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SAT Math Formulas You Should Know

The key SAT Math formulas in flashcard form: algebra, geometry, coordinate geometry and data.

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Quadratic formula

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Quadratic formula

For

a x^{2} + b x + c = 0

:

$

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

Discriminant and number of real solutions

b^{2} - 4 a c

: positive → 2 real solutions; zero → 1; negative → none.

Slope of a line through

(x_{1}, y_{1})

and

(x_{2}, y_{2})

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

Slope-intercept form

y = m x + b

, where

m

is the slope and

b

the

y

-intercept.

Distance between two points

d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

Midpoint of a segment

(\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})

Vertex form of a parabola

y = a (x - h)^{2} + k

has its vertex at

(h, k)

Pythagorean theorem

In a right triangle:

a^{2} + b^{2} = c^{2}

, with

c

the hypotenuse.

30-60-90 triangle side ratio

Short leg

x

, long leg

x 3

, hypotenuse

2 x

45-45-90 triangle side ratio

Legs

x

and

x

, hypotenuse

x 2

Area of a circle

A = π r^{2}

Circumference of a circle

C = 2 π r

Arc length (angle

θ

in degrees)

arc = \frac{θ}{360} \cdot 2 π r

Area of a triangle

A = \frac{1}{2} bh

Area of a trapezoid

A = \frac{1}{2} (b_{1} + b_{2}) h

Sum of interior angles of an

n

-sided polygon

(n - 2) \cdot 18 0^{\circ}

Volume of a cylinder

V = π r^{2} h

Volume of a cone

V = \frac{1}{3} π r^{2} h

Volume of a sphere

V = \frac{4}{3} π r^{3}

Percent change

\frac{new - old}{old} \times 100%

Compound growth

A = P (1 + r)^{t}

for a rate

r

per period over

t

periods.

Arithmetic sequence,

n

th term

a_{n} = a_{1} + (n - 1) d

Geometric sequence,

n

th term

a_{n} = a_{1} \cdot r^{n - 1}

Mean of a data set

Sum of the values ÷ number of values.

Product rule for exponents

x^{a} \cdot x^{b} = x^{a + b}

Power of a power

(x^{a})^{b} = x^{ab}

Difference of squares

a^{2} - b^{2} = (a - b) (a + b)

Perfect-square trinomial

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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