Dugopolski's 111 College Algebra Chapter Test Keys CHAPTER ...... Chapter 1 Test Key 7. 8. 9. # -6 -4 -2 2 4 6-6-4-2 2 4 6-6 -4 -2 2 4 6-2 2 4 6 8 10 10. 11. 12. 13. 14. 5 liters % 2 Cœ$B ( ! ( ,œ + ( 15. 16. disc = 180, real solutions in ... 10. 11. 12. 13. 14. 15. 16. 17. 18. a d c c d a c b d Form F: 1. 2. 3. 4. 5. 6. 7. 8. 9. a c a a a d b a b 10. 11. 12. 13. 14. 15. 16. 17. 18. b a d d d d b c a. Dugopolski's College

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  • Dugopolski's 111College Algebra Chapter Test Keys

    CHAPTER P

    Form A:

    1. 2. 3. 4. 5. 6, , 0, 1.2, , 5 6, 0, 5 15 4 2 $ "'% &

    6. 7. 8. 9. 10. " "' )B

    # $ , %+, %+ , * ' $ $BC B# $ 11. 12. 13. 14. & "#3 " 3 B B $ "!B (BC "#C $ # # #

    15. 16. 17. 18. #B $B $# &B ##B $ B# B# , "B "B"B ' BB # B #B +

    = #

    #

    19. 20. 21. + " #+ " #+ " %+ $B # #B $ #B " #B "( )( )( ) ( )( ) ( ) ( ) # #

    22. 23. 24. $900 ( )& "! T B B #B $ #B $B$ #

    Form B:

    1. 2. 3. 4. 5. 6. $ , 4 8 2 1 * (% $

    7. 8. 9. 10. 11. 12. 0 1 #+ , %+ , #+ &3 " 3$ #% $13. 14. 15. B B 'B % "#B BC C $B $B #$ # # # #

    16. 17. 18. 19. ( )( ) B %B% B" "B B B$ "#B

    #

    #

    B B $ B #

    20. 21. 22. ( )( )( ) ( )( ) B $ B # B # # " %B " %B "'B # "!# (

    23. 24. 141 feet ( )TB B #B # B B"#

    #

    Form C:

    1. 2. 3. 4. 5. 6. ' # & ' % "$ & $ $ * # 2, 1.999 , , 0, , 32 5

    7. 8. 9. 10.*#

    & # #%+ , &B # #B $ $ # # B $ $11. 12. 13. 14. # $

    "$ "$$ # $ # # 3 * $3 B #B &B " + , + , $+ $,

    15. 16. 17. 18. %B )B & # B$ B$ B# "B " B B " B " B

    ( )( + 1) #

    19. 20. 21. ( )( ) %B & #B $ # #B $C #B $C B " B " a b# # #22. 23. 24. 25. ( ) 4 0 $3500 &B % #&B #!B "' " TB B &B # # #"

    #

  • 112 Chapter P Test Key

    Form D:

    1. 2. 3. . "1, 0.020020002 , 0, , 6 or 1 "! $ #& "## % "$ "$

    %5. 6. 7. 8. 9. 4 ( B

    "& #' $ ##+ %+ , %, #BC #B%

    10. 11. 12. 13. ( # "! # 3 " 3 $B B #B # % $14. 15. 16. 17. 18. * $ " "

    % # % B "# #B B #B B " B $ B C

    19. 20. 21. ( )( ) ( )( ) ( ) $B % #B $ + , + , $ #B B $# # #

    22. 23. 24. 25. % # $B # $B $ "! B #B( )( ) $1300 ' #"$

    Form E:

    1. 2. 3. 4. 5. 6. 7. 8. 9. 10. F T T F F F F T F F

    11. 12. 13. 14. 15. 16. 17. 18. 19. 20. d a a b a a d c a b

    21. 22. 23. 24. 25. 26. 27. 28. 29. 30. c b a d d b d c a b

    Form F:

    1. 2. 3. 4. 5. 6. 7. 8. 9. 10. T F F F F T F F F F

    11. 12. 13. 14. 15. 16. 17. 18. 19. 20. a c d c d a d c b b

    21. 22. 23. 24. 25. 26. 27. 28. 29. 30. d c b b d d c c b a

  • Dugopolski's College Algebra 113Chapter Test Keys

    CHAPTER 1.

