ACT Math Formulas and Vocab

All the math formulas needed to smash the math section of the ACT!

midpoint

midpoint

add end points together and divide by two

distance

√(x-x)²- (y-y)²

slope

rise/run

slope-intercept

y=mx+b

point slope

y-y1=m(x-x1)

circle

(x-h)²+(y-k)²=r²

ellipse

((x-h)²/a²)+((y-k)²/b²)=1

volume of cube

s³

volume of rectangular prism

lwh

volume of triangular prism

1/2lwh

volume of cylinder

πr²h

volume of cone

1/3πr²h

volume of sphere

4/3πr³

area of square

s²

area of rectangle

lw

area of triangle

1/2bh

area of trapezoid

1/2(b1+b2)*h

surface area of rectangular prism

2lw+2wh+2lh

surface area of cube

6s²

circumference of circle

2πr

area of circle

πr²

degrees to radians

180°=1 radian

similar triangles

same angles different side lengths

Imaginary (complex) numbers

i²=-1

i^4=1

Integers

positive whole numbers

Absolute Value

The positive distance on a number line from 0

[3]=3, [-3]=3, [3-5]=[-2]=2

Logarithm

logB A=P, B^P=A

log2 8=3, 2³=8

PEMDAS

The preformed order of operations

1.Parentheses, 2.Exponents, 3.Multi, 4.Divide, 5.Add, 6. Subtract

Commutative Property

a + b = b + a

a x b = b x a

Associative Property

a+(b+c) = (a+b)+c

a x (b x c)=(a x b) x c

Distributive Property

a x (b+c)=(a x b) + (a x c)

Percent Change

% Change= (amount of change/original amount) x 100%

Sale Price

initial $ - discount OR

(initial $ - % discount) x initial price

FOIL (First, Outer, Inner, Last)

(x+5) (x+2)= x² - 2x + 5x - 10 → x² + 3x - 10

Factoring Quadratic

Given: ax² + bx + c = 0

x² + 9x + 18 = 0 → (x+6) (x+3) = 0 → x = -6,-3

Quadratic Formula

x = -b + √b² - 4ac / 2a

Discriminant

b² - 4ac

b² - 4ac > 0, there are 2 solutions

b² - 4ac < 0, there are NO solutions

b² - 4ac = 0, there are 1 solution

vertical angles

m<1 = m<3, m<2 = m<4

m<1 + m<3 = 180° , m<2 + m<4 =180°

SOH CAH TOA

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent

CSC SEC COT

csc = hypotenuse/opposite

sec = hypotenuse/adjacent

cot = adjacent/opposite

triangle degrees of SOH CAH TOA

sin 30° = ½ sin 60°=√3/2

cos 30° = √3/2 cos 60°= 1/2

tan 30°= 1/√3 tan 60°=√3

special right triangles

45° - 45° - 90°,

hypotenuse = x√2 , sides = x

30° - 60° - 90°

hypotenuse = 2x , adjacent(of 30°)= x√3 , opposite(of 30°) = x