PART 1 MULTIPLE CHOICE Circle the appropriate response to each of the questions below. Each question has a value of 1 point.


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1 PART MULTIPLE CHOICE Circle the pproprite response to ech of the questions below. Ech question hs vlue of point.. If in sequence the second level difference is constnt, thn the sequence is:. rithmetic b. liner qudrtic d. cubic A first level difference indictes n rithmetic sequence. A second level difference indictes qudrtic sequence. A third level difference indictes cubic sequence. A sequence with common rtio between terms indictes geometric sequence.. The eqution of the xis of symmetry of the prbol represented by the function y x is :. x b. x y d. x 0 When the eqution is plced in trnsformtionl form, y + x, the vertex cn be tken from the horizontl trnsltion nd the verticl trnsltion, in this cse, (0,). The eqution of the xis of symmetry is lwys the xvlue of the vertex becuse the xis of symmetry will lwys be verticl line. Therefore, the eqution for the xis of symmetry ( verticl line) is x 0.. Given the eqution x , then x is equl to:. ± 4 b. ± 4 i 6. 9 d. no possible vlue To solve for the vlue of x, we need to use order of opertions in reverse to isolte the vrible. We would subtrct 48 from both sides to give x 48. Then we would squre root both sides, giving us x ± 48. Since you cnnot squre root negtive numbers, we re now deling with complex numbers (IMAGINARY!!!). We would need to simplify the root 48. The solution would give x ±4 i. 4. For the function y x + bx + c, the yintercept is lwys: b.. c c 4c d. 4 y x + bx + c When in the generl form, intercept., the vlue of c will lwys give you the y. If the eqution kx 4x + 0 hs two equl rel roots ( rel root), then the vlue of k is:. k 0 b. k > 0 k d. k > equl rel roots (or rel root) mens tht the discriminnt, b 4c ( 4) 4( )(), is equl to 0. We would plug in ech vlue s follows: k 0. We would then simplify the eqution to 6 8k 0 nd then solve for the vlue of k, which would be. 6. An Olympic diver dives from the high diving bord. The distnce, d, in meters, from the surfce of the wter vries with the time, t, in seconds, tht hve pssed since she left the bord, ccording to the eqution d t + t + 0. Wht is her mximum elevtion bove the wter during the dive? (round to the nerest unit).. meters b. 0 meters meters d. meters We lredy know the eqution nd we re being sked for the MAXIMUM height. I should ( ) immeditely think VERTEX. We find the x of the vertex, x vertex or0. 7. This is the time of the mximum height. To solve for the y, I plug in the vlue of t into the originl eqution d (0.7) + (0.7) + 0., round to the nerest unit, is meters Which of the following is the trnsformtionl form of the function y ( x ) +?
2 . ( y ( x ) b. y ) ( x ) d. ( y ) ( x ) y ( x ) I would use my formul sheet which tells me tht trnsformtionl form looks like this ( y k) ( x h). I would then strt to rerrnge the eqution given until it looks like trnsformtionl form. This would strt by subtrcting from both sides to give y ( x ) nd then I would divide both sides by to give ( ) ( x ) 8. Wht vlue of b mkes the expression x + bx + perfect squre? b. d. y. When I complete the squre, I will tke the vlue of b (ssuming tht the vlue of is lredy ) nd divide it by two, then squre it. I hve the finl vlue, so I need to work 6 6 bckwrds. I would squre root to give me, but then I would hve to multiply by, so I would end up with s my finl nswer. 9. The students t Est High School re plnning surprise prty for the principl. One student tells two other students who in turn tell two other people. These people ech tell two other people nd so on. Wht type of sequence is generted in this sitution?. cubic b. geometric qudrtic d. rithmetic One person would tell, then would tell more ech, et This would be sequence tht looks like {,, 4, 8, 6..} which hs common rtio of, therefore, it would be geometric becuse of wht we lredy discussed in question. 0. Which of the following is NOT geometric sequence? 9. {,,, } b. {4, 8,., } {0.8, 0.08, 0.008, } d. {,, 4, } For geometric sequence, there needs to be common rtio. In, the common rtio when I tke the rd term nd divide it by the nd nd the nd divided by the st is.. In b, the common rtio is 0.7. In c, the common rtio is 0.. However, in d, when I divide the rd term by the nd term I get 0.7 nd when I divide the nd term by the first term, I get twothirds ( ). There is no common rtio in d, therefore, it is NOT geometri
