ACT Math Formulas

Sum of interior angles of a polygon with n sides is

(n-2)*180degrees

Measure of each interior angle of a regular polygon with n sides is

(n-2)*180degrees / n

Triangle Area

A = ½ h*b

Rectangle Area

A = l*w

Rectangle perimeter

P = 2(l+w)

Square Area

A = a²

Square Perimeter

P = 4a

Parallelogram Area

A = b*h

Trapezoid Area

A = ½ *h(b₁+b₂)

Cylinder Volume

V = pi * r² * h

Cylinder Surface Area

2*pi*r²+2*pi*r*h

Rectangular Solid Volume

V = l * w * h

Rectangular Solid Surface Area

A = 2wl + 2wh + 2lh

Rectangular Solid Longest Diagonal

d = square root (a²+b²+c²)

Pythagorean Theorem

a²+b²=c²

30-60-90 Triangle lengths

a = length (touching 60 degrees)

a root 3 = base (touching 30 degrees)

2a = hypotenuse

45-45-90 Triangle

a = length

a = base

a root 2 = hypotenuse

Third side of a triangle rule

a + b > c

c is the longest side

A triangle is obtuse if..

a²+b²<c²

c is the longest side

A triangle is acute if..

a²+b²>c²

c is the longest side

Circumference of a Circle

C = 2*pi*r

C = pi*d

Area of a Circle

A = pi*r²

Slope-intercept form of line

y=mx+b

To find the y-intercept of a line..

Set x=0, solve for y

To find the x-intercept of a line:

Set y=0, solve for x

Slope formula

m = y₂-y₁ / x₂-x₁

Slope of horizonal line

is always =0

Slope of a vertical line

undefined

Parallel lines have..

the same slope

Perpendicular lines have..

negative reciprocal slopes

(2→-1/2)

Midpoint Formula

x _m=1/2(x₁+x₂)

y_m=1/2(y₁+y₂)

M = ((x₁+x₂)/2),((y₁+y₂)/2)

Distance Formula

d = square root ((x₂-x₁)² +(y₂-y₁)²)

Equation of a circle in the coordinate system

(x-h)²+(y-k)²=r²

Center (h,k)

Radius= r

x-axis reflection

(x,-y)

y-axis reflection

(-x,y)

the orgin yields

(-x,-y)

Quadratic Formula

Root of equation: ax²+bx+c=0

x= -b±square root (b²-4ac) / 2a

Standard form of a parabola

y = ax²+bx+x

Vertex form of a parabola with vertex (h,k)

y=a(x-h)²+k

Percent of

is/of = %/100

Percent greater than

new/original = (100+%) / 100

Percent less than

new/original = (100-%)/100

x⁰ =

1

x^-n =

1/xⁿ

(xⁿ)^m =

x^nm

xⁿyⁿ=

(xy)ⁿ

xⁿx^m=

x^n+m

xⁿ/x^m

x^n-m

x^1/n=

square root of n (x)

Arithmetic Sequences

nth term in the sequence: a_n=a₁+(n-1)d

First term a₁

Common difference d

Sum of first n terms S_n=(a₁+a_n)n/2

Geometric Sequences

nth term in the sequence: a_n=a₁r^n-1

First term a₁

Common ratio r

Average

total / #

Median

The middle number (or average of the two middles) of an ordered set of numbers

Mode

The number which occurs most often in a set of numbers

Standard Deviation

Measurement of how spread out numbers are from the middle of a set

Expected Value

The weighted average of a set

Probability = or

add the probabilities

Probability = and

multiply the two probablilities

Real number

any number that can be expressed on a number line (whether rational or irrational)

Volume of a Cone

v=1/3*pi*r²*h

Volume of Cube Triangle

V = 1/3*b*h

(x/y)ⁿ

xⁿ/yⁿ

Probability

# of successes / total possible outcomes

Point-slope form

y-y₁=m(x-x₁)

(x₁,y₁) is a point

Standard Form

Ax+By=C

log_bx=n

bⁿ=x