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Math
| Question | Answer |
|---|---|
| compound interest formula | A= p (1 + (r/n)) ^nt A= what you earn/how much you need p = present value r = rate (change to dec) t = years n= # of times its compounded (annually, semiannually, etc) |
| logarithmic form VS exponential form | base ^exponet = ans Log base^ans =exponent |
| continuous compounding formula | A = Pe^rt e = button on calculator |
| anything to the power of __ is one | zero |
| Log properties | Logb^MN =logb^M+logb^N logb ^M/N = logbM - log b^n Logb^(M^k) = klogb^M log (X+Y) = can't be simplified |
| how to undo a log | log Y --> 10^x = Y |
| how to undo an e | loge^X = y e^(loge^X) = e^y x = e^y |
| radioactive decy formula | XYo = Yoe^(-0.0001216t) X = coefficient --> EX: if it says half life then put 0.5 there Yo = initial amount |
| when you have X as a exponent on both sides of the euqation | #^x+3 = #^2x take the log of both sides log # (X+3) = (log 5) (2x) |
| when to put the plus or minus symbol in front of your answer | when you clear an even exponent by taking an even root of both sides. |
| when to add the absolute value symbol in front of your answer | -radical rules: 1. even index 2. EVEN Exponent Inside the radical 3. ODD Exponent Outside: variable's power in final answer odd |
| Ln = Log base e | |
| what is the common difference | -represented by d -arithmetic sequence: a sequence where terms differ by a fxed number |
| formula for finding the nth term for arithmetic sequences | An = Ab + (n-b)d -always put the bigger number further to the left |
| what is the Sn and equation | -arithmetic series: sum of the erms of an erithmetic sequence Sn = n/2 (a1 + an) OR Sn = n/2 [2a1 + (n-1)d] |
| geometric sequence | a sequence in which each term after the 1st is multiplied by a common ratio (r) r = (x)/(term directly before x) |
| formula for finding the nth term for a geometric sequence | An = A1 (r^n-1) |
| how to find the sum of the first n terms in a geoseries | -r can't be equal to one Sn = a1 (1- r^n) -------------- 1 - r |
| how to find the sum of the terms in an infinite geosequence | Sinf = a1/(1-r) the absolute value of r must be less than one r = the number you multiply a term by to get the next one |
| summation notation | n ___ \ (Formula) /__ i=1 n = the ending point: the last term you plug into formula 1 = the starting point, the 1st term you plug into formula to get A1 |
| how to find n given a summation problem | top number - (bottom #) + 1 |
| when given a word problem on sequences, | if you are given a percent.... -it is always geometric -convert to decimal |
| pascel's triangle | start with 1 at row zero add up the terms nextt to each other to get the term that goes between them on the row below |
| how to use pascel's triangle to factor a binomial | -row number corresponds to power of binomial -the row shows coefficients of expanded binomial -first term in binomial: start w/ exponent and go to 0 -2nd term; zero--> exponent -note negatives go in the () |
| how to find the __ term in the expanded version of a binomial | (exponent of binomial)! ------------------------------ (power of 1st term in expanded form)!(power of 2nd)! -multiply the above answer by (first term)^(power from above)(second term)^(power from above) |
| how do you know if a geometric series converges | You know a geometric series converges if the absolute value of its common ratio (\(r\)) is strictly less than 1. |
| coterminal angles | their measures differ by a multiple of 360 -does a full circle around and ends up back at the same spot |
| sine wave formula | y = a sin b (x -c) + d |
| cosine curve | if a is positive, then it should be a dip if a is negative them it should be a hill -the period is the final point minus the initial point |
| sine wave variables | amp= |a| (the height above and below d) period = 360/b (point where the cycle ends) if a is +, then go up 1st increment length = per/4 c = where you start your graph (horizontal shift) d = vertical translation |
| csc or sec graph | -draw an asymptote (vertical dotted line) through any point on the d line -flip each hill/line inside the lines |
| tangent graph (positive a) | -have zero as one of your tick marks w/ two ticks on each side -the tan squiggle is centered at 0 and starts on the right -period = 180/b IL = per/4 (your 1st tick mark after 0) |
| cot graph (positive a) | period = 180/b IL = 280/4 -starts on the left - four of the five tick marks should be to the right of the origin |
| how to draw graphs from points | d = (high + low)/2 per = 360/b |
| when finding the approximate values of trig circular functions for CSC, Cot, and Sec, what do you do | csc x = 1/sin x -invert them! -remember to check the mode on your calculator (if there is a degree symbol, use degrees, if there is no symbol, use the radians mode -when solving triangle, always use degrees |
| given sm like : Cot theta = #, how to solve | tan-1(1/#) |
| Pythagorean identities | sin^2X + cos^2 X = 1 1 + tan2 X = sec 2 X 1 + cot^2X = Csc^2 X |
| tan (A+B) | Tan A + Tan B ---------------- 1- Tan A Tan B |
| cofunctions | complements (add up to 90) cos & sin Tan & cot Sec & CSC |
| sin 2A | 2 sinAcosA |
| Tan 2A | 2tan A ---- 1-tan^2A |
| cos 2A | Cos^2 A - Sin^2 A 1 - 2Sin^2 A 2Cos^2 A - 1 |
| when solving trigonometric equations for exact values, why can't you divide by an exponet | that is assuming that X is not equal to zero, eliminating the posibiliy that X = 0 |
| given a sequence, how to write using summation notation | 1. find r or d 2. write equation for An 3. put that formula in () next to the summation symbol 4. set the first and last term in the sequence equal to the formula to find the starting and ending terms |
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Blessed Rectangle 10