    Form A:1. 2. 3. 4. e f e f#* "

    & $ , # $ $

    5. 6. [ , ) ( , ) ( , ) # _ _ " ! _

    7. 8. 9. 10. 1 C B" "# #

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    11. 12. 13. 14. 10 liters 13 inches $% B #-%

    15. 16. disc = 0, 1 real solution lb.C $*B "%*" )"

    Form B:1. 2. 3. 4. e f 4 , % # $

    & # $ #"!

    5. 6. ( 1, ) (3, 7) _

    7. 8. 9. 10. 11. $ C #B ' )&

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    12. 13. 14. 6 quarts 4 units by 5 units 23 C "

    B#

    15. 16. disc = , real solutions lb. $' ! C $*B "%*" "$"(

    Form C:1. 2. 3. 4. e f e f & ( $ no solution , 1

    $ #$

    5. 6. ( , 6] ( , 2) _ _ $ _

  • 114 Chapter 1 Test Key

    7. 8. 9. #&

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -2

    2

    4

    6

    8

    10

    10. 11. 12. 13. 14. 5 liters % 2 C $B "( "!" ( , + (&

    15. 16. disc = 180, real solutions in. ! C !&*B "'*& $&)$

    Form D:1. 2. 3. 4. 5. 6. ' _ , , , ) ( 5, 1)# ( " ) $ #

    $ $ $ & # $

    7. 8. 9. 10. 11. # # "*& & &

    C B )&

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    12. 13. 14. B ! # $& !#C##$ #

    ( "$ a b a b

    15. 16. $32.50 46.45 in.C !&*B "'*&

    Form E:1. 2. 3. 4. 5. 6. 7. 8. a b a c a a a d 9. 10. 11. 12. 13. 14. 15. 16. a c b c d d b d

    Form F:1. 2. 3. 4. 5. 6. 7. 8. c c c b d a d a 9. 10. 11. 12. 13. 14. 15. 16. b b c b c d a d

  • Dugopolski's College Algebra 115Chapter Test Keys

    CHAPTER 2

    Form A:

    1. 2. 3. 4. Yes No d: ( , ) , r: [0, ) d: [0, ) , r: [ 1, )_ _ _ _ _

    5. 6. 7. 8. open circle at (2, 3)

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    9. 10. 11. 12. 13. 20 30 2 ( 3, ) B "

    # _

    14. 15. 16. symmetric about the origin ( , 0) (2, ) 10 per card _ _17. 18. 93T #B '!

    B

    Form B:

    1. 2. 3. 4. Yes No d: ( , ) , r: [ , ) d: [ , ) , r: ( , )_ _ " _ " _ _ _

    5. 6. 7. 8.open circle at ( , )" !

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    9. 10. 11. 12. 13. $ % & " _ ( , ) B "&

    14. 15. 16. not symmetric to -axis, -axis, or origin ( , 0) 8 per card B C #17. 18. E &B B (

  • 116 Chapter 2 Test Key

    Form C:

    1. 2. 3. 4. No No d: ( , ) , r: [ , ) d: ( ) , r: , )_ _ # _ _ ! ! _ $ _

    5. 6. 7. 8.

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    9. 10. 11. 12. 13. , for 2 , ) # ' & B B ! %B #2 " # _ #14. 15. 16. 17. 18. ( )( ) ( , 0) per flyer $4401 2 B # (! E ."

    ##

    Form D:

    1. 2. 3. 4. Yes Yes d: [ , ] , r: [ , ] d: ( , ), r: ( , ] ( , ) # # ! # _ _ _ " # _

    5. 6. 7. 8.

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    9. 10. 11. 12. 13. 14. 11 2 + + 1 ( , 0) ( )( )B"#

    ! B 2 _ 0 1 B

    15. 16. 17. 18. 80 per flyer $340 & $ E ."#

    #

    Form E:

    1. 2. 3. 4. 5. 6. 7. 8. 9. d a b a a b a d a 10. 11. 12. 13. 14. 15. 16. 17. 18. c a b d c b a c d

    Form F:

    1. 2. 3. 4. 5. 6. 7. 8. 9. c c a d b d d c b 10. 11. 12. 13. 14. 15. 16. 17. 18. a c a c b c b d b

  • Dugopolski's 117College Algebra Chapter Test Keys

    CHAPTER 3

    Form A:

    1. C #B # & # & B # C ! $ B # !# "!#

    , vertex: ( , ), axis: , -int: ( , ), -int: , , range: [ , ) ( )( )( ) & _ $ B # #B " B $ B #B %B ) !2. 3. 4. $ #5. 6. 7. 8. 9. 3 "%) %# % B " C # ft 41 , " %

    $ $

    1 . 11. 14.! e f e f ! $ $3 #3 # #3 # #, , (mult ), (mult ) ""$

    1. 12. 13.

