Algebra 2 Semester 1 Practice Final

Transcription

1 Alger 2 Semester Prtie Finl Multiple Choie Ientify the hoie tht est ompletes the sttement or nswers the question. To whih set of numers oes the numer elong?. 2 5 integers rtionl numers irrtionl numers nturl numers Grph the numer on numer line Evlute the expression for the given vlue of the vrile(s) ; = Use n lgeri eqution to solve the prolem. 5. Two rs leve Denver t the sme time n trvel in opposite iretions. One r trvels mi/h fster thn the other r. The rs re 3 mi prt in 3 h. How fst is eh r trveling? 35 mi/h n 45 mi/h 45 mi/h n 55 mi/h 55 mi/h n 35 mi/h 55 mi/h n 65 mi/h Solve the eqution or formul for the inite vrile. 6., for t

2 7., for U Solve the inequlity. Grph the solution set (3 + 4) ll rel numers 2 2 no solutions Solve the ompoun inequlity. Grph the solution. 9. 5x + n 7x 7 4 x 4 or x x 4 or x 3 x n x x n x 3. 4x 5 < 7 or 5x + 6 > 3 x < or x > 5 x < or x > x < 5 2 or x > 72 5 x < 5 2 or x > 5.

3 Solve the solute vlue eqution. Grph the solution. 2. x = 4 or x = 2 x = 2 or x = x = 2 or x = 2 x = 2 or x = x = 3 8 or x = x = 3 8 or x = x = or x = 2 x = 3 8 or x = x = 2 or x = 2 x = or x = x = 2 or x = x = 2 or x = Solve the eqution. Chek for extrneous solutions. 5.

4 x = 7 x = 7 or x = 6 7 x = 7 or x = x = 3 Solve the inequlity. Grph the solution x 8 6 x x Mke mpping igrm for the reltion. {(, ), (, 4), (2, ), (6, )}

5 Write the orere pirs for the reltion. {(, 5), (, 4), (,.5), (, 4), (5, 5)} {(5, ), (4, ), (.5, ), (4, ), (5, 5)} {(, 5), (4, ), (,.5), (, 4), (5, 5)} {(5, ), (, 4), (.5, ), (4, ), (5, 5)} For eh funtion, wht is the output of the given input? 2. For,. 9 2 Determine whether y vries iretly with x. If so, fin the onstnt of vrition k n write the eqution. 2. x y

6 yes; k = 4; y =4x yes; k = 6; y =6x yes; k = 3; y =3x no Wht is n eqution of the line in slope interept form? 22. m = 2 2 n the y-interept is (, ) Write the eqution in slope-interept form. Wht re the slope n y-interept? ; slope: 8 ; y-interept: ; slope: 5 8 ; y-interept: slope: ; 5 8 ; y-interept: 8 8 slope: 5 8 ; y-interept: Wht is the grph of the eqution?

7 Wht re the interepts of the eqution? Grph the eqution. 25. x-interept: (, ) y-interept: (, ) x-interept: (, ) y-interept: (, ) x-interept: (, ) y-interept: (, ) x-interept: (, ) y-interept: (, )

8 Wht is the eqution of the line in slope-interept form? 26. the line prllel to through (, 6) the line perpeniulr to through (3, 3) Wht is the grph of the solute vlue eqution?

9 29. Wht is the grph of eh solute vlue inequlity? 3. y < x + 2 2

10 3. x > y 5

11 Solve the system y sustitution. 32. (, ) (, ) (5, 4) (4, 5) Solve the system using elimintion. 33. (3, 5) (, ) (5, 3) (, ) 34. ( 7, ) (7, 8) (, 7) (8, 7) Wht re the solutions of the following systems? 35. infinitely mny solutions (5, ) (, 2) no solutions 36. (5, ) (, 6)

12 no solutions infinitely mny solutions 37. A group of 52 people ttene ll gme. There were three times s mny hilren s ults in the group. Set up system of equtions tht represents the numers of ults n hilren who ttene the gme n solve the system to fin the numer of hilren who were in the group. ; 39 ults; 25 hilren ; 25 ults; 39 hilren ; 39 ults, 3 hilren ; 3 ults, 39 hilren Solve the system of inequlities y grphing. 38. Solve the system of inequlities y grphing.

13 39. Wht point in the fesile region mximizes the ojetive funtion? 4. Constrints Ojetive funtion: Solve the system y elimintion.

14 4. (5,, ) (,, ) (,, ) (,, ) Solve the system y sustitution. 42. (, 7, 5) (8, 7, 5) (, 7, 5) (, 7, ) 43. (,, 3) (,, ) (,, ) (,, ) Wht is the grph of the funtion? 44.

