SAT Math Cheat Sheet

Slope of a line formula

M = rise/run or (y2 - y1)/(x2 - x1

Slope-intercept form (equation of the line)

y=mx + b

m = slope

b = y-intercept

Point slope formula

y- y1 = m(x - x1)

m = slope

(x1, y1) = any point on the line

Midpoint Formula (middle point between two points)

(x1 + x2)/2 + (y1 + y2)/2

(x1,y1) = first point

(x2, y2) = second point

Length of an Arc of a Circle

L = [n/360] 2πR

n = central angle

R = radius

Distance Formula (distance between any two points on the xy-plane, can be used for circles)

D = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Quadratic Formula

Quadratic Formula -b +/- sqrt(b^2 - 4ac)/2a

A = x^2 coefficient

B = x coefficient

C = constant

Area of a sector of a circle

A = [n/360]πR^2

n = central angle

R = Radius

SOHCAHTOA

SIN =(Opposite/Hypotenuse)

COS= (Adjacent/Hypotenuse)

TAN= (Opposite/Adjacent)

Circle Equation

(x - h)^2 + (y - k)^2 = r^2

(h,k) = center of circle

r = radius of circle

Exponential Growth formula

y = a (1+/-r)^t

a = Initial value

r = Growth rate

t = Time (usually years *AKA convert to years)

Vertex of a parabola

-b/2a

a = x^2 coefficient

b = x coefficient

Vertex Form of a Quadratic

y = a(x - k) + k

a = x^2 coefficient

(h,k) = vertex

Standard quadratic form

ax^2 + bx + c = 0

Speed/ rate formula

D = R * T

d = distance

R = rate/speed

t = time

Make sure r & t are using the same unit of time rate formula

Pythagorean Theorem (right triangle)

a^2 + b^2 = c^2

a & b = legs

c = hypotenuse

Sin and Cosine

Sin (x) = Cos( 90 - x)

Cos (x) = Sin (90 - x)

Sin of an angle = cosine of its complement

The Discriminant of a Quadratic

b^2-4ac

a = x^2 coefficient

b = x coefficient

c = constant

sum of solutions of quadratic equation

-b/a

a = x^2 coefficient

b = x coefficient

(Use when asked for the sum of the solutions to a quadratic)

Area of an Equilateral Triangle

(S^2 (sqrt of 3))/4

s = side length

Pythagorean Triples for Right Triangles

Common Triples

3,4, 5

6, 8, 10

5, 12, 13

7, 24, 25

8, 15, 17

Sum of Interior Angles of a Polygon

Sum = (n - 2) * 180

N = number of sides of the polygon

Perpendicular Slope

perpendicular slope = negative reciprocal

slope = a/b

perpendicular slope = -b/a

Degrees to Radians

Radians = Θ * π/180

Θ (theta) = given angle in degrees

Probability Formula

p = number of favorable outcomes/total number of outcomes

Change in percent formula

C = [(New value - old value)/old value] * 100

Standard Form of a Linear Equation

Ax + By = C

*convert to slope intercept form:

Ax + By = C

By = -Ax + c

y = -A/Bx + C/B

Average Formula

Average or mean = (sum of values)/total number of values

Median

The middle value in a data set.

Range

R = maximum (biggest) value - minimum (smallest) value in a data set

Mode

The value that occurs most frequently in a given data set.