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    Form B:

    1. C $B # " # " B # C ! "" B # !# $$

    ,vertex:( , ), axis: , -int: , -int: , range: [ , ) ( + 1)( 2) 5" _ $ B B B B *B %& !2. 3. 4. # $ #5. 6. 7. 8. 9. feet , ! %3 %3 "!# '! ') ! % B # C $e f e f10. 11. 14.e f e f ! # #3 $3 # $3 # #, , (mult ), (mult ) &

    #

    1. 12. 13.

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

  • 118 Chapter 3 Test Key

    Form C:

    1. 2. 3. 4. No, remainder = ( ) ( ) %) C #B $ $& B B # B * !*)

    # $ #

    5. 6. 7. $&' $ ! ! " ! # B " C B # feet pos, neg, imag or pos, neg, imag ,

    8. 9. 10. 11. 12. , (mult ) , e f e f&%

    " "' $ # # # $3

    13. 14.

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    Form D:

    1. 2. 3. 4. No, remainder ( ) ( #% C $B # #* B B # B " !#&"#

    # # #

    5. 6. 7. #!! " # ! " ! # B " C #B " feet pos, neg, imag or pos, neg, imag ,

    8. 9. 10. 11. 12. , (mult ) e f e f e f e f ' #& # $ & " # $ #"#

    13. 14.

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    Form E:1. 2. 3. 4. 5. 6. 7. 8. 9. c d c d b c a d a 10. 11. 12. 13. 14. 15. 16. 17. 18. a d c c d a c b d

    Form F:1. 2. 3. 4. 5. 6. 7. 8. 9. a c a a a d b a b10. 11. 12. 13. 14. 15. 16. 17. 18. b a d d d d b c a

  • Dugopolski's 119College Algebra Chapter Test Keys

    CHAPTER 4

    Form A:

    1. 2. 3. 4. 5. 2 2 4 log log(7 ) C $BD"

    C$

    6. 7. 8. 9. 10. 2 3.8188 6.4031 % "

    11. 12. 13. 2

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    14. 15. 16. 4.3 yrs. 0.08 3 + log ( ) B #

    Form B:

    1. 2. 3. 4. 5. 3 1 5 log log # $$B #C B # #6. 7. 8. 9. 10. 2 1 3 9.6377 4.4721

    11. 12. 13. 14. "# 6.5 yrs.

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    15. 16. 0.11 2 + log ( )$ B

  • 120 Chapter 4 Test Key

    Form C:

    1. 2. 3. 4. 5. log (4) = 2 1 $ !B / " B

    6. 7. 8. 9. 10. 15 No solution 1, 4 2.5850 0.3467 11. 12. 13. 14. "

    % 1

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    15. 16. 17. 18. ln(3 5) ln(7) 3 ln( ) 2 9.75 grams" "% #

    B B

    Form D:

    1. 2. 3. 4. 5. log (6) = 10 = 1 4 2& ! "#B

    6. 7. 8. 9. 10. 0.5350 0.2236 " $ '% # &

    11. 12. 13. 14. 4 1

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    15. 16. 17. 18. ln(3) + 2 ln( ) ln(2 + 1) No -intercept 9.03 grams" ""' #

    B B B

    Form E:1. 2. 3. 4. 5. 6. 7. 8. c a b a d b a c 9. 10. 11. 12. 13. 14. 15. 16. a c c a a d c b

    Form F:1. 2. 3. 4. 5. 6. 7. 8. d d c c a c d b9. 10. 11. 12. 13. 14. 15. 16. d c d a c c b a

  • Dugopolski's 121College Algebra Chapter Test Keys

    CHAPTER 5

    Form A:

    1. 2. 3. 4. 5. (0, 1) , (1, 2) Dependent Independente f e f " $# #

    6. 7. 8. 9. (1, 2, 3) 4, , (3, 2) e f $#

    #C B " B C # C B "

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    10. 11. % $

    B B "# # Lacey is 9 years old, Rachel is 6 years old, Jennifer is 3 years old

    Form B:

    1. 2. 3. 4. 5. (3, 1) , (5, 1) Inconsistent Independente f e f " $# #

    6. 7. 8. 9. (2, 1, 0) (1, 1), 3, > e f "$

    #C B " B C # C B "

