SAT math notes

Area of a Trapezoid

((b₁+b₂)/2)h

Equation of a circle

(x-h)²+(y-k)²=r²

^{center: (h,k)}

^{radius: r (don’t forget to take square root)}

Midpoint formula

(x1+x2/2, y₁+y₂/2)

Standard deviation

the measure of how spread out the numbers are (especially relative to the average)

lots of variance- high standard deviation

little/no variance- low standard deviation

i_¹

i

i²

-1

i³

-i

i⁴

1

Discriminant formula

b²-4ac

use the discriminant when there is a reference to the number of solutions for a quadratic equation

If the discriminant is positive, how many solutions do you have?

Two real solutions

If the discriminant is zero, how many solutions do you have?

One real solution

If the discriminant is negative, how many solutions do you have?

No real solutions

Graph translations

• use desmos to graph the original function

• enter each choice in desmos and check which graph matches the shift

• if needed, use the table for exact measurements

Exponential vs Linear

If the slope is changing or inconsistent, the graph is exponential

Calculating percent change

absolute value difference between 0 and 1 value / original value

a² x a³

a⁵

add exponents when multiplying

x⁶/x²

x⁴

subtract exponents when dividing

(x²y³)⁵

x¹⁰y¹⁵

multiply exponents when raised to a power

b^-3

1/b³

negative exponent changes to reciprocal

1/m^-2

m²/1

negative exponent changes to reciprocal

f^2/5

⁵√f²

fractions as an exponent simplify to a square root

numerator stays attached to variable

denominator moves to outside square root

0³⁷⁶²

0

anything with zero in the base stays zero

x⁰

1

anything raised to zero is one