The semester B examination for Algebra 2 will consist of two parts. Part 1 will be selected response. Part 2 will be short answer.

Transcription

1 ALGEBRA B Semester Em Review The semester B emintion for Algebr will consist of two prts. Prt will be selected response. Prt will be short nswer. Students m use clcultor. If clcultor is used to find points on grph, the pproprite clcultor function (i.e. zero, intersect, minimum or mimum) should be used. The trce function should not be used. Deciml pproimtions must be ccurte to three plces fter the deciml point. Unless otherwise specified, the domin of n function f is ssumed to be the set of ll rel numbers for which f is rel number. The formuls below will be provided in the emintion booklet. Qudrtic Formul: If b c 0, then b b c Fctoring: b b b b b b b b Compound Interest (continuous compounding): A Pe rt r Compound Interest (n times per er): A P n nt Arithmetic Sequence nd Series: n d n n d n Sn n n Geometric Sequence nd Series: n n r Sn n r r MCPS 0 0

2 ALGEBRA B Semester Em Review Eqution of circle with center t the origin nd rdius r: r Equtions of prbol with verte t the origin, with p the distnce from the verte to the focus nd verte to directri: p or ; opens up if p 0, opens down if p 0 p p or ; opens right if p 0, opens left if p 0 p Equtions of n ellipse with center t the origin, with Mjor is horizontl: Mjor is verticl: b b Equtions of hperbol with center t the origin: Trnsverse is horizontl: Trnsverse is verticl: b b MCPS 0 0

3 ALGEBRA B. Given the sequence,, 8, 9, Semester Em Review Write the recursive rule for the sequence. n Write n eplicit rule for the sequence. n c. Use formul to determine the th term of the sequence. d. Use formul to determine the sum of the first terms of the series Given the sequence,, 7, 0, Write the recursive rule for the sequence. n Write n eplicit rule for the sequence. n c. Use formul to determine the 60 th term of the sequence. d. Use formul to determine the sum of the first 60 terms of the series A blloon is filled with 000 cm of helium. It immeditel begins losing helium such tht it loses one fourth of its helium per d How much helium will it hve lost (correct to three plces fter the deciml point) b the end of the ninth d?. A rumor is going round tht ems hve been cncelled! At :0 there re 0 people tht hve herd the rumor. At :0, more people hve herd the rumor. At :0, 6 more people hve herd the rumor. How mn people hve herd the rumor t :0? MCPS 0 0

4 ALGEBRA B. Rewrite using rtionl eponent nottion. Semester Em Review 7 6. Rewrite using rdicl nottion Evlute c. 7 d Simplif ech of the following. Assume ll vribles re positive. b 6 6 c. d. bc 7 b c e. 0 f. 8 g. 8 h. 8 i Grph ech function nd stte its domin nd rnge. 0. Describe how to obtin the grph of g from the grph of f. g, f 8 g, f. The pproimte time t, in seconds, tht it tkes n object to fll distnce d, in feet, is d t Smmi is prchuting nd flls feet before she opens her prchute. How long does it tke Smmi to fll this distnce? MCPS 0 0

5 ALGEBRA B Semester Em Review. A cr trveling on Interstte 70 ws involved in n ccident. To pproimte the speed of the cr t the time of the ccident, the police use the function 00 6 is the speed in miles per hour nd d is the length of the skid mrk in feet. The driver sid he ws trveling t 0 miles per hour. s. d, where s Wht should be the length of the skid mrk (our nswer should be correct to three plces fter the deciml point)?. Solve. Check for etrneous solutions. 0 c. 7 6 d. 8. Mtch ech function to its grph. f f c. f d. f e. f i. ii. iii. iv. v. MCPS 0 0

6 ALGEBRA B Semester Em Review. Grph ech eponentil function. Identif the -intercept, the smptote, stte the domin nd rnge, nd whether the function is incresing or decresing. c. 6. Grph the function f e. Stte the -intercept, the smptote, the domin, the rnge, nd whether the function is incresing or decresing. 7. In 900, the popultion of town ws,000. The popultion incresed t n verge rte of.% per er. Wht ws the popultion (nerest whole number) in 90? Wht ws the popultion (nerest whole number) in 90? 8. A luur cr originll costs $7,000. It deprecites t rte of % per er. Wht will the cr be worth (to the nerest dollr) fter ers? Wht will the cr be worth fter t ers? 9. A town hs popultion of 0,000. Due to loss of jobs in the re, the popultion of the town decreses t rte of % per er. Write n eponentil model tht describes this sitution. Wht is the epected popultion (to the nerest whole number) of the town in 0 ers? 0. An ccount ps % interest compounded monthl. You deposit $6,000 into the ccount. If ou do not deposit or withdrw mone from the ccount, how much mone (to the nerest cent) will be in the ccount in ers?. You deposit $,000 in n ccount to sve mone for cr. The bnk ps 7.% interest. If ou neither deposit nor withdrw n mone from the ccount, how much mone (to the nerest cent) will be in the ccount fter 6 ers if the interest is compounded continuousl?. In bcteril culture, the number B of bcteri present is modeled b where t represents time in hours since :00 noon. B e. t, How mn bcteri (nerest whole number) will be present t :00 PM? How long (correct to three deciml plces) will it tke for there to be over 0,000 bcteri? MCPS 0 0 6

