Practice Test 2

1. Evaluate without a calculator

  =10          =7            =2

 

 2. Evaluate to nearest 0.1

  =1.31             =2.51

 
3. Evaluate without a calculator

 = 1000       =25     = 625

 		4.Write in Simplest Radical Form

5(3/2) =

=    

  
5. change to simplest radical form

                          

 

 		6. Write in Simplest Radical Form 

              

 
7.

x 2 = 100

 x = plus or minus 10 

 8  Solve:  x = - 49    no real solution  

 
9. Solve    2 x3 - 1 = -55                      x = -3 10 Solve

       (x + 4 ) 2  - 1 = 99         x = 6,  x = -14

 
11. solve

                                             x = 144

 

 12. Evaluate the expression  if x = 9

   x (3/2) =   27

 
13. Solve for x ( note extraneous solutions)

                  = x - 4

x =6

 

 		14. Solve for x give exact values in simplest radicalform:

                     x2 + 2x -7 = 0

 
15. y varies directly as the CUBE of x

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

If y = 24 and x = 2 find variation constant

a =  3 

Find y if x = 4

y = 192

Find x if y = 291

x =  4.6 approximately  

 

 16

The distance an object is dropped varies directly as the square of the time since it was dropped. In 3.5 seconds the object drops 60.025 meters. How many seconds will it take the object to drop 920 meters?

a = 4.9 

 

It will take 20 seconds to drop 920 meters 

 

 
17.

Use the exponential function

y = 2(4)x  

to complete this table

       x         y

        0        2

        1         8

        2         32

        3         128

What is initial value? _2____

By what factor do the outputs 

increase ____4______

18.

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

What is A0   $25,000  what is the r = .07

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

How much money would you have after 6 months? $25,883

Find the money after 8 years $ 43555 

How many years until your investment was worth 75,000 dollars.( to the nearest whole year) 15.83years

If you invested $30,000, how long would it take until you had $ 75,000.    13.2 years

.

 
19        10-x+6 = 10 3x                         x = 3/2 or 1.5

 

 

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

f(g(x) =  1/3(3x + 12) - 4                    g(f(x) = 3((1/3)x -4) + 12

          =  x + 4 - 4                                        = x -4 + 4

          = x                                                     = x

 21.If a machine is worth $3000 and depreciates by 1/4 of its value each year,Write a decay functions that models this 

y=3000(.75) x

What is value after 2 years?

$1687.50

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

2.4 years 

 22.  What is the domain and what is the range of

f(x) = domain  [-2, +infinity)       range [0, +infinity)

                      

g(x) = 1/(x+3) domain  (-infinity to -3) or (-3, +infinity)

 

 
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.

y = a x 3

b) Put in data pair and find constant of variation

 a = .13

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

y = 2031.25 watts

24.The 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  368 feet

b) At what time does the projectile reach maximum height? 3 sec

c) what is the maximum height of projectile? 384 feet 

d) At what time does the projectile hit the ground? 7.9 sec

e) what time(s) does the projectile reach 200 feet in the air? 6.4 sec

 
25.  Solve and find the EXACT value of

x:           6 log (x) = 5 

 

                    answer:  x = 10^(5/6)

 26.  Solve for x : correct to 2 decimal places.

              10 3x-1  = 300

 

  answer:  x is approximately   1.16
27.  A seismologist recorded the recent earthquake in Pakistan/India with an adjusted amplitude of 39,810,717.06 mm

Estimate the Richter Magnitude of the earthquake by indicating between which two consecutive whole numbers it lies.

between 6 and 7 

Richter magnitude of 7.6

 Applications of logarithms:

The pH scale in chemistry measure the acidity of a liquid

Logarithms are also used to measure the intensity of sound in decibels. Everytime the intensity of sound is multiplied by 10, 1 bel (B) is added to the scale.  A decibel is one tenth of a bel.