Math Formula Reference
Algebra Formulas
Quadratic Formula
x = (-b ยฑ โ(bยฒ - 4ac)) / 2a
Used to find the roots of a quadratic equation axยฒ + bx + c = 0
Distance Formula
d = โ((xโ - xโ)ยฒ + (yโ - yโ)ยฒ)
Calculates the distance between two points (xโ, yโ) and (xโ, yโ)
Slope Formula
m = (yโ - yโ) / (xโ - xโ)
Finds the slope of a line passing through points (xโ, yโ) and (xโ, yโ)
Arithmetic Sequence
aโ = aโ + (n - 1)d
nth term of an arithmetic sequence with first term aโ and common difference d
Geometry Formulas
Area of Circle
A = ฯrยฒ
Area of a circle with radius r
Pythagorean Theorem
aยฒ + bยฒ = cยฒ
In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides
Volume of Sphere
V = (4/3)ฯrยณ
Volume of a sphere with radius r
Surface Area of Cylinder
SA = 2ฯrยฒ + 2ฯrh
Surface area of a cylinder with radius r and height h
Calculus Formulas
Power Rule
d/dx(xโฟ) = nx^(n-1)
Derivative of x raised to the power n
Chain Rule
d/dx[f(g(x))] = f'(g(x)) ยท g'(x)
Derivative of a composite function
Integration by Parts
โซu dv = uv - โซv du
Method for integrating products of functions
Fundamental Theorem of Calculus
โซโแต f(x)dx = F(b) - F(a)
Relates derivatives and integrals, where F'(x) = f(x)
Statistics Formulas
Mean (Average)
xฬ = ฮฃxแตข / n
Sum of all values divided by the number of values
Standard Deviation
ฯ = โ(ฮฃ(xแตข - xฬ)ยฒ / n)
Measure of spread in a dataset
Combination Formula
C(n,r) = n! / (r!(n-r)!)
Number of ways to choose r items from n items (order doesn't matter)
Normal Distribution
Z = (X - ฮผ) / ฯ
Z-score formula for standardizing normal distributions
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