SAT Math Formulas

Sum of roots

-b/a

Product of roots

c/a

Discriminant

D=b²-4ac

If D>0

2 real solutions

If D=0

1 real solution

If D<0

no real solution

Vertex form (quadratics)

y=a(x-h)²+k

Vertex coordinates

(h,k)

Equation of a circle

(x-h)²+(y-k)²=r²

(h, k) represents what?

center

r represents what?

radius

Exponential growth

y=a(1+r)^t

Exponential decay

y=a(1-r)^t

A means what?

initial amount

R means what?

rate (decimal)

T means what?

time

Area of a circle

A=πr²

Circumference

2πr

Area of triangle

1/2bh

Pythagorean theorem

a²+b²=c²

30 60 90 triangle

x, 2x, x root 3

45 45 90 triangle

x, x, x root 2

Volume of a cylinder

πr²h

Volume of a sphere

4/3πr³

Volume of a cone

1/3πr²h

Volume of a pyramid

1/3lwh

Midpoint formula

(𝑥1+𝑥2)2,(𝑦1+𝑦2)2)

Distance formula

[(𝑥2−𝑥1)2+(𝑦2−𝑦1)2]

Length of an arc

• 𝐿arc=(2𝜋𝑟)(degreemeasurecenterofarc/360)

Area of an arc sector

• 𝐴arcsector=(𝜋𝑟2)(degreemeasurecenterofarc/360)

Average Speed

total distance/total time

Probability of an outcome

number of desired outcomes/total number of possible outcomes

Find x percent of a given number n

n(x/100)

Find out what percent a number n is out of another number m

(n100)/m

Find out what number n is x percent of

(n100)/x

cos(x)

measure of the adjacent side to the angle/measure of the hypotenuse

sin(x)

measure of the opposite side to the angle/measure of the hypotenuse

tan(x)

measure of the opposite side to the angle/measure of the adjacent side to the angle