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StudyGuide:FinalExam§6–2LearningObjective:SWBATsolvesystemsofequationsusingsubstitution.

1.y = 2x − 102y = x − 8

2.x + 2y = 14y = 3x − 14

3.2y = x + 1−2x − y = 7

4.x − 9y = −106x + y = −5

§6–3LearningObjective:SWBATsolvesystemsofequationsusingelimination.

5.x + y = 2x − y = 4

6.x + 2y = −4x + y = 2

7.2x − 4 y = −6x − y = −1

8.−4x − 3y = 53x − 2y = −8

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§6–5LearningObjective:SWBATgraphlinearinequalities.

9. y ≤ 3x − 6 10. y >23x + 2

§7–1LearningObjective:SWBATsimplifyexpressionsinvolvingzeroandnegativeexponents.11. 60 12. −60

13. 7bc0 14. 2

4−1

15. 5−3 16. −7−2

17. 3m−8p0 18. 5a−4

2c

19. 2m3n

⎛

⎝⎜⎞

⎠⎟

−3

20. 8−2q3r−5

21. 5m−1

9 ab( )−4 c7 22. 7s0t−5

2−1m2

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Evaluateeachexpressionfora = −4 ,b = 3 and c = 2 .23. 3a−1 24. 4a2b−2c3 §7–2LearningObjective:SWBATmultiplypowerswiththesamebase.Rewriteeachexpressionusingeachbaseonlyonce.25. 45 ⋅ 43 26. 79 ⋅ 73 ⋅ 7−10 Simplifyeachexpression.27. x8 ⋅ x5 28. −4k−3 ⋅ 6k4 29. 13x8( ) 3x10( ) 30. −2h5 ⋅ 4h−3

31. 12mn( ) −m3n−2p5( ) 2m( ) 32. 6a3b−2( ) −4ab−8( )

33. 1614 34. 9

12

35. 823 36. 25

32

37. 1.5 × 103( ) 4.3 × 102( ) 38. 16r−7( ) −2r( )

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§7–3LearningObjective:SWBATraiseapowertoapowerandraiseaproducttoapower.

39. x4( )3 40. 4x5( )6

41. 2xy( )3 42. v7( )12

43. b b−8( )−3 44. v2( )3 w4( )13

45. 10m3( )−2 46. 4a3( )2 a5( )

47. m47 n3

⎛

⎝⎜⎜

⎞

⎠⎟⎟

7

m4( )3 48. 5x−5y2 2x−14( )2

49. 3b−4c−2( )6 c3( ) 50. 2y−5( )3 x11y−10( )2 §7–4LearningObjective:SWBATdividepowerswiththesamebaseusingthequotientruleandraiseafractiontoapower.

51. 55

52 52. x7

x3

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53. m−3

m−5 54. x

58

x38

55. x6y9

x2y5 56. 3x

2y⎛

⎝⎜⎞

⎠⎟

3

57. 47

⎛

⎝⎜⎞

⎠⎟

−2

58. −3x4

2y5⎛

⎝⎜

⎞

⎠⎟

−3

59. 3x2y5x−2

5xz5⎛

⎝⎜

⎞

⎠⎟

−3

60.4m2( ) 3n5( )

2m−3( ) −mn( )3

§7–5LearningObjective:SWBATrewriteexpressionsinvolvingradicalsandrationalexponents.Writeeachexpressioninradicalform.

61. a23 62. 64b( )

34

63. 27a23 64. 24c( )

23

65. 25x( )12 66. 8x( )

13

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Writeeachexpressioninexponentialform.

67. xy 68. b23

69. 81x24 70. x2y35

71. x6y93 §7–6LearningObjective:SWBATevaluateandgraphexponentialfunctions.Grapheachexponentialfunctionusingatableofvalues.72. y = 3x 73. y = 8 ⋅ 1.2x §7–7LearningObjective:SWBATmodelexponentialgrowthanddecay.

