SAT Formulas

Slope of a Line

m = (y2-y1)/(x2-x1)

Slope-Intercept Form

y = mx+b

Point-Slope Form

y-y1 = m(x-x1)

Midpoint Formula

midpoint = (((x1+x2)/2), ((y1+y2)/2))

Distance Formula

distance = sqrt((x2-x1)²+(y2-y1)²)

Length of an Arc

length = (n/360)2pir

Area of a Sector

area = (n/360)pir²

Quadratic Formula

x = (-b±sqrt(b²-4ac))/2a
y = ax²+bx+c

SOHCAHTOA

Sin = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent

Probability

# of favorable outcomes/total number of outcomes

Circle Equation

(x-h)²+(y-k)²=r²
h = x coordinate of the middle of the circle
k = y coordinate of the middle of the circle

Exponential Growth

y = a(1+r)^t
a = initial value
r = rate
t = time

Vertex of a Parabola

x = -b/2a
“banana” in the quadratic formula

Vertex Form

a(x-h)²+k
vertex = (h, k)

Pythagorean Theorem

a²+b² = c²

Distance = Rate x Time

d = rt

Sine & Cosine

sin(x) = cos(90-x)

Discriminant

b²-4ac

b²-4ac < 0 | no real solutions
b²-4ac = 0 | 1 real solution
b²-4ac > 0 | 2 real solutions

Pythagorean Triples

3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17
can be multiples of any of these too

Perpendicular Slope

opposite reciprocal
neg → pos or pos → neg, then swap numerator/denominator

Sum of Angles

sum = (n-2)180
n = number of sides