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    10. 11. 3 1

    B B$ B# + Lacey is 9 years old, Rachel is 9 years old, Jennifer is 3 years old #

  • 122 Chapter 5 Test Key

    Form C:

    1. 2. 3. 4. 5. ( 2, 1) , (5, 4) Inconsistent Independente f e f " $# #

    6. 7. 8. 9. ( 1, 0, 2) (4, 3), (3, 4) 2 2 4 3 6e f e f C B B C B #C #

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    10. 11. 3 1

    B B"#

    B" + 15 #

    Form D:

    1. 2. 3. 4. 5. 6. (1, 0) (2, 1) , 2 (3, 0) (3, 1, 1) (2, 1)e f e f e f e f #$

    7. C B " #

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    8. 9. 17 {( , 10 10 , 8 7 ) | is any real number} orB B B B

    , , | is any real number or , , | is any real number "!C "!(C"! "! ( (

    )D "!D"!C C D D

    10. The solution is a point of intersection of 3 planes.

    Form E:1. 2. 3. 4. 5. 6. 7. b a d c a a d 8. 9. 10. 11. 12. 13. 14. c a a c b d a

    Form F:1. 2. 3. 4. 5. 6. 7. c d a d b b a8. 9. 10. 11. 12. 13. 14. b b d b c c b

  • Dugopolski's College Algebra 123Chapter Test Keys

    CHAPTER 6

    Form A:

    1. 2. 3. 4. 5. (1, 2) (1, 2, 3) 3 4 141 1 3

    e f e f

    $ " *#! #! #!" ( $#! #! #!" " "% % %

    6. 7. 8. 9. 10. 11. 4 20 Not possible (5, 4)73 c d e f%

    12. 13. B # C "

    , inverse matrix = , solution set: (5, 1) e f" $( (# "( (

    14. Chase: $28, Jason: $5.50, Sean: $15.50

    Form B:

    1. 2. 3. 4. 5. (1, 0) ( 1,2, 6) Not possible 201 41 1e f e f

    6. 7. 8. 9. 10. 11.

    c d e f$ " *#! #! #!" ( $#! #! #!" " "% % %

    %

    4 (5, 4)

    1 1 1 4

    12. 13. B C

    # "$ #

    # &"* "*

    $ #"* "*

    , = inverse matrix , solution set: (1, 2) e f

    14. Mary: $5.50, Joan: $28.00, Katy: $15.50

    Form C:

    1. 2. 3. 4. 5. , ( 1, 0, 2) 3 6 192 2 4

    e f

    " $# #

    "$ ) #"( "( "(# % ""( "( "(

    ' & $"( "( "(

    6. 7. 8. 9. 10. 11. 4 17 Not possible 7 , 105 c d ' "$"" ""

    12. 13. B " C "

    , inverse matrix = , solution set: (5, 1) e f# "& &$ "& &

    14. Luke: $3, Kim: $4, Joe: $8

  • 124 Chapter 6 Test Key

    Form D:

    1. 2. 3. 4. 5. (1, 1) (3, 0, 2) Not possible 171 42 6e f e f

    6. 7. 8. 9. 10. 11.

    c d "$ ) #"( "( "(# % ""( "( "(

    ' & $"( "( "(

    "& $'"$ "$

    14 7 ,

    3 02 5

    12. 13. B " C ! #

    , = inverse matrix, solution set: ( 2, 1)

    31 2 e f

    14. Mark: 36, Joe: 10, Tim: 8

    Form E:1. 2. 3. 4. 5. 6. 7. 8. c a b a b a d a9. 10. 11. 12. 13. 14. 15. 16. a d a a a c b c

    Form F:1. 2. 3. 4. 5. 6. 7. 8. a c a c c c a c9. 10. 11. 12. 13. 14. 15. 16. a c c b a d c a

  • Dugopolski's College Algebra 125Chapter Test Keys

    CHAPTER 7

    Form A:

    1. 2. 3. 4.

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -8 -6 -4 -2 2 4 6 8

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    5. 6. 7. 8. ( ) ( ) ( ) B # C " "' C B # " "# # #" B B% * ) % "#

    C C# ## #

    9. 10. center: , ; radius vertex: , ; focus: , ; directrix: $ $$ " #& "# # % ) %

    '"C "$

    %

    11. 12. C B C B ! # "! ! # "!$ $ $ $# # # #

    , foci: , , ; length of major axis is ; length of minor axis is "% '

    Form B:

    1. 2. 3. 4.