Usethecompoundinterestformula A = P 1 +rn

⎛

⎝⎜⎞

⎠⎟

nt

tofindthebalanceineachaccount

afterthegivenperiod.74. $8000principleearning5%compoundedannually,after6years

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75. $5000principleearning4%compoundedquarterly,after10years§8-1LearningObjective:SWBATaddandsubtractpolynomials.Addorsubtractasindicated.Writeeachanswerinstandardform.76. 6 j2 − 2 j + 5( ) + 3 j2 + 4 j − 6( ) 77. 3k + 5( ) + 16x2 + 7( )

78. g4 − 4g2 + 11( ) + −g3 + 8g( ) 79. 7x4 + 9( ) − 8x4 + 2( ) 80. 3d2 + 8d − 2( ) − 2d2 − 7d + 6( ) 81. 3a2 + a + 5( ) − 2a − 5( ) §8–2LearningObjective:SWBATusedistributiontomultiplyamonomialbyapolynomial.82. 4t t2 − 6t + 2( ) 83. −m 4m3 − 8m2 + m( ) 84. 5d −d3 + 2d2 − 3d( ) 85. 6h2 3h2 − h + 7( )

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§8–2LearningObjective:SWBATfactorouttheGCFfromapolynomialusingdistribution.86. 15x + 27 87. 6w3 − 14w 88. 9m3 + 30m − 24 89. b3 + 5b2 − 20b 90. 14b3 + 21b2 − 42b 91. 12 j8 + 30 j4 − 6 j3 Simplifyandwriteinstandardform.92. p p + 4( ) − 2p p − 8( ) 93. t t + 4( ) − t 4t2 − 2( ) §8–3LearningObjective:SWBATmultiplytwobinomialsusingFOIL.94. x + 3( ) x + 8( ) 95. 2r − 5( ) r + 3( ) 96. 5t − 1( ) 3t − 2( ) 97. 3x + 1( ) 5x − 3( ) 98. 5h − 3( ) h + 7( ) 99. m + 9( ) m − 3( )

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8–3LearningObjective:SWBATmultiplyabinomialbyatrinomialusingtheboxmethod.100. x + 3( ) x2 − 2x + 4( ) 101. k2 − 5k + 2( ) k − 5( ) §8–4LearningObjective:SWBATfindthesquareofabinomial.

102. x + 7( )2 103. 6m − 2( )2 §8–4LearningObjective:SWBATmultiplybinomialsthatarethe“differencebetweentwosquares”pattern.104. v + 8( ) v − 8( ) 105. 6p2 + 2q( ) 6p2 − 2q( ) §8–5LearningObjective:SWBATfactortrinomialsintheformx2+bx+c.106. k2 + 11k + 30 107. x2 + 16x + 63 108. q2 + q − 56 109. n2 − 6n − 40 110. v2 − 17v + 60 111. y2 + 18y + 65

“Whatmultipliestocandaddstob?”

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112. k2 + 4kn − 96n2 113. m2 − 4mn − 32n2 §8–6LearningObjective:SWBATfactortrinomialsintheformax2+bx+c.(Hint:FactorouttheGCF,ifthereisone,first,andthenusetheboxmethod.)114. 2w2 + 13w + 15 115. 3d2 + 20d + 12 116. 3p2 − 7p − 40 117. 4n2 + 62n − 32 118. 3x2 + 9x − 84 119. 2c2 − 23c + 11 §8–7LearningObjective:SWBATfactorperfectsquaretrinomials.120. p2 − 24p + 144

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121. 25r2 − 80r + 64 122. 49d2 − 84d + 36 §8–7LearningObjective:SWBATfactorthedifferenceoftwosquares.(Hint:FactorouttheGCFfirst,ifthereisone.)123. 64n2 − 1 124. 27x2 − 48 125. 8d2 − 8 126. 25x2 − 36 127. x2 − 1 §8–8LearningObjective:SWBATfactorafour-termpolynomialbygrouping.(Hint:FactorouttheGCFfirst,ifthereisone.)128. 2m3 + 8m2 + 9m + 36 129. 6x3 + 9x2 + 2x + 3 130. 8w3 + 12w2 + 10w + 15 131. 36n3 − 27n2 − 8n + 6

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§9–1LearningObjective:SWBATgraphquadraticequationsintheformy=ax2andy=ax2+c.Identifythevertexofeachgraph.Tellwhetheritisaminimumoramaximum.132. 133. §9–2LearningObjective:SWBATgraphquadraticequationsintheformy=ax2+bx+c.Findthevertexandtheaxisofsymmetryforeachfunction.Thengrapheachfunction.134. y = x2 − 8x + 12 135. y = x2 + 1 §9–3LearningObjective:SWBATsolvequadraticequationsbyusingsquareroots.Solveeachequationbyfindingsquareroots.Iftheequationhasnoreal-numbersolution,write“nosolution”.136. x2 = 256 137. 7x2 + 28 = 0

