11 Precalculus Questions

11 pre-calculus questions must show all work, please be familiar with and check answers.

Microsoft word compatible.

 

12/18/2012 due

MAT206-981 Final Examination

Prof. Krishnamachari

Answer all questions. Show complete work to get full credit.

This exam is due by 10 P.M Friday, December 21, 2012

1) a) Find the value of 3
5

log 125

b) Write the following expression in condensed form

2 2

2

32 121 4
log log log

11 16 5
 

2) Write each expression in expanded form

a)
2 2

5 ( 1)
log

( 1) 7 3

x

x

x x



 

b)
5 2

5
ln

x y

z

3) Find the domain of each function :

a) g(x) =
2

log( )x x

2

1
) ( ) log

1
b f x

x

 
  

 

4) Solve the given expression and give your answer correct to three decimal places

6

119

7
14

x
e




5) Solve for x:

a) 4 4log log (6 10) 1x x  

b)
2

log( 144) log( 12) 1x x   

6) a) Given sin
1

3
  and cos 0  find the exact value of the remaining trigonometric

functions of  using identities.

b) Find the exact value of

19
tan

6



7) Find exact values without using a calculator

a)
1 1

cot[sin ]
3

  
 
 

b)
1 3

csc[cos ( ]
2


 

  
 

8) a) Solve the equation
2

4 cos 1, 0 2    

b) Find all solutions of the equation
2

sec sec 2x x  in the interval, 0 2  

9) a) Simplify :
3

cos( )
2


 

b)
Establish the identity:

cos sin
sin cos

1 tan 1 cot

 
 

 
  

 

10) Sketch the graph of the following function over the interval [ 2 , 2 ]  . Indicate the

amplitude, period, and phase shift. (Include a table of values)

f(x) = sin ( )
4

x




11) Extra Credit (optional) (10 points)

Find the domain, x-intercept, and vertical asymptote of the logarithmic

function and sketch its graph. (Include a table of values)

f(x) =
5

log ( 1) 4 x