SAT Math Formulas

These are the math formulas you need to know for the SAT.

Area of a Circle

A=π*r²

Circumference of a Circle

C=2*π*r

Area of a rectangle

A=l*w

Area of a triangle

a=(1/2)*b*h

Pythagorean Theorem

a²+b²=c²

Volume of a rectangular prism

V=l*w*h

Volume of a cylindar

V=π*r²*h

Volume of a sphere

V=(4/3)*π*r³

Volume of a cone

V=(1/3)*πr²*h

Volume of a pyramid

V=(1/3)*l*w*h

Special right trialngles

Increase by a percent

multiply by (1+r)

where r is the percent in decimal form

Decrease by a percent

multiply by (1-r)

where r is the percent in decimal form

Simple interest

A=P(1+r*t)

where r is the percent in decimal form

Interest Compounded Annually

A=P(1+r)^t

where r is the percent in decimal form

Interest Compounded n times per year

A=P(1+(r/n))^(n*t)

Multiplication Rule for Exponents

Division Rule for Exponents

Power Rule for Exponents

Negative Exponents

Fractional Exponents

Quadratic formula

f(x)=ax²+bx+c

Factored out quadratic formula

a*(x-u)*(x-v)

u and v are the x-intercepts

x is the solution*

Vertex of a polabora

y-intercept

c

x-intercepts

Sum of solutions

(-b)/a

Discriminant

b²-4ac > 0 (two or more solutions)

b²-4ac = 0 (one real solution)

b²-4ac < 0 (no real solutions)

x-coordinate of vertex

(v+u)/2

Vertex form of a quadratic

f(x)=a(x-h)²+k

vertex: (h,k)

Difference of squares

a²-b²=(a+b)(a-b)

Perfect Square Trinomial

Completing the Square

Slope Formula

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

Slope of horizontal line

0

Slope of verticle line

undefined

Quadrents

Standard form for a line

Ax-By=C

Slope-Intercept Form

y = mx+b

Point-Slope Form

y - y1 = m*(x-x1)

Distance formula

Midpoint formula

True or False: Parallel lines do NOT have equal slopes

False

True or False: Perpendicular lines have equal slopes

False, their slopes are opposite reciprocals

Average formula

Median

The middle number in a data set

(ex. “1, 2, 3” the median is 2)

Range

maximum-minimum

Probability formula

True or False: Vertical angles are equal

True

True or False: Three angles of a triangle add up to 180˚

True

True or False: A radius and tangent make a right angle

True

Formula for a Circle

Area of a trapezoid

Sum of the interior angles

180(n-2)

n = number of sides

Sum of the exterior angles

360˚

Sine?

opposite/hypotenuse

Cosine?

adjacent/hypotenuse

Tangent

opposite/adjacent

360˚ is equal to how many radians?

2π radians

y=x

y=|x|

y=x²

y=x³

y=a^x

y=√x

Shift up by k units

f(x)+k

Shift down by k units

f(x)-k

Shift left by h units

f(x+h)

Shift right by h units

f(x-h)

Reflect over the x axis (flip upside down)

-f(x)

Stretch vertically by a factor of c (becomes skinnier)

cf(x)

Shrink vertically by a factor of c (becomes fatter)