7.  Extract  the  cube  root  of  the  following:

8  x«  +  48  ax*  +  60  a«  x*  -  80  a»  x»  -  90  a*  x«  -h  108  a»  x  -  27  a*.
8.  Two  pipes.  A  and  B,  will  fill  a  cistern  in  70  minutes;  A  and  0  will  fill  it  in  84

minutes,  and  B  nud  C  in  140  minutes.  How  long  will  it  take  each  alone  to  fill
the  cistern?

9.  Find  the  L.  C.  M.  of  the  following:

x«  _  6  x«  +  11  X  -  6,  x^  -  9  X*  +  26  X  -  24,  and  x»  -  8  x«  -h  19  X  —  12.
10.    Find  H.  C.  D.  of  the  following:

2  abx*  -  164  abx  -  6ab  and  3  m*  nx*  +  84  m«  nx«  -  27  m«  n.
How  do  you  find  the  L.  C.  M.  when  the  simple  factors  cannot  be  found  by
inspection?

ARITHMETIC.
1.  Define  and  illustrate  fractional  unit.    What  is  a  decimal?

2.  How  many  grains  in  a  troy  ounce?    In  an  avoirdupois  ounce?    Tell  something  of

interest  about  the  size  and  weight  of  the  five-cent  nickel.
8.    How  many  cubic  inches  in  a  bushel?    In  a  gallon?    How  do  you  compute  inter*
est  by  the  six  per  cent  method?

14


106  DEPARTMENT  OF  PUBLIC  INSTRUCTION.
