Kaplan GRE Quicksheet

GRE

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Formula Sheet

 Use this sheet to help you remember your math content.

Triangles

 Angles

b° 

 + y  +  +  z  =  = 180° (interior angles)  x  +

 y° 

 = 360° (exterior angles) a + b + c  =

Area =

1 2

×

a° 

a°

x°  

60° a

b

45°

 x √ 2 60°

d 

30°

360

Time

% Increase = l

(  x  ) (  x  ) = x 2

b1

 x  –a = h

Sum of the terms Average =

1  x a

 x 0 = 1  x a x b = x a + b

b2  )h  A = 12 ( b1 + b2 ) h

 A = bh

Circum.

Number of terms

Original Amount

(  x a )b = x ab  x a = x a – b  x b (negative)odd = negative (negative)even = positive

Miscellaneous  = a(  ( b + c  ) ab + ac  = a

Uniform Solids  = y % of  x   x % of  y   y  = y 

a + b a b = + c  c  c 

Total Time

% Decrease =

Radical Rules a b = ab

V = π r  r2  h SA = 2π r  r 2+ 2π rh rh

V = lwh 2(lw + lh + wh) SA = 2(lw

a b

=

a c  + b c  = (a + b) c 

Mode:

the most common number(s) in a set

Median:

the middle term in a set of ascending or descending numbers; when the set has an even number of numbers, the average of the two middle terms

a + b

(  a  )2 = a

Work Formula  = T  =

ab a + b

Only (odd) ×(odd) and (odd) ± (even) yield odd numbers.

| – x | = | x |  x |

Standard form of a line: y  line: y  =  = mx + b (where m (where  is the slope, and b is the y  the y -intercept) -intercept)  m is

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 100%

×

0 is an even integer. 1 is not prime. 2 is the lowest prime number and the only even prime number.

a b

In the xy  the xy -plane, -plane, the y  the y -axis -axis is vertical, and the x  the  x -axis -axis is horizontal.

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Quantity of B

Number Properties

Coordinate Plane w 

Quantity of A of A Rate =

Original Amount

h

l

Area of circle O

Original Amount – New Amount  100%

×

r  h

Area of sector OABC

Total Distance Average Speed =

a+ b= b

=

First, Outer, Inner, Last ( a + b )( c  c +  + d  ) = ac  +  + ad + bc + bd 

Exponent Rules

 A = lw 

Arc ABC  Arc ABC 

PEMDAS — Parentheses, Exponents, Multiplication and Division, Addition and Subtraction

New Amount – Original Amount

w 

=

FOIL

Distance

h

n

Other Formulas and Things to Know Speed =

 s  A = s2

O

Order or Operations

 x √ 3

Sum of interior angles = 360°

r 

d  =  = 2r  c = 2π r or π d  d   A = π r  r 2 360° around

 x 

Quadrilaterals

C 

n° 

2 x 

45°  x 

║ l2

B

 A

a2 + b2 = c 2

 x 

l1

Circles

Side Ratios (Pythagorean Triples Triples)) 3:4:5 5:12:13 7:24:25 8:15:17 9:40:41

c 

d° 

c° 

a + b =  180

base

Right Triangles

d° 

 z°  c° 

Third side > difference of any two sides

Isosceles

c° 

l2

Sum of any two sides > third side

d° 

c° 

a°  b° 

base × height 

Equilateral

d° 

b° 

height

 +  z ; b = x + z ; c  = x  a = y  +  = x  + y   + y 

c° 

l1

Slope =

rise = run

 y 2 – y 1  x 2 – x 1