SAT Math Rules and Equations

Linear Equations - One Solution

There is only one value that works for the variable of X.

Linear Equations - No Solution

There is no variable that works for the variable of X.

Linear System of Equations - How to solve for No Solution problem?

Rearrange the variable so that it cancels out on both sides. Then, the equation should have two numbers that don’t equal each other as the remaining equation.

Linear Equations - Infinite Solutions

When any number works for the variables.

Linear System of Equations - How to solve for Infinite Solutions

When the variables cancel out on both sides and what remains is true. For example, when the variable cancels out and what remains is true.

Exponential Growth / Decay Formula (General Form)

y = ab^x

A is the Starting Value

B is the growth of decay factor (ratio / rate)

X is the number of time intervals

Exponential Growth / Decay Formula (Over Time)

f(x) = a(1+r)^x

A is the Starting Value

R is the growth or decay rate (Positive = growth, Negative = Decay)

X is the number of time intervals

Quadratic Formula - Standard Form

y = ax²+bx+c

c is the y-intercept

Quadratic Formula - Factored form

y = a (x-m)(x-n)

M and N are the zeros or x-values when y = 0

Quadratic Formula - Vertex Form

y = a(x-h)²+k

The Vertex is (h,k)

Quadratic Discriminant

b² - 4ac

Discriminant Number of Solutions - Discriminant is Positive

Discriminant - Two Real Solutions

Discriminant Number of Solutions - Discriminant is Zero

Discriminant - One Real Solution

Discriminant Number of Solutions - Discriminant is Negative

Discriminant - No real Solution