EXPONENT RULES Add Multiply Subtraction Flip

Transcription

1 Algebr II Finl Em Review Nme Chpter 7 REVIEW: EXPONENT RULES Add Multiply Subtrction Flip Simplify the epression using the properties of eponents. Assume ll vribles re positive RADICAL FORM « » RATIONAL EXPONENTS Write using rtionl eponents... Write in rdicl form

2 Write the epression using rtionl eponents Write the epression in rdicl form Evlute ech epression. (CALCULATOR) Write ech rdicl epression in SIMPLEST FORM. Assume ll vribles re positive. (Remember to mke your ldder OR fctor tree nd look for groups bsed on the inde.) 08 inde = y 8. 5 inde = b 9 inde = y inde =

3 Solve ech eqution. Remember to write both nswers when the rdicl hs n EVEN INDEX! Solve the eqution. Mke sure to check your nswer for ny etrneous solutions

4 Perform the opertions given f, g, h 5, nd j h g. g h. h g Find ech composition. g nd f 5. g f. f g Find the inverse of ech function. 4. ( ) 5 f 5. f 5 Grph the PARENT grph for both the squre root function nd the cube root function. 6. y h y k 0,,,,

5 7. y h y k -, 0,,, Grph the squre root nd cube root equtions nd then describe the trnsformtion from the prent grph. 8. y = SHRINK STRETCH FLIP h = RIGHT LEFT k = UP DOWN h y k 0,,,, 9. y = SHRINK STRETCH FLIP h = RIGHT LEFT k = UP DOWN h y k -, 0,,,

6 8. y = SHRINK STRETCH FLIP h = RIGHT LEFT k = UP DOWN h y k 0,,,, 9. y = SHRINK STRETCH FLIP h = RIGHT LEFT k = UP DOWN h y k -, 0,,,

7 Algebr II Finl Em Review Nme Chpter 8 REVIEW: Determine the bse (b) nd then circle whether the function represents eponentil growth or eponentil decy.. y 8 5. y. y 5 4 b = growth decy b = growth decy b = growth decy Determine the, b, h, k, s well s the eqution for the Horizontl Asymptote, nd if it represents growth or decy. Describe ny shifts on the line provided. Then, fill out the tble nd grph the function. Round ll decimls to two deciml plces. 4. y = b = Growth OR Decy h = k = HA = h y k, 0,,, 5. y = b = Growth OR Decy h = k = HA = h y k, 0,,,

8 6. y = b = Growth OR Decy h = k = HA = h y k, 0,,, 7. y 4 = b = Growth OR Decy h = k = HA = h y k, 0,,, 8. The grph of which function is shown?

9 Solve the following eponentil equtions. Check for ny etrneous solutions. Round to deciml plces. #9 nd #0 THE BASES ARE THE SAME! Solve the following eponentil equtions. Check for ny etrneous solutions. Round to deciml plces. # 4 THE BASES ARE NOT THE SAME! m

10 KNOW YOUR FORMULAS FOR THE FINAL EXAM. Below ech formul write wht ech one is used for. Mke sure to write them on your note sheet! y r t y r t A nt rt r P n A Pe 5. You buy new stereo system for $640. The vlue of the system decreses by 7% ech yer. Wht will the vlue of the stereo system be in yers? 6. You deposit $00 into n ccount tht pys % interest compounded qurterly. How much will be in your ccount fter 5 yers? 7. You deposit $000 in n ccount tht pys 5% nnul interest compounded continuously. Wht is the blnce in the ccount fter yers? 8. In 990, the popultion of town ws 00. If the popultion incresed by bout % ech yer, bout how mny people will live in the town fter 5 yers? LOG FORM « » EXPONENTIAL FORM Write using eponentil form... Write using logrithmic form... 9 Rewrite in logrithmic form Convert to eponentil form log log 6 6

11 Condense the epression.. log 7 log 7 4. log 7 log 7 log 6. log y log 7 5. log 5 4 Epnd the epression. 7. log y 5 8. log log y 0. log 7 Evlute ech epression. (Set ech epression equl to nd rewrite in eponentil form to help!). log 69. log 64. log log

