MATH 109E - Useful Formulas & Resources

A comprehensive collection of formulas and definitions including statistics, probability, finance, and geometry from the MATH 109E resources.

Mean

$$\bar{x} = \frac{\sum x}{n}$$

Weighted mean

$$\bar{w} = \frac{\sum(x \cdot f)}{\sum f}$$

Standard deviation

$$s = \sqrt{\frac{\sum(x - \bar{x})^2}{n-1}}$$

Permutation

$$P = \frac{n!}{(n-r)!}$$

Combination

$$C = \frac{n!}{r!(n-r)!}$$

Addition rule of probability

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Conditional probability

$$P(B|A) = \frac{P(B \cap A)}{P(A)}$$

Probability of a complement

$$P(\text{not } E) = 1 - P(E)$$

Simple interest

$$I = Prt$$

Future value for simple interest

$$A = P(1 + rt)$$

Future value for compound interest

$$A = P(1 + \frac{r}{n})^{nt}$$

Effective yield

$$Y = (1 + \frac{r}{m})^m - 1$$

Payoff amount

$$(K + 1)R - u$$

Finance charge per $\$100$ financed

$$\frac{\text{finance charge}}{\text{amount financed}} \times 100$$

Volume of a Box

$$V = lwh$$

Surface Area of a Box

$$S = 2lw + 2lh + 2hw$$

Volume of a Cube

$$V = s^3$$

Surface Area of a Cube

$$S = 6s^2$$

Volume of a Right Circular Cylinder

$$V = \pi r^2 h$$

Surface Area of a Right Circular Cylinder

$$S = 2\pi rh + 2\pi r^2$$

Volume of a Sphere

$$V = \frac{4}{3}\pi r^3$$

Surface Area of a Sphere

$$S = 4\pi r^2$$

Volume of a Right Circular Cone

$$V = \frac{1}{3}\pi r^2 h$$

Surface Area of a Right Circular Cone

$$S = \pi r \sqrt{r^2 + h^2} + \pi r^2$$

Volume of a Pyramid

$V = \frac{1}{3}Bh$ where $B$ is area of base

Area of a triangle

$$A = \frac{1}{2} bh$$

Area of a rectangle

$$A = bh$$

Area of a parallelogram

$$A = bh$$