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No. 14.
l^ORMAL SCHOOL FOR UPPER CAJSTADA.
THIRTY-FIFTH SESSION, JUNE, 186().
Examiners in Department of Mathematics, Chem/iatry, ami Natural PhiluHtyfihy :
John Herbert Sangster, Esq., M.A., Second Master, Normal School.
Rev. William Ormiston, D,D.
1.
2.
3.
4.
6,
C.
7.
ALGEBRA — Junior Division.
*
Time — Three Hourn.
Resolve (o^ — fn**) into twelve elementary factors.
Find the co-efficients of a?" and x' • in the expansion of (2.'c» + .3j? - l)« by the binomial thereoni.
Find, without actual expansion or multiplication, the co-efticients of a:' and .r'* in the expansion of
(I - 2x* + 3x^ - Ix* + 2x^y.
Given ^-^ + f^- = 3. + '^ and^-l^ti _ llL=_« = 4 - ^^^^^ totiudthe vah.e3 of . and ,
Prove that a simple equation can only have one root.
.^^i
8.
9.
10.
11.
12.
13.
14.
15.
Find the value of the symbols ", "j, |-, ^, and «», and prove your answers.
A father leaves a number of children, and a certain sum of money to l)e divided among them as follows :— The
first is to receive $100 and a tenth of the remainder, the second $200 and a tenth of the remainder, the
third $300 and a tenth of th' remainder, and so on ; at last it was found that all the children had received
the same sura— What was the fortune left and how many children were tliere?
Find the G. C. M. of 3ar'' — 10x« + ISir 4- 8 and x" - 2x* - (ix» + 4x'^ + 13a- + G.
.„ a c , ma±nh mc + nd
Prove that if ^ :-• -^ then j^^-^^ = j^T^f-
Divide 28*8 — x* — 2x^ — Sx'^ by 5x' — 4!X'' synthetically.
Find the 1. c. m. of (a» - i')(« — *)"'(«*- ^ ')(''-*)' '^"'^ ('^^ •" ^')"-
Find the value of (-
a + h a — h
4 /)' \
a + b
2b '•
A railway train after travelling for three hours meets with an accident which delays it two hours, after which
it proceeds at three-fifths its former rate and arrives at the terminus () hours behind time ; had the acci-
dent occurred /O miles further on the train would have been 4 li. 40 niiii. behind lime. Required the
length of the line and the original speed per hour.
Extract the square root of 12z' + Qx* - 24r» — 8x' + ICrx'' — 10x« + ix^" + .r« + 4a;^
, (a6 + 1) (x' + 1) X + 1 . 1 I a , \ +b
Find the value of g^}-j7.^rii " ^Tx ^''^" ^ = ^1 '^"'' ^ = 1~^'