3 . Given the grph below, determine the generl form of the function WITHOUT using regression on your clcultor. [ points] I hve three points but I m not llowed to use regression. I need to strt with the trnsformtionl form becuse I know the vertex. ( y k) ( x h) nd plug in the vlues of my vertex to get ( y 6) ( x + ). Then I would substitute in one of the other two points nd solve for. (0 6) ( 6 + ) which simplifies to give ( 6) ( 4) nd then ( 6) 6so when I divide both sides by 6, I get. ( 6) ( x + ) I plug this bck into ( y 6) ( x + ) to get ( y 6) ( x + ). I then multiply both sides by  to get y nd then strt to simplify to get ( y 6) ( x + 4x + 4) nd then I get y 6 x 4x 4) nd then dd 6 to both sides to get y by itself, which is generl form. y x 4x +. Solve lgebriclly to find the exct roots of the following equtions. Simplify where possible. ) 6x [. points] + 6x 0 ( x + ) 0 0 x + 0 x 0 x 4 b) + 4 x x + [ points] ( x + ) 4( x) + ( x)( x + ) ( x)( x + ) ( x + ) + 4( x) 4 ( x)( x + ) x x x x x + x x + 8 4x 0 4x ± () + x + 6 ( 4) ± ± 8 + 4x + 4 4( 4)(6) x 4 x
4 . {, +k, 6k } is geometric sequence. ) Find the vlue of k [ points] 6 k + k + k (6 k)( ) ( + k)( + k) k k + 4k k k k + 4.k 9 + 4k ( k + 6)( k.) x. x 6 b) Find the eqution of the generl term [ points] There re two possible solutions for the sequence, therefore the sequences would be: {0.,., 4. } with common rtio of 7 so t n n (7) {0., 4, } with common rtio of 8 so t n n ( 8) 4. A footbll is kicked into the ir. The eqution h 4.9t + expresses the reltionship between the height, h, in meters nd time, t, in seconds. ) Determine the mximum height reched by the footbll. [ points] We lredy know the eqution nd we re being sked for the MAXIMUM height. I should ( 4.9) immeditely think VERTEX. We find the x of the vertex,. This is the time of the mximum height. To solve for the y, I plug in the vlue of t into the originl eqution h 4.9() + 9.8() x vertex The mximum height reched by the footbll ws.90m. b) For how long ws the bll t height of t lest meters bove ground? [ points] The yellow re indictes the time tht the bll would hve been t lest m in the ir. We would tke the two vlues.4 nd 0.7 nd find the difference seconds. The bll is t lest meters bove the ground for 0.86 seconds. 4.9t 0 4.9t + 4 ± ± (9.8) ( 4.9) ± 7.64 ± 4. 4( 4.9)( 4) x 0.7 x.4
5 . A piece of lnd in the shpe below hs to be fenced. If 600m of fencing re to be used, find the vlues of x nd y tht will produce mximum re. [ points] x + 8y 600 A y x 00 4y A y(00 4y) A 900y y A y + 900y The perimeter of the fencing used The formul of the fenced re The perimeter formul rerrnged to isolte x The re formul with substitution for x The re formul fter distributive property The re formul simplified We now hve the eqution nd we re being sked for the MAXIMUM re produced. I should immeditely think VERTEX. It is very importnt tht we understnd tht the formul is telling us the re bsed on the length of y. Yes, we re looking for the xvlue of the vertex, but tht is only telling us the length of y in this sitution. See the grph below. We find the x of the vertex, x vertex 40. 9m ( ). This is the length of y tht produces the mximum re. To solve for the length of x, I plug in this vlue into the eqution x 00 4y 00 4(40.9) 6. 6m. The vlues of x nd y tht would produce the mximum re would be 6.6m nd 40.9m.
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