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SAT Math Formula Practice

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Linear Equations

Slope-Intercept Form

Slope Formula

Point-Slope Form

Formulas with Points

Midpoint Formula

Distance Formula

Rewriting Expressions

(Factor) a2 − b2 =

(Expand) (a+ b)2 =

−ab− c

⋅−1−1

=

If a = xb+ x

, then x =

abcd

=

y− y1 =m(x − x1)

x1 + x22

, y1 + y22

⎛⎝⎜

⎞⎠⎟

d = x2 − x1( )2 + y2 − y1( )2

a+ b( ) a− b( )

a2 + 2ab+ b2

ac− b

−aba−1

or ab1− a

ab⋅dc

y =mx + b

m =y2 − y1x2 − x1

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Quadratics

Standard Form

y =

Vertex

x = y =

Methods to find the x-intercepts

1) 2)

Quadratic Formula

x =

Vertex Form

y =

Vertex

( , )

x-intercepts

Factored Form

y =

Vertex

x = y =

x-intercepts

y = substitute for x

1) Try factoring

2) Quadratic formula

(h,k)

x = h± −ka

y= substitute for x

or

y = ax2 + bx + c

x = − b2a

−b2a

x = −b± b2 − 4ac2a

y = a(x − h)2 + k

y = a(x − p)(x − q)

x = p+ q2

p+ q2

x = p x = q

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Trigonometry

sinθ =

cosθ =

tanθ =

Given: opposite and adjacent Use _______ to find θ .

Given: adjacent and hypotenuse Use _______ to find θ .

Given: opposite and hypotenuse Use _______ to find θ .

Most Common Pythagorean Triples

Circles

Standard Equation

Center Point

Radius

opphyp

adjhyp

oppadj

tan−1 oppadj

⎛

⎝⎜

⎞

⎠⎟

cos−1 adjhyp⎛

⎝⎜

⎞

⎠⎟

sin−1 opphyp⎛

⎝⎜

⎞

⎠⎟

3-4-5 (and multiples)

5-12-13 (and multiples)

(h, k) r

(x − h)2 + (y− k)2 = r2

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Radians

Degree and Radian Conversion Formula

Arc Length (in Radians)

s =

Sector Area (in Radians)

A =

Arc Length (in Degrees)

s =

Sector Area (in Degrees)

A =

Imaginary Numbers

i =

i2 =

i3 =

i4 =

Complex Numbers

Conjugate of a+ bi

Conjugate of a− bi

A = r

2θ2

A = θ360

⋅πr2

−1

−1 −i 1

a− bi a+ bi

deg180

=radπ

s = rθ

s = θ360

2πr

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Exponent Rules

xaxb =

xa

xb=

xa( )b=

x−a =

x0 = (for x ≠ 0 )

xy( )a =

xy⎛

⎝⎜⎞

⎠⎟

a

=

xy⎛

⎝⎜⎞

⎠⎟

−a

=

xab =

or

Exponential Growth

Exponential Growth Formula

Initial Value

Rate of Change

xa+b xa−b

xab

1xa

1

xaya

xa

ya

ya

xa

xab or xb( )a

A(t) = A0 (1+ r)t

A0

r

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Radical Rules

xy =

xy

a x + b x =

a x − b x =

xab = or

Solve for x: x2 = a

Rates

Relationship between Distance, Rate, and Time

Relationship between Work, Rate, and Time

Averages

Average (Mean) of Items

of items of items

Undefined Values

Denominator is…

Expression under radical is...

x y

xy

a+ b( ) x

a− b( ) x

xab or xb( )a

x = ± a

d = rt w = rt

sum of items s number of items

Equal to 0

Less than 0