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Flashcards covering key mathematical formulas, conversions, interest types, annuities, and probability rules from the Math 1001 Formula Sheet.

U.S. Customary Units of Length

Length equivalences in the U.S. Customary system: $12\,\text{in.} = 1\,\text{ft}$, $3\,\text{ft} = 1\,\text{yd}$, and $5280\,\text{ft} = 1\,\text{mi}$.

U.S. Customary Units of Weight

Weight equivalences in the U.S. Customary system: $16\,\text{oz} = 1\,\text{lb}$ and $2000\,\text{lb} = 1\,\text{ton}$.

U.S. Customary Units of Capacity

Capacity equivalences in the U.S. Customary system: $8\,\text{fl oz} = 1\,\text{c}$, $2\,\text{c} = 1\,\text{pt}$, $2\,\text{pt} = 1\,\text{qt}$, and $4\,\text{qt} = 1\,\text{gal}$.

Metric System Prefixes for Length

Metric length equivalences based on the meter: $1\,\text{km} = 1000\,\text{m}$, $1\,\text{hm} = 100\,\text{m}$, $1\,\text{dam} = 10\,\text{m}$, $1\,\text{dm} = 0.1\,\text{m}$, $1\,\text{cm} = 0.01\,\text{m}$, and $1\,\text{mm} = 0.001\,\text{m}$.

Metric System Prefixes for Mass

Metric weight equivalences based on the gram: $1\,\text{kg} = 1000\,\text{g}$, $1\,\text{hg} = 100\,\text{g}$, $1\,\text{dag} = 10\,\text{g}$, $1\,\text{dg} = 0.1\,\text{g}$, $1\,\text{cg} = 0.01\,\text{g}$, and $1\,\text{mg} = 0.001\,\text{g}$.

Metric System Prefixes for Capacity

Metric capacity equivalences based on the liter: $1\,\text{kL} = 1000\,\text{L}$, $1\,\text{hL} = 100\,\text{L}$, $1\,\text{daL} = 10\,\text{L}$, $1\,\text{dL} = 0.1\,\text{L}$, $1\,\text{cL} = 0.01\,\text{L}$, and $1\,\text{mL} = 0.001\,\text{L}$.

Customary to Metric Conversion (Length)

Length conversions between U.S. Customary and Metric systems: $1\,\text{in.} = 2.54\,\text{cm}$, $1\,\text{m} = 3.28\,\text{ft}$, $1\,\text{m} = 1.09\,\text{yd}$, and $1\,\text{mi} = 1.61\,\text{km}$.

Customary to Metric Conversion (Weight)

Weight conversions between U.S. Customary and Metric systems: $1\,\text{oz} = 28.35\,\text{g}$, $1\,\text{lb} = 454\,\text{g}$, and $1\,\text{kg} = 2.2\,\text{lb}$.

Customary to Metric Conversion (Capacity)

Capacity conversions between U.S. Customary and Metric systems: $1\,\text{L} = 1.06\,\text{qt}$ and $1\,\text{gal} = 3.79\,\text{L}$.

Simple Interest Formulas

Formulas for calculating simple interest $I = Prt$ and total accrued amount $A = P + I = P + Prt = P(1 + rt)$.

Compound Interest Formulas

Formulas for compound interest compounded $n$ times per year: $PV = \frac{FV}{\left(1 + \frac{r}{n}\right)^{nt}}$ and $FV = PV\left(1 + \frac{r}{n}\right)^{nt}$.

Annuity Variables

Key variables in annuity formulas where $PMT$ is equal payment amount, $n$ is total number of payments, and $i$ is interest rate per compounding period (annual interest rate / periods per year).

Ordinary Annuities

Annuities with payments made at the end of the period, defined by $FV = PMT \left[\frac{(1+i)^n - 1}{i}\right]$ and $PV = PMT \left[\frac{1 - (1+i)^{-n}}{i}\right]$.

Regular Payments to Reach a Financial Goal

Formula used to determine payments required to hit a goal amount in an ordinary annuity: $PMT = FV \left[\frac{i}{(1+i)^n - 1}\right]$.

Installment Loans

Loans with payment derived from the $PV$ formula for ordinary annuities: $PMT = PV \left[\frac{i}{1 - (1+i)^{-n}}\right]$.

Due Annuities

Annuities with payments made at the beginning of the period, defined by $FV = PMT \left[\frac{(1+i)^n - 1}{i}\right](1+i)$ and $PV = PMT \left[\frac{1 - (1+i)^{-n}}{i}\right](1+i)$.

Mutually Exclusive Events

Events that cannot happen at the same time, with probability calculated as $P(A\text{ or }B) = P(A) + P(B)$.

Not Mutually Exclusive Events

Events that can happen at the same time, with probability calculated as $P(A\text{ or }B) = P(A) + P(B) - P(A \cap B)$.