12 Solve the following eponentil equtions. Check for ny etrneous solutions. Round to deciml plces. #5 nd #6 WHEN YOU CAN T REWRITE WITH THE SAME BASE! Solve the following logrithmic equtions. Check for ny etrneous solutions. Round ny decimls to the 00 th. #7 nd #8 WHEN THE BASES ARE THE SAME WITH LOGS on BOTH SIDES! 7. 9 log log 4 log log Solve the following logrithmic equtions. Check for ny etrneous solutions. Round ny decimls to the 00 th. #9 nd #40 WHEN THERE IS ONLY A LOG ON ONE SIDE! log 8 log 7

13 Algebr II Finl Em Review Chpter : REVIEW Nme SOH CAH TOA & CSC SEC COT Evlute the si trigonometric functions of the ngle θ shown in the tringle. (Answer should be simplified rtios!). Hypotenuse = Cos = Sec = Sin = Csc = Tn = Cot =. 8 7 Hypotenuse = Cos = Sec = Sin = Csc = Tn = Cot = Find the vlue of for ech missing side. Round your nswer to two deciml plces. (SOH CAH TOA) = = =

14 Find the vlue of ngle for the tringle. Round ngles to the nerest degree θ 5 7 θ (SOH CAH TOA) 0 θ = = = REVIEW: Fill in the ptterns below nd then use them to find the vlues of nd y y y y 5 45 = y = = y = = y = Solve the following word problems by drwing picture.. You len 0 foot ldder ginst wll. The bse of the ldder is 4 feet from the wll. Wht is the ngle of elevtion to the top of the ldder.. A flgpole csts shdow 0 feet long. The ngle of depression from the top of the flgpole is 6. Sketch digrm tht represents this sitution. Wht is the height of the flgpole? Round your nswer to the nerest hundredth.

15 Find one positive nd one negtive ngle tht is COTERMINAL with the given ngle. Angle + Angle Use clcultor to evlute the following. tn 6. cos sin Determine if the given trig function in the specified qudrnt is positive or negtive. 9. tngent in qudrnt II 0. sine in qudrnt IV. Cosine in qudrnt IV Use the given point on the terminl side of n ngle θ in stndrd position. Find the ect vlue of sine, cosine, nd tngent.. (8, 5). (, 4) Cos = Sin = Tn = Cos = Sin = Tn =

16 Convert to rdins. Convert to degrees. Multiply by: Multiply by: 7. Drw n ngle with the given mesure in stndrd position. Determine which qudrnt the terminl side lies nd find the reference ngle Qudrnt = Reference Angle= Qudrnt = Reference Angle= Find the following ect vlues. Do you remember how to determine if the function is positive or negtive depending on the qudrnt? 0. sin 50. cos 5 Use clcultor to evlute ech qudrntl ngle.. sin 90. sec tn 80

17 Use the Lw of Sines to find the specified vlue = Use the Lw of Cosines to find the specified vlue. 7. C = 8. A = Sine Grphs: = Cosine Grphs: Sine grph lwys strts t: How to find the mplitude: y sin b Cosine grph lwys strts t: How to find the period: y cos b

18 Directions: Identify, b, nd the length of one period. Then complete the tble, nd sketch the grph. 9. y sin = b = Length of period = 40. y cos = b = Length of period = 4. y 4cos = b = Length of period = 4. y sin 4 = b = Length of period =

19 5 4. y sin = b = Length of period = y cos = b = Length of period = Choose the best nswer for ech multiple choice question. 45. Wht is the mplitude of the grph? 46. Which of the following is the eqution for the trig grph shown? A. 0 B. C. D. 0 A. y 5sin B. y 0sin C. y 5cos D. y 0cos Mtch the grph with its eqution by writing the pproprite letter net to the eqution. 48. y sin 49. y cos 47. y sin

