Kaplan GMAT Quicksheet

GMAT

Formula Sheet Use this sheet to help you remember your math content.

®

Triangles

Angles

b°

x + y + z = 180° (interior angles)

y°

a + b + c = 360° (exterior angles)

1 × base × 2

Area =

b°

a°

x°

60°

b

45°

x √2 60°

Isosceles

l

b1

h

b A = bh

A = (b1 + b2 )h

Time

Average =

Sum of the terms

× 100%

Original Amount

a b = ab

xa = xa – b xb

x0 = 1

(negative)odd = negative

a b

(negative)

ab + ac = a(b + c) x% of y = y% of x

% Decrease =

Radical Rules

(xa)b = xab

a+b

Average Speed =

Number of terms

New Amount – Original Amount

even

= positive

Miscellaneous

Uniform Solids

=

Circum.

Area of sector OABC Area of circle O

FOIL

1 x –a = a x

x x =x

1 2

360

Arc ABC

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

(x) (x) = x2

a b

b2

=

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

Exponent Rules

A = lw

h

Distance

% Increase =

s A = s2

n

Other Formulas and Things to Know Speed =

w

O

Order or Operations

x √3

Sum of interior angles = 360°

r

d = 2r c = 2πr or πd A = πr2 360° around

30°

45° x

C

n°

d

2x

x

B

A

a2 + b2 = c2

x

l1 ║ l2

Circles

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

c

a

d° c°

a + b = 180

base

Right Triangles

d°

z° c°

Third side > difference of any two sides

Quadrilaterals

c°

l2

Sum of any two sides > third side

d° c°

a°

a°

height

Equilateral

d°

b°

height

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

c°

l1

a+b a b = + c c c

=

Total Time

a c + b c = (a + b) c

Quantity of A Quantity of B

Original Amount – New Amount Original Amount

× 100%

Number Properties

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=

Rate =

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

a b

a+ b=

Total Distance

ab a+b

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

| –x | = | x |

r h h w V = πr2h SA = 2πr2+ 2πrh

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

Coordinate Plane In the xy-plane, the y-axis is vertical, and the x-axis is horizontal. Standard form of a line: y = mx + b (where m is the slope, and b is the y-intercept)

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Slope =

rise = run

y2 – y1 x2 – x1

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