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    5. 6. 7. 8. ( ) ( ) ( ) B " C # % B C " " "# # #" B B) "! * % #"

    C C# ## #

    9. 10. center: , ; radius vertex: ( , ); focus: ( , ); directrix: % " # " " C $ #

    ((

    11. 12. C B " C B " % ! "!% %& &

    , foci: ( , ) ; length of major axis is ;

    length of minor axis is '

  • 126 Chapter 7 Test Key

    Form C:1. 2. 3. 4.

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    5. 6. 7. 8. ( ) ( ) ( ) B # C $ #& C B $ " C "# # # #" B B

    ) $$ %* %*C# ##

    9. 10. 11. c: , ; r = v: ( , ); f: ( , ); dirx: = , = # # " # $ C " C B C B& * *# # ) )

    $ &

    12. $!

    Form D:1. 2. 3. 4.

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    -6 -4 -2 2 4 6

    -6

    -4

    -2

    2

    4

    6

    5. 6. 7. 8. ( ) ( ) ( ) B # C B C $ # " "# # #* & " B B# % ) % %! #& *

    C C# ## #

    9. 10. center: ( , ); radius = vertex: ( , ); focus: ( , ); directrix: ! % % " ! # ! B !

    11. 12. C B C B , parabola& &( (

    -6 -4 -2 2 4 6

    -10

    -8

    -6

    -4

    -2

    2

    4

    6

    8

    10

    Form E:1. 2. 3. 4. 5. 6. 7. 8. c a b b a c c a 9. 10. 11. 12. 13. 14. 15. 16. d c a b a c b a

    Form F:1. 2. 3. 4. 5. 6. 7. 8. a d a a b a b b9. 10. 11. 12. 13. 14. 15. 16. d d a a c a b a

  • Dugopolski's College Algebra 127Chapter Test Keys

    CHAPTER 8

    Form A:

    1. 2. 3. 4. " &$ $

    $ 8", , , , , " $ & # $ 8 $ #

    5. 6. 7. 8. 9. $ & 8 " &8 ) #$!! '& $% *) $% '&!( ) or . ,

    10. 11. 12. $*# B "#B C &%B C "!)BC )"C 7 8 % $ # # $ % #&4 4#&

    4!

    #&4

    ! 13. 14. 15. 16. " "" ' %(" !!# to , , Induction"

    (#!

    Form B:

    1. 2. 3. 4. % &$ $

    # 8", , , , , # ( * "' #& 8 % $

    5. 6. 7. 8. 9. # % 8 %8 ' & )% ##'" "!! *! (#!( 1) or . ,

    10. 11. 12. $)% "'B $#B C #%B C )BC C + , % $ # # $ % #!4#!

    4!

    #!4

    4! 13. 14. 15. 16. " ) %)( '$& to , Induction"

    &!%!

    Form C:

    1. 2. 3. 4. & $ " "! #! #!! %!!! 8 $ % 8 %8 ", , , , , ( 1) or %

    5. 6. 7. 8. 9. 10. # % # " %*&! )* '! "*&8" #8"or

    11. 12. ( ) + "!+ , %!+ , )!+ , )!+, $#, #7 8& % $ # ")4 4# $ % &")

    4!

    ")4

    ! 13. 14. 15. 16. "!)" *

    #(!(#& $) , , Induction% ")( "!'

  • 128 Chapter 8 Test Key

    Form D:

    1. 2. 3. 4. # ' ") ' ") "!) "*%% # $ # " $ #, , , , , ( ) or ( )$8" 8" 8 8"

    5. 6. 7. 8. 9. ( ) or & $ 8 " $8 # ""!# $ *& (#

    10. 11. 12. "*" $#+ )!+ , )!+ , %!+ , "!+, , + #, ( ) & % $ # #%4 4# $ % %

    4!

    #%4

    ! 13. 14. 15. 16. %( *

    #(!(#& $) , , Induction"& )*! (!!

    Form E:

    1. 2. 3. 4. 5. 6. 7. 8. 9. d a b a c a b c b 10. 11. 12. 13. 14. 15. 16. 17. 18. a c a a d c b d c

    Form F:

    1. 2. 3. 4. 5. 6. 7. 8. 9. c d d c b c c a b 10. 11. 12. 13. 14. 15. 16. 17. 18. c b b c a b d c a

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