MTE 180                                                       Place label hereel her

 

Phil Clark

 

Test  #2 - Covers 2.3, Chapters 3 and 4 and  Section 5.1

 

 

No note cards! 

 

Scratch paper is provided.

 

Use of calculators is encouraged.

This test is 8 pages and includes 10 problems and one extra credit problem.

 

 

Instructions:

To receive credit, you must show all work and explain all your reasoning. If you use you calculator, tell me how. If you guess-and-check, tell me how.

 

 

Honor Statement:

By signing below you confirm that you have neither given nor received any unauthorized assistance on this exam.  This includes any use of a graphing calculator beyond those uses specifically authorized by the Mathematics Department and your instructor.  Furthermore, you agree not to discuss this exam with anyone until the exam testing period is over.  In addition, your calculator’s program memory and menus may be checked at any time and cleared by any testing center proctor or Mathematics Department instructor.

 

 

                                                                                                                                                                               

                  Signature                                                                            Date

 

 

 

 

 

 

 

1.      True and False.  If the statement is false give a counter example.  [2 pts each]

 

a) The operation of subtraction is commutative                                                        T      F

 

 

b) The operation of multiplication is associative.                                                       T      F

 

 

c) The operation of addition is distributive over multiplication.                      T      F

 

 

d) If  a½c  and  bôc  then abôc.                                                                             T      F

 

 

e) For all a and b, .                                                             T       F

 

 

f) GCF(a,b) x LCM(a,b) = a x b for all a and b (x means multiplication) .          T      F

   

 

g) If  then .                                                                                       T      F

 

 

 

2.  On Sparky Island, the natives have an unusual money system. 

10 J can be traded in for 1 ˜,

3˜ can be traded in for 1 8

48 can be traded in for 1 y.

Gary has a booth at the bizarre.  He sells a coconut shell necklace for 888˜˜y J J J J,  A straw hat for J J J J J˜˜88 and a key chain for 88˜JJJ.  Add his earnings together, and make trades so that he has the fewest possible coins.  Show all your trades and explain your reasoning [8 pt]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.   Perform the following: [2 pts each for a-c]

 

a)      Tell what comes after:

i)       

 

 

 

ii)      

 

 

 

b)      Tell what comes before:

i)       

 

 

 

ii)      

 

 

 

c)      Convert the following to base 10:

i)       

 

 

 

ii)      

 

 

 

d)      Convert the following number from base 10 into base 6 [4 pts]:

i)       

 

 

 

 

 

 

 

 

 

 

 

 

 

4.   Suppose you had a standard deck  of 52 playing card.  You are to make groups of six cards.  Describe how you figure the number of left over cards (may want to use a sketch): [10 pts]

a)      Using the partitive model for division.

 

 

 

 

 

 

 

b)      Using the measurment (or repeated subtraction) model for division.

 

 

 

 

 

 

 

c)      How many stacks will there be?

 

 

 

 

d)      How many cards will be left over?

 

 

 

 

 

 

5.  Write all the primes between 123 and 133.  Show your work. [8 pts]

 

 

 

 

 

 

 

 

 

 

 

 

 

6.  Solve the following using logic and justify your answers:  [3 pts each]

a)      What can you say about two numbers if their sum is even and their product is odd?

 

 

 

 

 

 

 

 

 

b)      Find a number between 250 and 280 that is divisible by 2 and 11.

 

 

 

 

 

 

 

 

 

c)      If you find the sum of seventeen odd numbers, will that sum be odd or even?

 

 

 

 

 

 

 

 

 

d)      If the LCM of two numbers is 90 and the GCF of the same two numbers is 5, what are the two numbers?

7.  Brian works part time over in the Rec Center.  He was asked to arrange the towels in the locker room into stacks of equal size.  When separated the towels into stacks of 4, he had one left over.  When he tried stacks of 5, one was still left over.  He had the same problem when he tried 6 to a stack.  Finally, when he placed the towels in stacks of 7, the stacks came out even.  What is the smallest number of towels in the locker room? [8 pts]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8.  Jay and Carmen are doing laps around a field.  If they start at the same time and place and go in the same direction, with Jay walking a lap in 10 minutes and Carmen running a lap in 6 minutes, how long will it take for them to be at the starting place at the same time if they continue to run at the same pace?  Show all your work and explain your reasoning.  [8 pts]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9.  Over the past two months, I have made the following transactions with my bank account:  a deposit of $928, a deposit of $715, a deposit of $1,521, a withdrawal of $200 (cash), wrote a check for $875, a deposit of $115 and wrote another check for $1,413.  Assuming my account balance was $1,230 before all of these transactions, how much do I have left at the end?  [8 pts]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10.  When I lived in Ohio, there was one winter where the difference between the highest temperature and lowest temperature in one month was 56°.  If I were to add 8° to the highest temperature and subtract 8° from the lowest temperature, they would be additive inverses of each other.  What were the highest and lowest temperatures of that month.  [8 pts]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Extra Credit

 

            You have three lights in a room and on the outside of the room there are three switches that you have to label (one for each light).  Unfortunately, you cannot see which lights turn on when you flip each switch.  You only have one opportunity to flip the switches and enter the room (i.e. you cannot go in and out of the room) How can tell which switch goes with which light.  (No, you cannot get someone to watch the lights as you do the switch).  [3 pts]