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The Ultimate Formula Sheet for SAT Math
These formulas are provided in the reference information at the beginning of each SAT math section:
Area of a Circle:

A = π r2

Circumference of a Circle: C = 2π r
Area of a Rectangle:

A = lw

Area of a Triangle: A =
Pythagorean Theorem:

1
bh
2

Volume of a Rectangular Prism (Box):
Volume of a Cylindar:

a2 + b 2 =
c2

Special Right Triangles:

V = π r 2h

Volume of a Sphere: V =

Volume of a Cone: V =

V = lwh

4 3
πr
3

1 2
πr h
3

Volume of a Pyramid: V =

1
lwh
3

Fractions, Decimals, and Percentages: (for this section, r is the percent in decimal form)

Fraction =
percent =

part
whole

part
100

Percent Increase or Decrease:

old − new
old

×100%

Increase by a percent: multiply by

(1 + r )

Decrease by a percent: multiply by
Simple Interest: =
A

(1 − r )

P(1 + rt )

Interest Compounded Annually: =
A P(1 + r )

t

Interest Compounded n times per year:

r

=
A P 1 + 
n


nt

Rates, Ratios, and Proportions:
General form of a conversion factor:

 ending _ units 
 starting _ units 



Concentration of A x Volume of A
+ Concentration of B x Volume of B
= Final concentration (Vol
...
of B)
Distance = Rate x Time

 12inches 
Example: 10feet 
 = 120inches
 1foot 

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Exponents, Roots, & Polynomials:
Multiplication Rule for Exponents:
Division Rule for Exponents:

Power Rule for Exponents:

ab ⋅ a c =
ab + c

Negative Exponents: a

ab
= ab − c
c
a

(a )
b

c

−b

b
c

=

1
ab

Fractional Exponents: a = a or

= abc

c

b

( a)
c

b

i 2 = −1 ; i 3 = −i ; i 4 = 1
i 4 n = 1 ; i 4 n+1 = i ; i 4 n+2 = −1 ; i 4 n+3 = −i

Parabolas:
Discriminant = b − 4 ac ; Pos=2 real roots Zero=
1 real root; Neg=2 imaginary roots

Standard Form: f ( x ) = ax + bx + c ;

2

2



b  b 
,f  −   ;
 2a  2a  

vertex=  −

Factored Form:

x-intercepts are m and n;

y-intercept = c;

x-coordinate of vertex =

−b ± b2 − 4ac
x-intercepts =
2a
Sum of solutions =

f ( x ) =a( x − m)( x − n) ;

m+n
2

Vertex Form: f ( x ) = a( x − h) + k ;
2

−b
a

vertex =

(h, k )

Difference of Squares: a − b =(a + b)(a − b)
2

2

(

Perfect Square Trinomial: a + 2ab + b = a + b
2

2

2

)

2

b
b 
Completing the Square: x + bx +   =  x + 
2
2 

(

and a − 2ab + b = a − b
2

2

)

2

2

2

The Ultimate Formula Sheet for SAT Math

©2020, Test Prep for Success LLC

Graphing Lines:
Slope Formula: m =

y 2 − y1
x2 − x1

Standard Form:

Ax + By =
C

Slope-Intercept Form:=
y

Slope of horizontal line = 0

mx + b

Point-Slope Form: y − y1 = m( x − x1 )

Slope of vertical line = undefined

Distance Formula: d=

( x2 − x1 )2 + (y 2 − y1 )2

 x1 + x2 y1 + y 2 
,
2 
 2

Midpoint Formula: M = 

Parallel lines: equal slopes
⊥ Lines: slopes are opposite reciprocals
Data and Probability:

average =

=
range max imum − minimum

sum _ of _ items
number _ of _ items

probability =

median = middle _ number

desired _ outcomes
possible _ outcomes

Angles:
Vertical ∠’ s are ≅

∠’s that form a linear pair are supplementary (add
up to 180°)
Triangles:
The three ∠’ s of a ∆ add up to 180°

∠’ s that form a circle add up to 360°

When ∥ lines are cut by a transversal, all acute ∠’ s
are ≅ and all obtuse ∠’ s are ≅
Pythagorean Triples: 3-4-5 and 5-12-13

An exterior ∠ is equal to the sum of the two
remote interior ∠’ s
Circles:

A central ∠ is double the inscribed ∠

A radius and tangent make a right ∠

x
arc
=
360 circumference

and

x
sec tor
=
360 area _ of _ circle

where x = central angle

Formula for a Circle: ( x − h) + (y − k ) =
r , where (h,k) is the center and r is the radius
2

2

The Ultimate Formula Sheet for SAT Math

2

©2020, Test Prep for Success LLC

Polygons: (for this section, n is the number of sides)
Area of a trapezoid:

One interior angle of a regular polygon:

1
(b1 + b2 )h
2

180(n − 2)
n

Sum of the interior angles: 180(n − 2)
Sum of the exterior angles: 360°
Properties of Parallelograms:
1
...
Diagonals bisect each other

3
...
Opp ∠’ s are ≅

4
...


Area
= base × height

Trigonometry:

sin =

opp
hyp

cos =

adj
hyp

tan =

opp
adj

360°=2π radians

=
sin( x ) cos(90 − x ) The sine of an ∠ is equal to the cosine of its complement

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