Math Formula Cheat Sheet - DAT Bootcamp

Math Formula Cheat SheetDistance/Velocity problemsDistance (velocity)(time)Average  velocity total  distance  traveledtotal  time*Important formulaGraphing formulasy mx by – y1 m(x-x1)Distance between two points make a right triangle and solve for thehypotenuseMidpoint average together the x values and the y values, or:X! X !Y! Y!M ,22ConversionsK C 273! F ! 𝐶 321 in 2.5 cm1 m 1.1 yd1 lb 454g1 kg 2.2 lbsExponent Rules (Xb)(Yb) (XY)b (Xb/Yb) (X/Y)b (Xn)(Xm) Xn m Xn/Xm Xn-mwww.datbootcamp.com1

Log Rules log (X) log (Y) log (XY) log (X) – log (Y) log (X/Y) n*log (X) log (Xn) When solving a log problem, remember:o log X b can be solved as X 10bPercent Increase/Decrease:[(X2 –X1)/X1] *100% percent changeProbability and StatisticsCombination vs. Permutation:You use combination when the order does not matter.You use permutation when the order does matter.Combination formula Permutation formula 𝑠𝑡. 𝑑𝑒𝑣 𝜎 !!!!! !    !!!!!!! !𝛴(𝑥 𝑥!"# )!𝑁variance 𝜎 !In a normal (or Gaussian) distribution, 68% of the data fall within 1 standarddeviation of the mean. 95% of the data fall within 2 standard deviations ofthe mean, and 99.7% of the data fall within 3 standard deviations of themean.www.datbootcamp.com2

GeometryArea formulasCircle πr2Sphere 4 πr2Hollow cylinder 2 πrhEllipse πabTriangle (1/2)bhRhombus bhEquilateral triangle !! !S side of triangle!Area of a regular polygon (1/2) N sin(360/N) S2Sum of interior angles (N-2) 180N number of sides, S length from center to a cornerVolume FormulasSphere (4/3) πr3Cylinder πr2hEllipseAssuming the major axis is the x-axisbacf2a major axisb minor axisc distance from center to focus (f2 in this example)Area of Ellipse πab𝑥! 𝑦! 1𝑎! 𝑏!c2 a2 – b2www.datbootcamp.com3

Trigonometrysin A oppositehypotenusecsc A hypotenuse1 oppositesin Acos A adjacenthypotenusesec A hypotenuse1 adjacentcos Atan A oppositeadjacentcot A adjacent1 opposite tan Asin A tan Acos Asin A cos(90 A)cos A sin(90 A)sin A sin Acos A cos  (A)sin  2A 2 (sin A) (cos A)cos  2A cos !  A   sin!  𝐴sin! A cos !  A 1*Know how to rearrange this identity, for example dividing this identity bysin2A gives:1 cot ! A   csc ! Awww.datbootcamp.com4

Unit Circlewww.datbootcamp.com5

Must know trianglesLaw of Sinesabc sin(A) sin(B) sin(C)www.datbootcamp.com6

Combined Work QuestionsEx. “If Tom gets a job done in 4 hours (t1) and Jerry gets it done in 3 hours (t2),how many hours does it take to get the job done working together (ttotal)?”1 1 11 𝑡! 𝑡! 𝑡!𝑡!"!# Simple and Compound InterestSimple InterestI PRTI interestP principalR annual rateT time in yearsCompound InterestFV PV (1 r)nFV future valuePV present valuer annual interest raten number of periodsex. If the interest is compounded quarterly (every 3 months), and the lengthof the investment is one year, then n 4 periods.www.datbootcamp.com7

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 y 2 – y 1 m(x 2-x