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23 terms

ACT Math Formulas

STUDY
PLAY
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