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GRE Math > Key Math Notes > Flashcards

Key Math Notes Flashcards

1
Q

Dilution or Mixture

A

Where w=weaker solution,

s=stronger solution,

and d=desired solution

______________

(w%-d%)w = (s%-d%)s

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2
Q

GROUP

A

Group 1

+ Group 2

+ Neither

  • Both

Total #

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3
Q

Permutation

of ways to arrange elements sequentially (with repitition)

A

nPk=

__n!_\_

(n - k)!

n= # in the large group

k= # being arranged

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4
Q

COMBINATION

When the order in an arrangement of the smaller group being drawn from the larger group doesn’t matter

A

nCk =

_\_n!__

k! (n - k)!

n = # in larger group

k = # being chosen

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5
Q

COMBINED WORK

A

The inverse of the time it would take everyone working together equals the sum of the inverse of the times it would take each owrking individually

1/r + 1/s = 1/t

r and s = the time it would take individuals working seperately

t = the time it would take them working together

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6
Q

P E M D A S

A

Parantheses

Exponents (or radicals)

Multiplication & Division

(from left to right)

Addition & Subtraction

(from left to right)

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7
Q

Multiples of 3

A

sum of digits is multiple of 3

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8
Q

Multiples of 4

A

last two digits are a multiple of 4

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9
Q

Multiples of 6

A

Even number whose sume is multiple of 3

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10
Q

Multiples of 9

A

sum of digits is multiple of 9

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11
Q

Multiples of 12

A

a multiple of both 3 and 4

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12
Q

Max and Minimum Sides of a triangle

A

The third side of a triangle is between the positive difference and sum of the other two sides.

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13
Q

Regular Polygon Angles

A

n = # of sides

Sum of interior angles:

(n - 2) x 180

Degree of one angle:

(n - 2) x 180

n

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14
Q

LENGTH of an ARC

A

ARC =

θ = angle

(θ / 360) x 2πr

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15
Q

AREA of a SECTOR

A

SECTOR =

θ = angle

(θ / 360) x πr2

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16
Q

ARC

SECTOR

SEGMENT

A
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17
Q

(xa)(xb)

A

xa+b

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18
Q

xa / xb

A

xa-b

19
Q

(xa)b

A

xab

20
Q

0x

A

0

21
Q

x0

A

1

22
Q

00

A

Undefined

23
Q

x-2

A

1 / x2

24
Q

x1/3

A

3√x

25
Q

x1/2

A

√x

26
Q

√x + √x

A

2√x

27
Q

(a√b)(c√d)

A

(ab)(√b+d)

28
Q
A

isosceles triangle

2 angles are the same

2 sides are the same

29
Q
A

Equalateral Triangle

All sides are equal

All angles are 60o

30
Q
A

Similar Triangles

Corresponding angles are equal

Sides are proportional

31
Q

Pythagorean Theorem

A

With right triangles only:

a2 + b2 = c2

32
Q

Special Right Angles

Side proportions (4)

A

3 : 4 : 5

5 : 12 : 13

30o - 60o - 90o

= 1 : √3 : 2

45o - 45o - 95o

= 1 : 1 : √2

33
Q

SLOPE

A

RISE / RUN

Change in Y / Change in X

34
Q

SIMPLE

INTEREST

A

Interest Earned (I) =

Principle (P)

x interest rate (r)

x time, in years (t)

I = Prt

35
Q

COMPOUND

INTEREST

A

Interest Earned (I) =

Principle (P)

Interest Rate (r)

time, in years (t)

of times compounded annually (c)

I = P ( 1 + r/c)tc

36
Q

Counting consecutive numbers

A

A => B =

B - A + 1

37
Q

Sum of Consecutive numbers

A

Sum = Average x # of terms

A => B

(A + B) / 2 = Average of terms

B - A + 1 = # of terms

(A + B) / 2

38
Q

Recognize this Polynomial

ab + ac

A

a (b + c)

39
Q

Recognize this Polynomial

a2 + 2ab + b2

A

(a + b)2

40
Q

Recognize this Polynomial

a2 - 2ab + b2

A

(a - b)2

41
Q

Recognize this Polynomial

a2 - b2

A

(a + b)(a - b)

42
Q

WEIGHTED

AVERAGE

A

Group A Average = x

Group B Average = y

Group A is z times as big as Group B

(zx + (1)y) / (z+1)

43
Q

COMMON FACTORS

eg: 135 and 225

A

1st: find the prime factors in each #

135 = 3 x 3 x 3 x 5

225 = 3 x 3 x 5 x 5

2nd: find the prime factors they have in common

3 x 3 x 5

3rd: multiply these common factors in every combination

3 x 3, 3 x 5, 3 x 3 x 5

So, common factors are 3, 5, 9, 15, 45

44
Q

STANDARD

DEVIATION

A
  1. Find the mean of the set
  2. Find the difference between the mean and each value
  3. Square each of the differences
  4. Find the average of the squared differences (3)
  5. Take the positive square root of the average (4)

GRE Math (1 decks)

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