Mathematics Common Formula Sheet, Cheat Sheet of Mathematics

Download Mathematics Common Formula Sheet and more Cheat Sheet Mathematics in PDF only on Docsity! Math 123 Common Formula Sheet Financial Formulas Financial Formulas Simple Interest 𝐼 = 𝑃𝑟𝑡 𝐴 = 𝑃(1 + 𝑟𝑡) Compound Interest 𝐴 = 𝑃(1 + 𝑟 𝑛 ) 𝑛𝑡 Continuously compounded Interest 𝐴 = 𝑃𝑒𝑟𝑡 Annuities Value of an annuity compounded n times a year 𝐴 = 𝑃[(1+𝑟 𝑛 ) 𝑛𝑡 −1] ( 𝑟 𝑛 ) Regular Payments Needed to Achieve a Financial Goal 𝑃 = 𝐴(𝑟 𝑛 ) [(1+𝑟 𝑛 ) 𝑛𝑡 −1] Installment Loans Amount Financed = Cash Price – Down Payment Total Installment Price = Total of All Monthly Payments + Down Payment Finance Charge = Total Installment Price – Cash Price Loan Payment Formula for installment Loans 𝑃𝑀𝑇 = 𝑃(𝑟 𝑛 ) [1−(1+ 𝑟 𝑛 ) −𝑛𝑡 ] Effective Annual Yield 𝑌 = (1 + 𝑟 𝑛 ) 𝑛 − 1 Income Taxes Adjusted Gross Income = Gross Income – Adjustments Taxable Income = Adjusted Gross Income – (Exemptions + Deductions) Income Tax = Tax computation – Tax credits Average Daily Balance Step 1) Make a table that shows the beginning date of the billing period, each transaction date, and the unpaid balance for each date. Step 2) Add a column to the table that shows the number of days at each unpaid balance Step 3) Add a final column to the table that shows each unpaid balance multiplied by the number of days that the balance is outstanding Step 4) Find the sum of the products in the final column of the table. This dollar amount is the sum of the unpaid balances for each day in the billing period. Step 5) Compute average daily balance = sum of unpaid balances for each day in the period number of days in billing period Metric System Prefixes kilo – k kilometer = 1000 meters hecto – h hectometer = 100 meters deca – da decameter = 10 meters no prefix meter = 1.0 meter deci – d decimeter = 0.1 meters centi – c centimeter = 0.01 meters milli – m millimeter =0.001 meters Temperature Celsius to Fahrenheit 𝐹 = 9 5 𝐶 + 32 Fahrenheit to Celsius 𝐶 = 5 9 (𝐹 − 32) Celsius to Kelvin 𝐾 = 𝐶 + 273.15 Kelvin to Celsius 𝐶 = 𝐾 − 273.15 Conversions Tables Length 12 inches 1 foot 3 feet 1 yard 36 inches 1 yard 5280 feet 1 mile 1 inch 2.54 cm 1 foot 30.48 cm 1 yard 0.9 m 1 mile 1.6 km Area 1 sq. foot 144 sq. inches 1 sq. yard 9 sq. feet 1 acre 43,560 sq. feet 1 sq. mile 640 acres 1 sq. inch 6.5 sq. cm 1 sq. foot 0.09 sq. m 1 sq. yard 0.8 sq. m 1 sq. mile 2.6 sq. km 1 acre 0.4 hectare Capacity 2 pints 1 quart 4 quarts 1 gallon 1 gallon 128 ounces 1 cup 8 ounces 1 cubic yard ~200 gallons 1 cubic foot ~7.48 gallons 231 cubic inches ~1 gallons 1cm3 1mL 1 dm3 = 1000cm3 1 L 1 m3 1kL Weight 16 ounces 1 pound 2000 pounds 1 ton (T) 1 ounce 28 grams 1 pound 0.45 kilograms 1 ton(T) 0.9 tonne (t) Water Weight 1 cm3 1 g 1 dm3 1 kg 1 m3 1000kg = 1t Algebra Slope intercept form (line) 𝑦 = 𝑚𝑥 + 𝑏 Standard form (quadratic) 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0 The quadratic formula 𝑥 = −𝑏±√𝑏2−4𝑎𝑐 2𝑎 X-coordinate for the vertex of a parabola 𝑥 = − 𝑏 2𝑎 Geometry Trapezoid Area 𝐴 = 1 2 (𝑏1 + 𝑏2)ℎ Prism Volume 𝑉 = 𝐵ℎ Cylinder Volume 𝑉 = 𝜋𝑟2ℎ Pyramid Volume 𝑉 = 1 3 𝐵ℎ Cone Volume V= 1 3 𝜋𝑟2ℎ Sphere Volume 𝑉 = 4 3 𝜋𝑟3