15 4 Grph eh funtion. How is eh grph trnsltion of? 45. trnslte up 3 unit(s) trnslte to the right 3 unit(s)

16 trnslte own 3 unit(s) trnslte to the left 3 unit(s) 46. Ientify the vertex n the xis of symmetry of the grph of the funtion. vertex: (, 4); xis of symmetry: vertex: (2, ); xis of symmetry: vertex: (, ); xis of symmetry: vertex: (2, 4); xis of symmetry: 47. Ientify the mximum or minimum vlue n the omin n rnge of the grph of the funtion. minimum vlue: 3 omin: ll rel numers rnge: ll rel numers mximum vlue: omin: ll rel numers rnge: ll rel numers mximum vlue: 3 omin: ll rel numers rnge: ll rel numers minimum vlue: omin: ll rel numers rnge: ll rel numers 48. Whih is the grph of?

17 49. Suppose prol hs vertex (, 7) n lso psses through the point ( 7, ). the prol in vertex form. Write the eqution of 5. Suppose prol hs n xis of symmetry t, mximum height of n lso psses through the point (9, ). Write the eqution of the prol in vertex form. Wht re the vertex n the xis of symmetry of the eqution? 5. vertex: (, 6) xis of symmetry: vertex: (, 6) xis of symmetry: vertex: (, 6) xis of symmetry: vertex: (, 6) xis of symmetry:

18 Wht is the grph of the eqution? 52. Wht is the vertex form of the eqution?

19 Wht is the eqution, in stnr form, of prol tht ontins the following points? 55. (, 8), (, 4), (4, 24) 56. Wht is the expression in ftore form? Wht is the expression in ftore form? Wht re the solutions of the qurti eqution? 62. = 2, 4 5 2, 2

20 , 2 2, 5 2 Wht is the solution of eh eqution? , , , , , Solve the qurti eqution y ompleting the squre Wht is the numer of rel solutions? 66. one solution two solutions no rel solutions nnot e etermine 67. one solution two solutions no rel solutions nnot e etermine 68. Ientify the grph of.

21 Wht is the solute vlue of eh numer? Simplify the expression i 3i 72.

22 73. Wht re the solutions? i, 4 3 i 3 4 i, 3 4 i 6 6 i, 9 9 i 4 3, 4 3 Write the polynomil in ftore form x 3 + 8x 2 96x 6x(x + 4)(x 4) 4x(x + 6)(x + 4) 4x(x 4)(x + 6) x(x + 6)(x + 4) 76. Wht is ui polynomil funtion in stnr form with zeros 5, 2, n? Wht re the zeros of the funtion? Wht re their multipliities? 77. the numers n re zeros of multipliity 2; the numer is zero of multipliity the numer is zero of multipliity 2; the numers n 3 re zeros of multipliity the numers n re zeros of multipliity 2; the numer 3 is zero of multipliity the numer is zero of multipliity 2; the numers n re zeros of multipliity Wht re the rel or imginry solutions of eh polynomil eqution? 78. 6,, 2, 6, 6, no solution

23 Wht re the rel or imginry solutions of the polynomil eqution? 79. no solution 8. Divie y x + 4., R 32, R Is ftor of? If it is, write s prout of two ftors. yes: yes: yes: is not ftor of 82. Use syntheti ivision to fin P(3) for Use the Rtionl Root Theorem to list ll possile rtionl roots of the polynomil eqution. Do not fin the tul roots. 9,,, 9 9,,,, 3, 9, 3, 9 no roots 84. A polynomil eqution with rtionl oeffiients hs the roots roots.. Fin two itionl 85. Fin thir-egree polynomil eqution with rtionl oeffiients tht hs roots n 2 + i.

24 Alger 2 Semester Finl Answer Setion MULTIPLE CHOICE. B 2. D 3. B 4. D 5. C 6. D 7. D 8. A 9. D. A. B 2. A 3. B 4. C 5. A 6. C 7. B 8. B 9. A 2. A 2. A 22. C 23. C 24. A 25. D 26. D 27. B 28. D 29. C 3. A 3. D 32. B 33. B 34. A 35. D 36. D 37. D 38. C 39. A 4. D 4. C

25 42. B 43. C 44. C 45. C 46. C 47. D 48. A 49. C 5. A 5. A 52. A 53. C 54. B 55. B 56. D 57. C 58. D 59. C 6. C 6. C 62. D 63. B 64. B 65. D 66. C 67. A 68. B 69. C 7. C 7. C 72. B 73. D 74. A 75. B 76. C 77. B 78. A 79. C 8. C 8. B 82. C 83. C 84. C 85. A