7 ALGEBRA B. Rewrite ech eqution in eponentil form. log log66 c. log d. ln 7 m. Rewrite ech eqution in logrithmic form. Semester Em Review 6 e c. 0 00, 000. Evlute ech epression. log8 log c. log00 d. log9 e. log6 f. log Simplif ech epression using the inverse reltionship between logrithms nd eponents. log log c. ln e d. ln e 7. The grph below illustrtes reltionship between the functions 7 nd log7. Wht is the reltionship between the two functions? Eplin how the reltionship is determined from the grph. 8. Solve ech eqution. Your nswer m be ect or correct to three deciml plces. 0 c. 0 0 d. e 9 e. 6 f. ln 8 g. log 8 h. log i. log 6 log 9 j. MCPS 0 0 7

8 ALGEBRA B 9. Write n eponentil function of the form points 0, nd, Semester Em Review b whose grph psses through the 0. For ech set of dt below: Bsed on the ptterns of chnge, which tpe of function best fits the dt: liner, qudrtic, rdicl, eponentil, or logrithmic? Write the function tht best fits the dt f() f() f() 0 f() f() f() 0. A rumor is spreding through cit tht liens from Mrs will rrive tomorrow. The number of people who hve herd the rumor Pt is function of the number of minutes since the rumor strted, t, represented b the tble of vlues below. t 0 P t Wht tpe of function best models this dt? Write function tht models the dt c. Predict how mn people will hve herd the rumor fter 9 minutes. MCPS 0 0 8

9 ALGEBRA B. Mtch ech eqution to its grph: Semester Em Review c. d. i. ii. iii. iv.. Mtch ech eqution to its grph: e e c. e e. log d. log0 i. ii iii. 0 iv. v. MCPS 0 0 9

10 ALGEBRA B Semester Em Review. Write n eqution relting the vribles. Use k for the constnt of vrition. s vries directl s r. vries inversel s. c. t vries directl s r nd inversel s s. d. V vries jointl with r nd h.. If vries inversel s, nd when, find when The time t required to empt pool vries inversel s the rte r of the pump. One pool tkes 60 minutes to empt t the rte of 0 gllons per minute. Write n eqution tht represents the reltionship between t nd r. Find the constnt of vrition k. c. How long will it tke to empt the sme pool with pump tht cn empt it t the rte of 00 gllons per minute? 7. Grph ech function. Identif the horizontl nd verticl smptotes. Identif the - nd -intercepts. Stte the domin nd rnge. c. d. 8. Perform the indicted opertions. Simplif the result Perform the indicted opertions nd simplif. c. MCPS 0 0 0

11 ALGEBRA B 0. Solve ech eqution. Check for etrneous roots. Semester Em Review 6 7. Mtch ech eqution to its grph. c. d. i. ii. iii. iv.. Identif ech locus of points in the plne. The set of ll points such tht the sum of the distnces from two fied points to ech point on the locus is constnt. The set of ll points such tht the difference of the distnces from two fied points to ech point on the locus is constnt. c. The set of ll points equidistnt from given point. d. The set of ll points tht is equidistnt from given point nd given line. MCPS 0 0

12 ALGEBRA B. Sketch the grph of ech eqution. Semester Em Review 6 0. Write the eqution of circle tht psses through the point, the origin. nd whose center is. Sketch the grph of the eqution 6nd stte the center nd rdius. 6. An ellipse hs center t 00,. One verte is t the point 00 the point 80,. Write n eqution of the ellipse., nd co-verte is t 7. Describe the grph of the eqution Sketch the grph of ech eqution. Identif the center nd the vertices Mtch ech eqution to its grph c. 9 6 d. e. f. 6 i ii iii iv v vi MCPS 0 0

13 ALGEBRA B Prctice Student Produced Response questions 0. Evlute. Evlute 6. Solve Semester Em Review. Evlute log 8 0. / / / / / / / / MCPS 0 0