ACT Math Formulas

Vertical angles are..

congruent

Adjacent angles are…

supplementary

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 = 2l*2w

Square Area

A = s²

Square Perimeter

P = 4s

Parallelogram Area

A = b*h

Trapezoid Area

A = ½ *(b₁+b₂) *h

Right Circular Cylinder Volume

V = pi * r² * 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

a root 3 = base

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

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

= 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)

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

a⁰ =

1

a^-x =

1/a^x

(a^x)^y =

a^xy

a^xb^x=

(ab)^x

a^xa^y=

a^x+y

a^x/a^y

a^x-y

a^1/x=

square root of x (a)

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

sum of things / number of things

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)