unit Conversion

Cancel out units

Combined Work Formula

1/a + 1/b + 1/c = 1/T | [1 job per unit of time T]

Solve Inequalities

1) Solution is range | 2) Mult or Div by negative number must reverse inequality sign

Solve for 2 unknowns

1) Substitution | 2) Combine (add)

FOIL

x^2 - 3x + 2 +2 : product of missing terms -3 : sum of missing terms

Quadratics: x^2 - y2

(x + y) (x - y)

Quadratics: x^2 + 2xy + y^2

(x + y) (x + y)

Quadratics: x^2 - 2xy + y^2

(x - y) (x - y)

Std Dev Formula

``` Square root of avg of squared differences to mean √Avg(differences^2) 1) Diff each value to mean 2) Square diff 3) Avg squared diffs 4) Square root of avg ```

Normal Distribution Std Devs

``` ±1 = 68% ±2 = 95% ±3 = 99.7% ```

Intersection

Shared = A ∩ B

Union

All of both = A U B --> |A U B| = |A| + |B| - |A ∩ B|

Exclusive

Exclusive union

Combination Formula (orderless)

n! / k!(n - k)! n = total number k = # in each subgroup

Permutation Formula (ordered)

n! / (n - k)! Ordered set n = total number k = # in each subgroup

Probability Formula

Prob = # Desired / # Possible

Independent Probability Formula

P(A) * P(B)

Dependent Probability Formula

Multiply but calculate P(A) and P(B) as if prior event resulted in success/desired outcome

Or Probability Formula (mutually exclusive)

P(A or B) = P(A) + P(B)

Or Probability Formula (not mutually exclusive)

P(A or B) = P(A) + P(B) - P(A and B)

Isosceles

2 sides, 2 angles

Equilateral

3 sides, 3 angles

Triangle Exterior Angle Sum

360

Triangle Area Formula

1/2 * b * h

Polygon Sum of Interior Angles

Sum interior angles = (n - 2) x 180

Trapezoid

One pair parallel sides | Area = Avg length of parallel sides * height

Parallelogram

Two parallel sides | Area = b * h

Rhombus

Parallelogram w/ 4 equal side lengths | Area = b * h

Circle Circumference

2πr

Circle Area

πr^2

Tangent

Line perpendicular to radius

Ratio of circumference to diameter

Arc Length

Ratio to Circumference equal to arc angle ratio to 360

Slope Form

y = mx + b

Slope Formula

y2 - y1 / x2 - x1

Perpendicular Lines Slope

Negative Reciprocal

Volume Cylinder

πr^2 * h

Cylinder Total Surface Area

2π4^2 + 2πrh | area of top/bottom + lateral surface area

Simple Interest

Principal * rate * periods

Rate Formula

Quantity A / Quantity B

GRE Math Flashcards

(88 cards)