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§9–4LearningObjective:SWBATsolvequadraticequationsbyfactoring.UsetheZero-ProductPropertytosolveeachequation.138. y + 6( ) y − 4( ) = 0 139. 3m 2m + 9( ) = 0

SolvebyfactoringandusingtheZero-ProductProperty.140. w2 + w = 12 141. k2 − 11k + 30 = 0 142. 3x2 − 10x − 8 = 0 143. x2 + 18x + 80 = 0 144. x2 + 12x = −20 145. 3x2 + 4x − 4 = 0

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§9–5LearningObjective:SWBATsolvequadraticequationsbycompletingthesquare.Solveeachequationbycompletingthesquare.Ifnecessary,roundtothenearesthundredth.146. z2 − 19z = 66 147. r2 + 8r + 13 = 0 §9–6LearningObjective:SWBATsolvequadraticequationsbyusingthequadraticformula.Usethequadraticformulatosolveeachequation.Ifnecessary,roundtothenearesthundredth.148. 4d2 − 8d + 3 = 0 149. −3p2 + 17p = 20 150. h2 − 2h − 2 = 0 151. 3n2 + 10n = 5

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§11–1LearningObjective:SWBATsimplifyrationalexpressions.Simplifyeachexpressionandstatetheexcludedvalues.

152. 6p − 3618

153. q + 1

q2 + 4q + 3

154. 3x2 + 19x − 14

x2 − 49 155. x + 1

x2 − 1

156. 6 − 3b

b2 − 4 157. n2 − n − 12

n2 − 4n

§11–2LearningObjective:SWBATmultiplyanddividerationalexpressions.

158. x + 35x − 20

⋅10x

x2 + 7x + 12

159. 5w − 255w − 10

⋅w

w2 − 25

160. j2 + 11 j − 4226 j − 52

⋅39 jj − 3

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161. 12 j − 362 j + 4

÷3 j − 9

4 j2 − 16

162. x2 − 16

2x2 − 9x + 4÷x2 + 7x + 124x + 4

163. 3x2 − 12x5x

÷ x2 − 3x − 4( ) §11–4LearningObjective:SWBATaddandsubtractrationalexpressions.

164. 5x − 24x

−x − 24x

165.

5

8x2+

2

3x2

166. 1g + 2

+3

g + 1

167. r + 2r + 4

−3

r + 1

168. x + 12x + 1

−2 − x2x + 1

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§11–5LearningObjective:SWBATsolverationalequationsandproportions.(Besuretoidentifyanyextraneoussolutions.)

169. 12 − j

+ 2 =4

2 − j 170. 1

2x+

310

=15x

171. 5

x2=6x

− 1 172. 52x − 3

=73x

173. 3a

+3

a − 3= −

32 174. 8

c + 2− 6 =

4c + 2

§10–2LearningObjective:SWBATsimplifyradicalsusingthemultiplicationanddivisionrules.175. 200 176. 68

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177. 48n3 178. 60m7 179. 6 ⋅ 30 180. 2 3 ⋅ 96

181. 3 40x ⋅ 2 56x5 182. 18y

36y3

183. 72

40 184. 25b

5b3

185. 24

3n

§10–3LearningObjective:SWBATadd,subtract,multiplyanddivideradicals.186. 8 3 + 3 187. 6 8 − 2 50 188. 5 18 + 4 32 189. 3 12 + 4( )

190. 3 − 4( )2 191. 2 3 + 5( ) 6 5 − 4 3( )

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192. 7 + 3 5( ) 7 − 3 5( ) 193. 12

11 − 7

194. 8

3 + 1

§10–4LearningObjective:SWBATsolveequationscontainingradicals.(Besuretocheckforextraneoussolutions.)195. x + 4 = 7 196. 4 − 2x = −6 197. 3t − 2 = 5 198. 4d + 3 = 7d − 3

199. a2 + 20 = 9a 200. x = 2x + 8