MHF4U Exponential and Logarithmic Test

MHF4U, December 2017

Time Completed______

Name_________________

Unit Test 5  –  Exponential  Exponential and Logarithmic Functions K/U /20

(25%)

TIPS /24

(25%)

APP /15

(30%)

COM /10

(20%)

Part One –  Knowledge  Knowledge and Understanding_________________________ ______________________________________ ____________________ _______ Multiple Choice  –  Identify the choice that best answers the following questions.

 =  is a) log   =  b) log   =  c) log   =   2.  _____ The function   =    has y-intercept of  1.  _____ Another way of writing

a) 5 3.  _____ Evaluate a) -1

b) -5

c) 1

d) -1

b) 0

c) 1

d) e

log5 = 2log6log4

b) 9

c) 1.33

5.  _____ The equation of the vertical asymptote for the function

 = 1 b)  = 2 6.  _____ log  45 can be written as: a)

a)

 

 b)

log 9

7.  _____ The x-intercept of a) 1

log  = 

log0.1 log 0.1  log log 

4.  _____ Solve the equation: a) 1.8

d)

d) 0.6

 = 2log3 3  3  4 is

c)

=3

d)

=4

c)

 

d)

 

 = 6   is

b) 6

c) 0

d) Does Not Exist

8. Evaluate without using a calculator. Show all steps for full marks. a)

log 

 b)

7 

c)

2log2 log25

d)

/1

/1 /2

log 441 - 2log 3

9. Match each of the following graphs with its function.

 ______

log 

 ______

log 

 ______

2

 ______



/2

    10. Expand and simplify the following expression  = log  √  .

 /3

Part Two –  Thinking/Inquiry/Problem Solving_________________________________________

.

11. Solve each of the following equations for  Express answers as exact solutions where  possible, otherwise round approximate answers to two decimal places. Also, state any extraneous roots.

a)

3+  2 ∙ 3+  45 = 0

 /4  b)

c)

log5  4  2log = 0

 /4

d)

5− = 3−

 /4

log7    log  6 = 2

 /4

12. Sketch the graph of

  = log − 

 and state its properties. Round your answers to two

decimal places where appropriate. Show all steps.

Domain

Range

 /8

Asymptote

 x-intercept

 y-intercept

Part Three –  Application____________________________________________________________

13. A massive earthquake measuring 7.8 on the Richter scale that hit Mexico this past summer was the strongest in 20 years. It resulted man y fatalities and billions of dollars in damage. Another earthquake hit Iraq two months later measu ring 6.8 on the Richter scale. How much more intense was the earthquake that hit Mexico than the one that hit Iraq?  /2

   = ()

14. A well-dressed math teacher was inspired to work on his dance steps for the Winter Formal. He found out that, on average, the number,  of dance moves he can learn after t  days of  practice is given by How many days of practice does it take for this mystery math teacher to learn 30 moves?  /3

,

 = 481   −. .

15. The population of OTHS alumni that attended various reunions up until 2007 was 9000. Another update in 2017 showed that this number had grown to 11500. How many alumni are expected to be attending OTHS reunions by the year 2030?  / 5

 = 86log  112

16. The OTHS science club has identified that the function  relates the speed of the wind, , in miles per hour, near the center of a tornado to the distance the tornado travels, d, in miles.



a) What is the speed of the tornado after 2 miles of travel?

 /2

 b) What distance does the tornado need to travel to reach speeds of 200 miles per hour?  /3

Part Three –  Communication_________________________________________________________

Question

Answer

A logarithm is an exponent.

T

F

T

F

T

F

T

F

T

F

T

F

The x-intercept for all logarithmic functions is In the equation The equation

 = 1.

log  = , the value of b can equal 1.

log 4 = 2 is meaningless.

log  =  is not defined for  = 1. The equation  = log  4  can be drawn using a vertical The equation

translation without applying a horizontal compression.

Communication Uses mathematical language, symbols, visuals, and conventions correctly.

1 mark

2 marks

3 marks

4 marks

Rarely

Sometimes

Usually

Always