20 Algebr II Finl Em Review Nme Sttistics REVIEW: Men Medin Mode Rnge For #, find the men, medin, mode, nd rnge, for ech dt set. DON T FORGET TO PUT THE NUMBERS IN ORDER FIRST!. The number mice born in nine different litters:. A student s quiz scores for the first semester of n 5, 7, 6,, 8, 6, 4, 5, 4 lgebr clss: 8, 0, 4, 5, 0, 7, 6 Men Medin Mode(s) Men Medin Mode(s) Rnge Rnge For #0, use ech bo-whisker plot to nswer the following questions. 4. Wht percent of the dt is greter thn?. Find ech: LQ: Rnge: 5. Wht percent of the dt is between 067 nd? Medin: IQR: UQ: 6. Wht percent of the dt is less thn? 8. Wht percent of the dt is less thn 7? 7. Find ech: 9. Wht percent of the dt is between 0 nd? LQ: Rnge: Medin: IQR: UQ: 0. Wht percent of the dt is greter thn?

21 Algebr II Finl Em Review Nme Probbility REVIEW: Counting Principle Permuttions Combintions Probbility Odds For # 4, find the number of possibilities. (COUNTING PRINCIPLE). Grhm hs 5 shirts, ties, nd 4 pirs of pnts. If. How mny four digit numbers cn be formed from the he wers shirt, tie, nd pir of pnts, in how mny digits 4, 5, 6, 7, 8, 9 if the digits MAY NOT REPEAT? different outfits cn he pper?. How mny license pltes cn be formed using letter followed by five digits (the digits MAY REPEAT)? 4. How mny license pltes cn be formed using three letters followed by two digits nd repetition is NOT ALLOWED? Use your clcultor to evlute #4. Mke sure you know how to find these keys on your clcultor for the em! 5. 8 C 6. 0 P 4 7. C 4 8. P 5 For #94, circle whether ech is Permuttion or Combintion nd then determine the number of possibilities. Mke sure to SHOW THE NUMBERS YOU USE! 9. An employee t pet store needs to ctch 5 tetrs in n qurium contining 7 tetrs. In how mny groupings cn the employee cpture 5 tetrs? 0. Fifty-two thletes re competing in bicycle rce. In how mny orders cn three of the bicyclists finish in first, second, nd third?. How mny different ll-str tems of 9 members cn be formed from group of 4 tlented plyers? Permuttion Combintion Permuttion Combintion Permuttion Combintion

22 . You re required to red 5 books from list of gret Americn uthors. How mny groups cn be selected?. At Hollywood Video, 4 DVDs re on sle. How mny different wys could you choose of them to buy? 4. Siteen people re competing in pie bking contest. In how mny wys cn first, second, third, nd fourth plce be wrded? Permuttion Combintion Permuttion Combintion Permuttion Combintion Given the spinner below, stte the probbility of ech outcome for #58 if lnding on ech number is eqully likely. Simplify ALL frctions. 5. Lnding on n EVEN number 6. Lnding on, 4, OR 7 7. Not lnding on, 4, or 7 8. Does not lnd on number tht is divisible by For #94 if crd is drwn t rndom from stndrd deck of 5 crds, find ech probbility or odds. Simplify ALL frctions. 9. P( red Jck is chosen) 0. P( blck 9 is chosen). P( blck crd is chosen). Odds in fvor of choosing n Ace. Odds ginst choosing 4. Odds ginst choosing Queen Disjoint Events: Formul: Overlpping Events: Formul: Independent Events: Formul: Dependent Events: Formul:

