Winter'2015'Math'112'Midterm'Exam'' ' ' ' Name_______________________________'

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Instructions:'

Show'ALL'work.'

Simplify'wherever'possible.'

Clearly'indicate'your'final'answer.'

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Problem'Number' Points'Possible' Score'

1' 20' '

2' 20' '

3' 20' '

4' 20' '

5' 20' '

Subtotal' 100' '

Extra'credit' 10' '

Total' 100' '

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1) Indicate'whether'each'of'the'following'statements'are'true'or'false'(no'explanation'necessary):'''

a) sin 5π6

⎛⎝⎜

⎞⎠⎟ =

12''

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b) sec 13π6

⎛⎝⎜

⎞⎠⎟ =

2 33'

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c) tan 4π3

⎛⎝⎜

⎞⎠⎟ =

33'

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d) sin 23π2

⎛⎝⎜

⎞⎠⎟ = −1 '

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e) There'is'no'value'of't'that'will'make' sin t( ),cos t( ) 'and tan t( ) 'all'negative.''

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f) If' tan t( ) 'and' sin t( ) 'are'negative,'then' cos t( )must'also'be'negative.''

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g) log2 0 = 1 '''

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h) log8 2 = −3 ''

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i) Extra'Credit:'Pick'the'winner'of'this'weekend’s'fight.'A'correct'pick'of'Floyd'Mayweather'(the'champion)'will'earn'2'EC'points.'A'correct'pick'of'Manny'Pacquiao'(the'challenger)'will'earn'4'EC'

points.'An'incorrect'pick'will'earn'no'EC.''

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2) Find'the'inverse'of'each'function'below" " " " " " " (20'points)'

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a) f x( ) = 2 ln3x+1 '''

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b) g x( ) = xx − 6

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3) Log'Rules:'' ' ' ' ' ' ' ' ' ' ' (20'points)'

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a) Rewrite'the'following'as'the'log'of'a'whole'number'

− 12log4 + 2 log6 '

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b) 'Using'laws'of'logarithms,'write'the'expression'below'using'sums'and/or'differences'of'logarithmic'expressions'which'do'not'contain'the'logarithms'of'products,'quotients,'or'powers.'

ln x7 x − 2x2 − y2

⎛⎝⎜

⎞⎠⎟'

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4) Log'Equations'–'Solve'the'following'for'x.''

a) 4e3t = 2e2.2t '''

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b) ' log x3 + log x2

log 4x( ) = 3 '

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5) Misc:''

a) Suppose'that'in'2010'there'were'20'warriors'fans'in'Southern'Oregon'and'now,'5'years'later,'there'are'60,000.'

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i) Find'a'formula'that'models'the'number'of'warrior'fans't'years'after'2010,'assuming'linear'growth.'

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ii) Find'a'formula'that'models'the'number'of'Warrior'fans't'years'after'2010,'assuming'exponential'growth.'

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b) Determine'the'amplitude,'midline,'phaseZshift'and'period'for'the'graph'below.'Then'express'it'asy = A Bx +C( ) + D 'i) Amplitude'='__________'

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ii) Midline:'y'='___________''

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iii) Phase'Shift'='___________''

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iv) Period'='______________''

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v) Equation'of'graph:'y'='____________''

EXTRA'CREDIT:'10'points'

What'number'is'the'mess'below'equal'to?'

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−2 ln 12

⎛⎝⎜

⎞⎠⎟+ ln16

2

ln 2 log6 2( )− 2 log613

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

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