Math Formula Cheat Sheet, Cheat Sheet of Mathematics

Download Math Formula Cheat Sheet and more Cheat Sheet Mathematics in PDF only on Docsity! www.datbootcamp.com 1 Math Formula Cheat Sheet Distance/Rate Problems Distance = (rate)(time) Mnemonic: “DIRT” D = Distance R=Rate T=Time Average Rate = Total Distance Traveled Total Time *Important Formula Graphing Formulas Slope Formulas: y = mx + b , m = slope and b = y-intercept y2 – y1 = m(x2-x1) à m = 7897: ;89;: Parallel lines: Slopes must be equal Perpendicular lines: slopes will be negative reciprocal (flipped) Distance between two points = make a right triangle and solve for the hypotenuse, or: d = x= − x? = + y= − y? = Midpoint = average together the x values and the y values, or: m = [ x? + x= 2 , y? + y= 2 ] Conversions K = °C +273 and °F = F G °C + 32 0°C = 32°F and −40°C = −40°F 1 in = 2.54 cm 1 mile = 5280 ft 1 ft = 12 in 1 yard = 3 ft 1 m = 1.1 yd 1 kg = 2.2 lbs 1 lb = 454g = 16 ounces Dilution Problems 𝐶?𝑉? = 𝐶=𝑉= C = Concentration, V = Volume *Can use with any concentration unit (Molarity, molality, % concentration) Quadratic Equations For any equation in the format: 𝑎𝑥= + 𝑏𝑥 + 𝑐 = 0 𝑥 + 𝑦 = = 𝑥= + 2𝑥𝑦 + 𝑦= 𝑥 − 𝑦 = = 𝑥= − 2𝑥𝑦 + 𝑦= 𝑥 + 𝑦 𝑥 − 𝑦 = 𝑥= − 𝑦= Exponent Rules • (xa)(xb) = xa+b • ; U ;V = xa-b • (xa)b = xW×Y • (xb)(yb) = (xy)b • (; V 7V ) = (; 7 )b Log Rules • log (x) + log (y) = log (x ∙ y) • log (x) – log (y) = log (; 7 ) • loga(xb) = b ∙ logW(x) • When solving a log problem, remember: o log x = b can be solved as x = 10b Percent Increase/Decrease: ;8 –;: ;: ×100% = percent change Percent Increase/Decrease Word Problems “of” = multiplication “equal to” = equal sign Example: 30% of 100 is equal to x (0.30)(100) = x www.datbootcamp.com 2 Data Sets ∪ = union. Includes all data but excludes duplicate values Ex) x = {1,2,3} and y = {1,3,4} X∪Y= {1,2,3,4} ∩ = intersection. Includes only data that exists in both x and y. Ex) x = {1,2,3} and y = {1,3,4} X∩Y= {1,3} Probability Combination vs. Permutation: You use combination when the order does not matter. (B,C,A / A,B,C / C,B,A are the same) You use permutation when the order does matter. (B,C,A / A,B,C / C,B,A are not the same) Combination formula = b! b9d ! (d!) n = number of objects from which you can choose k = number of objects to be chosen Permutation formula = b! b9d ! Dice Problems Rolling 2 Dice: Total number of permutations = (6)(6) = 36 Ex) What is the probability of rolling two dice and having the two numbers add to 4? Three possibilities: 2+2, 1+3, and 3+1. Therefore probability = 3/36 = 1/12 Deck of Cards Total # of Cards = 52 (without jokers) 4 suits (heart, club, ace, diamond) 13 cards per suit With Replacement – Total number of cards must go back to 52 and cards of interest must go back to initial amount Without Replacement – Must decrease total number of cards by 1 and decrease number of cards of interest by one Ex) Probability of pulling 3 spades in a deck without replacement? ?e G= × ?= G? × ?? Gf = ee =GGf Letter Problems Ex) How many ways can the letters in APPALOOSA be arranged? If no repeating letters = 9! If repeating letters, we must divide by the factorials of numbers of repeats: Repeats of A = 3 Repeats of P = 2 Repeats of O = 2 Number of Total Probability = F! e!×=!×=! = 15120 Statistics Mean: average Median: middle number of a set of data (remember to order them numerically and then find the middle number) Mode: number that occurs most often in a set st. dev = σ = Σ(x − xWjk)= N variance = 𝜎=