Practice Test 2

1. Evaluate without a calculator

                                            

 

 2. Evaluate to nearest 0.01 (two decimal places )

                                   

 
3. Evaluate without a calculator (no decimals)

                                          

 

 4.Write in Simplest Radical Form (no decimals)

              5(3/2)                        

 

 
5. Write in Simplest Radical Form

                                                                

 

 

 6. Write in Simplest Radical Form

                           

                                  

 

 

 
7. solve             x 2 = 100

 

8 solve            x2 = - 49 

 

 
9   2 x3 -1 = -55

 

 

 

 10 Solve      (x + 4)2  -  1 = 99

 

 

 

 
11. Solve for x:               

 

 

 

 12.  simplify  and Evaluate the expression in  if x = 9 

 

 
13. Solve for x ( note extraneous solutions)  

=  x - 4

 

 

 

 

 

 14. Solve for x and give the exact values

        x 2 + 2x -7 = 0

 

 

 

 

 
15. let y = a x 3 where a is constant of variation

If y = 24 and x = 2       find variation constant

 

 

Find y if x = 4

 

Find x if y = 291

 16. The distance an object is dropped varies directly as the square of the time since it was dropped. 

find the variation constant if in 3.5 seconds the object drops 60.025 meters. 

Write the direction variation equation

How many seconds will it take the object to drop 920 meters?

 

 

 
17    Use the exponential function

y = 2(4)x  

to complete this table

       x         y

        0

        1

        2

        3

What is initial value? _____

By what factor do the outputs 

increase __________

  18.     

If you had $ 25,000 dollars invested at 7% compounded quarterly (n = 4)

What is A0 _______  what is the r________ 

Write the function to find the amount of money you would have after  t    years.

How much money would you have after 6 months?

Find the money after 8 years 

How many years until your investment was worth 75,000 dollars.( to the nearest whole year)

If you invested $30,000, how long would it take until you had $ 75,000.

 

 

 

19               10-x +6 = 10 3x

 

 

 

 

 20Show that    f(x) = 1/3x - 4  and  g(x) = 3x + 12   are inverses of each other   Verify algebraically and graphically.

 

 

 

 

 

21. If a machine is worth $3000 and depreciates by 1/4 of its value each year, using  y = y0 bkx

what is the y0 __________what is the b ________

Write a decay functions that models this 

What is value after 2 years?

Approximate the number of years before it is worth one half its value. 

 22. Find the domain and range of

f(x) = 

 

g(x) =

23. The amount of power generated by a windmill varies directly as the cube of the wind speed.  When the wind speed is 10 miles per hour, a windmills will generate 130 W of power. 

a) write the general direct variation equation.

 

b) Put in data pair and find constant of variation

 

c) Use this variation constant  find how much power is generated when the wind is 23 miles per hour.

24.If a path of a projectile is represented by the function

 h(t) = -16 t2 + 96t + 240 where h is in feet and t is in seconds.

a) how high is projectile after 2 seconds?

b) At what time does the projectile reach maximum height?

c) what is the maximum height of projectile?

d) At what time does the projectile hit the ground?

e) what time(s) does the projectile reach 200 feet in the air?
25.  Solve and find the EXACT value of

x:           6 log (x) = 5 

 

 

 26.  Solve for x :

              10 3x-1  = 300

 

 
27.  A seismologist recorded the recent earthquake in Pakistan/India with an adjusted amplitude of 39,810,717.06mm.  Estimate the Richter magnitude of the earthquake by indicating between which two consecutive whole numbers it lies.  Explain How you found these.

 

 28.  Name two other applications of where you would use Logarithms.