ACT Math Formulas

Midpoint Formula

(x₁+x₂)/2, (y₁+y₂)/2

FOIL

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

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

Percent Formula

Part=Percent x Whole

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

Negative Exponent

X⁻ⁿ = 1/Xⁿ

Multiply Power Exponents

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

Area of square

area = (side)²

Circumference of a circle

area = 2πr

Area of parallelogram

area= base x height

Area of rectangle

area= length x width

Area of a Triangle

area= ½ (base)(height)

Quadratic Equation

ax²+bx+c= 0 EX: x²+ 9x+ 18=0

Factoring Difference of squares

a²-b² = (a-b) (a+b)

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

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

Raising Power to Powers

multiply the exponents EX: X² · X³ = X⁶

Dividing Power Exponents

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

Slope Intercept

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

Absolute Value

|-3| = 3

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

Area of a circle

πr²

Rational Exponent

ⁿ√x