Answer:  
<u>On Thursday</u> I <u>drove</u> up north<u> to move</u> a couch for a friend.
 (prepositional) (participial)         (infinitive)
  If your shoes <u>have</u> a lot of surface area, <u>hiking</u> <u>through</u> a snow drift gets a lot easier.    (infinitive)                         (gerund)  (prepositional)
<u>
Already exhausted by </u>the second quarter, <u>we were</u> no match for the 
(past participial)  (prepositional)                 (participial)
division champions.  
That award, <u>offered once a year</u> to only one teacher in the entire state,
                    (participial)   (prepositional)
 is quite an honor<u> to win</u>.  
                              (infinitive)
<u>Hoping</u>     <u>against</u>     all hope that the balding tires would <u>hold</u> and the 
(gerund)  (prepositional)                                                    (infinitive)
rusting fuel pump would <u>continue</u> to work, I <u>loaded</u> up all of the 
                                      (infinitive)                  (participial)
possessions that would <u>fit</u>, <u>discarded</u> the rest in a dumpster <u>behind</u> a truck 
                                    (infinitive)  (participial)                          (prepositional)
stop, and <u>set</u> out to cross the country.
             (participial)