Formula sheet

Bookmark formulas to build your personal reference sheet.

Applications

Quadratic discriminant

Δ=b²−4 ac

For a≠0: positive gives two distinct real roots; zero gives one repeated root.

Arithmetic series

Sₙ=n (first+last)/2

Identify the last included term before using the formula.

Trigonometric identity

sin²θ+cos²θ=1

The identity determines magnitudes; the quadrant determines signs.

Logarithm laws

log_b (xy)=log_bx+log_by; log_b (x/y)=log_bx−log_by

b>0, b≠1; arguments must be positive.

Power derivative and integral

d (xⁿ)/dx=nxⁿ⁻¹; ∫xⁿdx=xⁿ⁺¹/(n+1)+C, n≠−1

Use only where the expression and domain make these operations valid.

Conditional probability

P (A given B)=P (A and B)/P (B)

The conditioning probability must be nonzero.