MATH 140  Final Exam Spring 1999                           Name ________________

Instructions:  Answer all the questions on the paper provided and show all your work so that partial credit can be given.

 

I.  a)  Find the next three terms of the sequence  2, 7, 15, 26, ___, ___, ___

    b)  Find the 200th term of   12,23,34,45,…                           ________

c)      How many terms are there in the progression 5,11,17,…,845?  ________

d)      Find 5 + 11 + 17 + …+ 845.                             ________

 

II.                 Suppose that n(U) = 10, n(A) = 9, n(B) = 6, and .  Find each of the following:

    a)  The largest possible value of .              a) _________

    b)  The smallest possible value of .                        b)_________

    c)  The largest possible value of n(C).                                    c)_________

    d)  if = 5.                                             d)_________

    e) The largest possible value of n(A-B).                                 e)_________

 

 

III.  Find d(1632).                                                                    __________

 

 

 

 

 

IV.  Prove that 4+5=9.

 

 

 

 

 

V.                 Why is  undefined?

 

 

 

 

VI.  Give an example of the distributive property for the integers.

 

VII.  Express 519 as a base 8 numeral.     ___________

 

 

 

VIII.         Express 2E712 as a base ten numeral.  _________

 

 

 

IX.              1002005 – 313245 = __________

 

 

 

 

X.                 41405 ¸ 435 = ____________

 

 

 

 

XI.  Find the prime factorization of 15120.                    ____________

 

 

 

 

XII.  Is 493 a prime number? Justify your answer.     _________

 

 

 

 

XIII.Find the repeating decimal expansion of 5/37.      __________

 

 

 

XIV.  Express   as a fraction in lowest terms.                __________

 

 

 

 

XV.           Give three examples of irrational numbers.   ________________

 

 

XVI.         Using the charged-field model show that (-2) – (-5) = 3.

 

XVII.      Give an example of a function from A={1,2,3,4} to B = {a,b,c} using ordered pairs.

 

 

 

 

 

XVIII.    Shade the Venn diagram below for the following set:  .

 

 

 

 

XIX.         Of the 30 patients in a certain hospital ward, 8 are allergic to Aspirin while 12 are allergic to Tylenol.  14 are not allergic to either.

a)      How many are allergic to both drugs?  _______

b)      How many are allergic to just one of the drugs?  _______

 

 

 

 

 

 

XX.    Express the following in lowest terms:  .

 

 

 

 

 

XXI.  Let U = {1,2,3,…,10}, A = {1,2,3,4}, B = {3,5,7,9}.

       a)  Let X be one of the above sets.  For which set is it not true that .

 

       b) Give an example of one element of the set .      _________

 

c)      Give an example of a set C such that , n(C)=3, .

C = {__________}.