The Formula Sheet for DIGITAL 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
Volume of a Rectangular Prism (Box):
Circumference of a Circle: C = 2π r
Area of a Rectangle:
Area of a Triangle: A =
Pythagorean Theorem:
V = π r 2h
Volume of a Cylindar:
A = lw
Volume of a Sphere: V =
1
bh
2
Volume of a Cone: V =
a2 + b 2 =
c2
Special Right Triangles:
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
Increase by a percent: multiply by
Decrease by a percent: multiply by
part
100
Simple Interest: =
A
old
(1 − r )
P(1 + rt )
Interest Compounded Annually: =
A P(1 + r )
t
Percent Increase or Decrease:
old − new
(1 + r )
Interest Compounded n times per year:
×100%
r

=
A P 1 + 
n

nt
Exponents, Roots, & Polynomials:
Multiplication Rule for Exponents:
Division Rule for Exponents:
Power Rule for Exponents:
Negative Exponents: a
ab ⋅ a c =
ab + c
ab
= ab − c
ac
(a )
b
c
b
= abc
2
(
)
2
Difference of Squares: a − b = (a + b)(a − b)
2
2
2
b
b 
Completing the Square: x + bx +   =  x + 
2
2 
2
=
1
ab
Fractional Exponents: a c = a or
Perfect Square Trinomial: a + 2ab + b = a + b
2
−b
2
(
and a − 2ab + b = a − b
2
2
)
2
c
b
( a)
c
b
Systems of Linear Equations
One solution: The lines intersect
at one point.
No solutions: The lines intersect
If the slopes of two lines are
different.
If the slopes of two lines are the
same (they are parallel) but the
y-intercept is different.
Infinite Solutions: The lines
intersect at infinite points (they
are overlapping lines).
nowhere.
If the slopes and y-intercepts
are the same for both lines.
Parabolas:
Standard Form: f ( x ) = ax + bx + c ;
2

b  b 
,f  −   ;
 2a  2a  
vertex=  −
2
Factored Form:
f ( x ) =a( x − m)( x − n) ;
x-intercepts are m and n;
y-intercept = c;
−b ± b2 − 4ac
x-intercepts =
2a
Sum of solutions =
Discriminant = b − 4 ac ; Pos=2 real roots Zero=
1 real root; Neg=2 imaginary roots
−b
a
x-coordinate of vertex =
m+n
2
Vertex Form: f ( x ) = a( x − h) + k ;
2
vertex =
(h, k )
©2020, Test Prep for Success LLC
Systems of Linear Inequalities
y ≤ 3x + 1
y ≤ 3x + 1 and y > -x + 2 graphed together.
The solution is the overlapping region.
y > -x + 2
Data and Probability:
average =
sum _ of _items
number _ of _items
median = middle _number
Strong positive
association
Weaker positive
association
=
range maximum −minimum
probability =
No association
desired _outcomes
possible _outcomes
Weaker negative
association
Strong negative
association
Data Set A has a larger standard deviation than
Data Set B since the values are spread farther
from the mean in general for Data Set A than for
Data Set B.
Sample Size: For SAT, a sample size of 30 is considered large enough to make accurate calculations for any
size population. Still, the larger the sample, the more accurate the statistics are that can be calculated from it.
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
Similar Triangles
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
2
©2020, Test Prep for Success LLC
Polygons: (for this section, n is the number of sides)
Area of a trapezoid:
1
(b1 + b2 )h
2
Properties of Parallelogram
1. Opp sides are ∥ and ≅
2. Opp ∠’ s are ≅
Sum of the interior angles: 180(n − 2)
3. Consec ∠’s are supplementary
Sum of the exterior angles: 360°
4. Each diagonal forms a pair of ≅∆’s
5. Diagonals bisect each other
If they are ≅ it is a rectangle
If they are ⊥ it is a rhombus
6.
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.
Parent Graphs & Transformations:
y=x
Transformation
f (x) + k
f (x) − k
f ( x + h)
f ( x − h)
−f ( x )
cf ( x )
1
f (x)
c
y= x
y = x2
y = x3
y = ax
y= x
Visual effect
Shift up by k units
Shift down by k units
Shift left by h units
Shift right by h units
Reflect over the x axis (flip upside down)
Stretch vertically by a factor of c (becomes skinnier)
Shrink vertically by a factor of c (becomes fatter)
©2020, Test Prep for Success LLC