ACT Math Formulas ALL SOLUTIONS 100% CORRECT SPRING FALL-2023/24 EDITION AID GRADE A+

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 CONTINUED...