2.  Add  the  product  (a  +  &  + 1)  (a  -  6 + 2)  to  the  product

(a  +  6-^l)(a-6-2);
and  verify  the  result  when  a  =  4,  b  =  1.
S.Divide  a?*  +  a:»-5ar^  +  13a;-6  by  a:«  +  3a:-2.
816  EXAMINATION  PAPERS

4.  Simplify:

1(1   l)  +  J(Ui)

...     a\a      0/       b\  a      h/

....    x-1  (,         1  2     )

5.  Solve  the  following  equations,  verifying  your  solutions :

^^^       5     "■    10        To"*
(ii)     a?+2y  =  3o-6,    2ar  +  y  =  3a  +  6.
6.  Divide  100  into  3  parts,  such  that  }  of  the  first,  f  of  the
second,  and  f  of  the  third  are  all  equal.
Part  II.
7.  Resolve  into  factors:

(i)    a*  +  db  +  ac^bc;  (ii)    a:*-6a?-187;

(iii)     (a?-2)f-(a?-2).
8.  Find  the  H.  C.  P.  and  the  L.  C.  M.  of

a»-3a:-2    and    a?-x^-bx-S,
expressing  them  as  products  of  factors.
9.  Solve  the  equations  :

(i)    a^-7ar  =  30;

(u)     =-  4-  rt  =  1

V  ^    x  +  l      x  +  2

correct  to  2  decimal  places.
10.  A  question  on  progressions.
11.  Taking  one  inch  as  unit,  draw  with  the  same  axes  the  graph
of  the  lines  2x-{-y  »  2,  2a;  +  6  =  3y,  y  =  1 ;  and  find  from  your
figure  the  co-ordinates  of  the  three  points  at  which  the  lines
interaect.
EXAMINATION  PAPERS  817

COLLEGE  OP  PRECEPTORS.
Third  Glass.     Christmas,  1907.
1.  tleariange  the  following  expression  in  ascending  powers  of  at,
and  show,  by  means  of  brackets,  what  are  the  coefficients  of  the
different  powers :

Sba^-l  ax-ax* '-eb"2bx^-^ba?'-l-laa^..
Find  also  the  value  of  the  expression  when  a  =  2,  &  =  0,
ar  =  — 1.
2.  Multiply  7/)*-2i>*gr-6jp'gr*  by  3i>' - jpg  +  gr».