23 Circle whether the events re disjoint, overlpping, independent, or dependent. Then, find the probbility. 5. You re selecting single crd from stndrd deck of 5 crds. Find the probbility tht you select 7 or Queen. 6. You re selecting single crd from stndrd deck of 5 crds. Find the probbility tht you select fce crd or Hert. DISJOINT OR OVERLAPPING ANSWER: DEPENDENT OR INDEPENDENT 7. A single die is rolled. Find the probbility tht or 6 is rolled. DISJOINT OR OVERLAPPING ANSWER: DEPENDENT OR INDEPENDENT 8. A single die is rolled. Find the probbility tht n even number or number whose nme contins 4-letters is rolled. DISJOINT OR OVERLAPPING ANSWER: DEPENDENT OR INDEPENDENT 9. If three coins re tossed one right fter the other, wht is the probbility tht the first is heds, the second is tils, nd the third is tils? DISJOINT OR OVERLAPPING ANSWER: DEPENDENT OR INDEPENDENT 0. You drw three crds one t time from stndrd deck of 5 crds. Find the probbility tht you select Club, then Dimond, nd then nother Club with replcement. DISJOINT OR OVERLAPPING ANSWER: DEPENDENT OR INDEPENDENT. You drw three crds one t time from stndrd deck of 5 crds. Find the probbility tht you select Club, then Dimond, nd then nother Club without replcement. DISJOINT OR OVERLAPPING ANSWER: DEPENDENT OR INDEPENDENT. The owner of bkery offers Den cookie from jr contining 4 chocolte chip cookies, sugr cookies nd 5 otmel cookies. Den selects one cookie, puts it bck in, nd then rndomly selects nother. Wht is the probbility tht the first selection ws sugr cookie nd the second ws nother sugr cookie? DISJOINT OR OVERLAPPING ANSWER: DEPENDENT OR INDEPENDENT DISJOINT OR OVERLAPPING ANSWER: DEPENDENT OR INDEPENDENT

24 . A bowl contins 0 purple jelly bens, 7 green jelly bens, nd 5 blck jelly bens. Three bens re drwn one t time. After ech ben is drwn, the color is recorded nd then it is eten. Wht is the probbility of drwing green, followed by blck, followed by nother blck? 4. A bowl contins 0 purple jelly bens, 7 green jelly bens, nd 5 blck jelly bens. Three bens re drwn one t time. After ech ben is drwn, the color is recorded nd then it is returned to the bowl. Wht is the probbility of drwing purple, followed by blck, followed by nother purple? DISJOINT OR OVERLAPPING ANSWER: DEPENDENT OR INDEPENDENT DISJOINT OR OVERLAPPING ANSWER: DEPENDENT OR INDEPENDENT

25 Algebr II Finl Em Review Nme Chpter REVIEW: Find the specified term of sequence given the rule. EXAMPLE: If you re looking for the Tenth term, you PLUG IN.. Find the tenth term of the sequence: n n. Find the seventh term of the sequence: 4n 5 n 0= 7 = Arithmetic is when you: ARITHMETIC Geometric is when you: GEOMETRIC d: r: To find the vlue of d: To find the vlue of r: Determine if the sequence is rithmetic (d) or geometric (r) nd write the net three terms in the sequence.. 4, 9,4,9, 4, ,, 6, 08,... ARITHMETIC GEOMETRIC,, ARITHMETIC GEOMETRIC,, d = r = d = r = ,,,, ,,,,... ARITHMETIC GEOMETRIC,, ARITHMETIC GEOMETRIC,, d = r = d = r =

26 The following formuls will NOT be given on the EXAM so mke sure you write them on your note sheet. Below ech formul, write wht ech is used for. n n d S n n n n r n S n r r n Given the rithmetic sequence, find the net terms. 7. 4,, 8, 4, 0, , 9,, 7... d =,, d =,, Write rule for the nth term of ech rithmetic sequence. 9. 0, 7, 4,,,... 0., 0,, , d, d Rule:. 0, d 6, d Rule:., d 5 5, d Rule: Rule:

27 n n d S n n n n n r S n r r n Find the sum of the first 0 terms of the rithmetic series d d n n S n Find the specified term of ech geometric sequence. 5. Find the fifth term if 6 r 6. Find the seventh term if 8 r S n 5 = 7 = Write rule for the nth term of ech geometric sequence. 7. 9, 8, 6, 7, 44,... 8, 7, 9,, 8...., r, d Rule: Rule: Find the sum of the first 7 terms of the geometric series r n r n S n S n