# ACT Math Formulas and Vocab

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midpoint

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## Description and Tags

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

### 42 Terms

1

midpoint

add end points together and divide by two

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2

distance

√(x-x)²- (y-y)²

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3

slope

rise/run

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4

slope-intercept

y=mx+b

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5

point slope

y-y1=m(x-x1)

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6

circle

(x-h)²+(y-k)²=r²

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7

ellipse

((x-h)²/a²)+((y-k)²/b²)=1

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8

volume of cube

s³

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9

volume of rectangular prism

lwh

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10

volume of triangular prism

1/2lwh

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11

volume of cylinder

πr²h

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12

volume of cone

1/3πr²h

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13

volume of sphere

4/3πr³

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14

area of square

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15

area of rectangle

lw

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16

area of triangle

1/2bh

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17

area of trapezoid

1/2(b1+b2)*h

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18

surface area of rectangular prism

2lw+2wh+2lh

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19

surface area of cube

6s²

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20

circumference of circle

2πr

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21

area of circle

πr²

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22

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23

similar triangles

same angles different side lengths

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24

Imaginary (complex) numbers

i²=-1

i^4=1

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25

Integers

positive whole numbers

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26

Absolute Value

The positive distance on a number line from 0

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

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27

Logarithm

logB A=P, B^P=A

log2 8=3, 2³=8

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28

PEMDAS

The preformed order of operations

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

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29

Commutative Property

a + b = b + a

a x b = b x a

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30

Associative Property

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

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

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31

Distributive Property

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

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32

Percent Change

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

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33

Sale Price

initial \$ - discount OR

(initial \$ - % discount) x initial price

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34

FOIL (First, Outer, Inner, Last)

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

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35

Given: ax² + bx + c = 0

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

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36

x = -b + √b² - 4ac / 2a

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37

Discriminant

b² - 4ac

b² - 4ac > 0, there are 2 solutions

b² - 4ac < 0, there are NO solutions

b² - 4ac = 0, there are 1 solution

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38

vertical angles

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

m<1 + m<3 = 180° , m<2 + m<4 =180°

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39

SOH CAH TOA

sin = opposite/hypotenuse

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40

CSC SEC COT

csc = hypotenuse/opposite

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41

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

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42

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

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