ACT Math Formulas

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

Slope Intercept

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

Quadratic Equation

ax²+bx+c= 0

EX: x²+ 9x+ 18=0

Quadratic Formula

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

Negative Exponent

X⁻ⁿ = 1/Xⁿ

Rational Exponent

ⁿ√x

Absolute Value

|-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 of square

area = (side)²

Circumference of a circle

area = 2πr

Area of a circle

πr²