# ACT Math Formulas

### 23 terms by orestes9

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### Distance Formula

d=√(x₁-x₂)² + (y₁-y₂)²
(EX: Find distance between (5,6) and (1,3)
√(5-1)² + (6-3)²=
√(4)² + (3)²=
√16 + 9=
√25=
5=Distance

### Slope

Slope= Rise/Run=Change in Y/Change in X
(y₂-y₁/x₁-x₂)
(EX: Find slope of (5,6) and (1,3)
6-3/5-(-1)=
3/6=
1/2

y=mx+b
Ex: y=2/3x + 5

### Midpoint Formula

(x₁+x₂)/2, (y₁+y₂)/2

### PEDMAS

Parenthesis, Exponents, Multiplication, Division, Add, Subtract.
EX: 9-2 x (5-3)² + 6÷3=
9-2 x (2)² + 6÷3=
9-2 x (4) +6÷3=
9-8 +2=
9-6=
3

ax²+bx+c= 0
EX: x²+ 9x+ 18=0

²x = −b ± √b²-4ac/2a
EX: Solve using quadratic formula x²+ 9x+ 18=0:
x= −9±√(9)² − 4(1)(18)/2(1)
−9 ± √81 − 72/2
−9 ± √9/2
−9 ± √3/2 = -9 + 3/2 and -9 -3/2
-9+3/2= -3 and -9-3/2= -6

### Percent Formula

Part=Percent x Whole

### Multiply Power Exponents

add exponents and keep the same base
EX: X₃ · X₂ = X₅

### Dividing Power Exponents

subtract exponents and keep same base
EX: X₄ ÷ X₂ = X₂

### Raising Power to Powers

multiply the exponents
EX: X² · X³ = X⁶

X⁻ⁿ = 1/Xⁿ

ⁿ√x

|-3| = 3

### FOIL

First, Outside, Inside and Last.
EX: (x-3) + (x+5) =
x² + 5x -3x -15=
x² + 2x-15

### Factoring Difference of squares

a²-b² = (a-b) (a+b)

### Area of a Triangle

area= ½ (base)(height)

### Pythagorean Theorem

for all right triangles
(leg₁)² + (leg₂)² = (hypotenuse)² (a²+b²=c²)
Special Triangles
3-4-5
30-60-90
5-12-13
45-45-90

### Area of rectangle

area= length x width

### Area of parallelogram

area= base x height

area = (side)²

area = 2πr

πr²

Example: