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GRE Math > Math Concepts > Flashcards

Math Concepts Flashcards

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0
Q

Consecutive integers

A

At least one is even and one odd

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1
Q

Combinations

A

When selecting a set of items from a group, when the order of the set does not matter.

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2
Q

Dividend

A

Numerator

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3
Q

Divisor

A

Denominator

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4
Q

Prime factorization of a perfect square

A

Includes an even number of each prime number.

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5
Q

Perfect square divisors

A

Has an odd number of divisors.

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6
Q

Divisibility rule for 2

A

One’s digit is 0, 2, 4, 6, 8

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7
Q

Divisibility rule for 3

A

Sum of digits is divisible by 3

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8
Q

Divisibility rule for 4

A

Last two digits are divisible by 4

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9
Q

Divisibility rule for 5

A

One’s digit is 0 or 5

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10
Q

Divisibility rule for 6

A

Divisible by 2 and 3

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11
Q

Divisibility rule for 9

A

Sum of digits is divisible by 9

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12
Q

Divisibility rule for 10

A

One’s digit is 0

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13
Q

Number of positive divisors

A

Get prime factorization:
p^a • q^b • r^c …
# = (a+1)(b+1)(c+1)…

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14
Q

GCD by prime factorization

A

Find all matching prime factors and multiply them out

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15
Q

LCM by prime factorization

A

Multiple common prime factors once by all uncommon prime factors.

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16
Q

composite number

A

not a prime number

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17
Q

a”-n

A

1/a^n

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18
Q

sqrt(a)*sqrt(b)

A

sqrt(ab)

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19
Q

sqrt(a)/(sqrt(b))

A

sqrt(a/b)

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20
Q

irrational number

A

cannot be represented by decimal that terminates or repeats

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21
Q

real numbers

A

irrational + rational numbers

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22
Q

|x|

A

distance from x to 0

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23
Q

|a + b|

A

< or = |a| + |b|

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24
Q

|a| |b|

A

|ab|

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25
Q

solving for inequality

A

sign is reversed if multiply or divide by negative number

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26
Q

compound interest with interest rate of r percent compounded annually

A

P(1+r)^t where r is percent (like 10% = .1) and t is time in years

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27
Q

compound interest with interest rate of r percent compounded n times per year

A

P(1+r/n)^nt where r is percent (like 10% = .1) and t is time in years

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28
Q

simple annual interest rate of r percent

A

P(1 + rt) where r is percent (like 10% = .1) and t is time in years

29
Q

calculate distance between two points

A

sqrt((x1-x2)^2+(y1-y2)^2) [Create a right triangle and use pythagorean theorem to determine hypotenuse distance]

30
Q

slope for y=mx + b

A

m

31
Q

y intercept for y=mx + b

A

b

32
Q

slope for two points

A

(y2 - y1) / (x2 - x1)

33
Q

word form of slope

A

“rise over run”

34
Q

slope for perpendicular lines

A

slopes are negative reciprocals

35
Q

slope for parallel lines

A

slopes are equal

36
Q

determining y intercept when given two points

A

calculate slope and then create formula y = mx + b and solve b for either point (x, y)

37
Q

equation for parabola

A

y = ax^2 + bx + c

38
Q

graph for a quadratic equation

A

parabola where the x intercepts are solutions to the quadratic equation

39
Q

equation for a circle

A

(x - a)^2 + (y - b)^2 = r^2 with center at (a, b) and radius r

40
Q

graph for x^2 + y^2 = z

A

circle with center at origin and radius z

41
Q

sum of all angles in a triangle

A

180 degrees

42
Q

sum of all angles in an n-sided polygon

A

(n-2) * 180 degrees

43
Q

relationship between sides of triangles

A

length of each side must be less than the sum of the lengths of the other two sides

44
Q

relationship of sides in 30-60-90 triangle

A

30 angle side is 1/2 hypotenuse and the other leg is the 30-angle side times sqrt(3)

1:sqrt(3):2

45
Q

relationship of sides in isoscoles right triangle

A

the two 45 degree sides are equal and the hypotenuse is that side times sqrt(2)

1:1:sqrt(2)

46
Q

area of a trapezoid

A

1/2(b1 + b2)(h)

47
Q

circumference of a circle

A

2(pr)r

48
Q

length of arc for circle with radius r and interior angle a

A

length/2(pi)r = a/360

i.e. ratio of length to circumference is equal to the ratio of the interior angle to 360

49
Q

area of circle

A

(pi)r^2

50
Q

volume of a rectangular solid

A

lwh

51
Q

volume if a right circular cylinder

A

(pi)r^2*h

52
Q

normal distribution

A

mean = median = mode (approx.)

53
Q

normal distribution 1 st. dev.

A

68% of data

54
Q

normal distribution 2 st dev

A

95% of data

55
Q

normal distribution 3 st. dev

A

99% of data

56
Q

variance

A

standard deviation squared

57
Q

range

A

top - bottom

58
Q

standard deviation

A

average distance from mean

59
Q

calculate standardization for x with std dev S and mean M

A

(x - M)/S units away from the S

60
Q

permutations for n items

A

n!

61
Q

0!

A

1

62
Q

select r items from n in a given order

A

n! /(n - r)!

63
Q

select r items from n in no particular order

A

n!/(r! *(n-r)!)

64
Q

probability of an event

A

number of outcomes included / total number of possible outcmes

65
Q

P(E or F or both)

A

P(E) + P(F) - P(both E and F)

66
Q

P(E and F) where E and F are independent

A

P(E)*P(F)

67
Q

expected value

A

the mean of a random variable

68
Q

a^2 - b^2

A

( a - b )( a + b )

69
Q

a^2 + 2ab + b^2

A

(a + b)(a + b)

70
Q

a^2 - 2ab + b^2

A

(a - b)(a - b)

GRE Math (3 decks)

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