SAT Math Formulas

Vertex Form of a Parabola/Quadratic

y=a(x-h)²+k

where (h,k) are the coordinates for the vertex

Distance Formula

d=√(x2-x1)²+(y2-y1)²

Quadratic Formula

(-b±√b²-4ac)/2a

Exponent Rule (Multiplication)

a³a²=a⁵

Exponent Rule (Division)

a⁴/a¹=a³

Exponent Rule (Power Raised to a Power)

(a²)³=a⁶

Binomial Product 1—Difference of Squares

(x-y)(x+y)=x²-y²

Binomial Product 2—Perfect Squares Trinomial (Positive)

(x+y)²=x²+2xy+y²

Binomial Product 2—Perfect Squares Trinomial (Negative)

(x-y)²=x²-2xy+y²

Complex Conjugate

(a+bi)(a-bi)=a²+b²

Exponential Growth and Decay

y=a(1±r)ⁿ

Simple interest

A=Prt

P=principal amount, r=interest date as a decimal, t=time

Compound interest

A=P(1+ r/n)^nt

How to calculate standard deviation

1. Step 1: Find the mean.

2. Step 2: Subtract the mean from each score.

3. Step 3: Square each deviation.

4. Step 4: Add the squared deviations.

5. Step 5: Divide the sum by one less than the number of data points.

6. Step 6: Take the square root of the result from Step 5.

Degrees to Radians

π/180

Radians to degrees

180/π

3-4-5 triangle

is a right triangle with side lengths in a ratio of 3:4:5

5-12-13 triangle

is a right triangle with side lengths of 5, 12, and 13 feet

Arc Length

s=r∅

Area of a sector

A=(∅/360)×πr² or A=(1/2)∅r²

Area of an Equilateral Triangle

A=(√3/4)s²

Midpoint formula

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