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 The Institute has attempted to obtain the best 
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 L'Institut a microfilm^ le meilleur exemplaire 
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 Additional comments:/ 
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 [Printed ephemera] 1 sheet (verse blank) 
 
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The copy filmed her* has been reproduced thanks 
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 University of Western Ontario 
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 The images appearing here are the best quality 
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 (Regional History Room) 
 
 Lee imagee suivantes ont M reproduites avec ie 
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 Lea exemplaires originaux dont ia couverture en 
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 No. 13. 
 
 ISTORMAL SCHOOL FOR UPPER CA1S(ADA. 
 
 TWENTY-FIFTH SESSION.— JUNE, 1861. 
 
 Examiners in Mathematici, Qiemistry and Natural Philosophy : 
 John Herbert Sangsteh, Esq., M. A., Second Master, 
 Rev. Wm. Ormiston, D. D., Irupector of Grammar Schools for Upper Canada. 
 
 ALGEBRA.— JUNIOR DIVISION. 
 
 Time— Tbres Hours. 
 V 1. What is the coefficient of x* in the expansion of (x—2yy 1 
 
 2. Reduce 6a^+10&;+9.^+15i^ ^^ .^^ j^^^^^ ^^^^^ 
 
 3. If two fractions are together equal to 1, shew that their difference is the same as the difference of their squares. 
 v4. Find the cube root 21«=» + 56:»r» +Ga; + H-llla!* + Cla;»+144;p»+204a;' + l74r» + 219a;«. 
 
 \ 5. Find the coefficient of a^ and of a'" in the expansion of (1 + ^a— a2+^a3_aB^g8^2a^+3a*+ai)* 
 
 6. Two fractions are together equal to f , and one exceeds the other by £ ; What are the fractions ? 
 
 d 
 
 ^7. Divide {2x-yYa* — {x-\-yya^x^ + {x-iryyax*—x'^ hy 4 a' x^—4i a^xy + a'^y^— 0x^—0x1/+ x^. 
 
 v8. Simplify (2«-3y) (3y+2a)—3 (2a-y)'>+3 (a+y) {2a^y)+^y (1-x) (a;+l)-3 (i/+ay 
 
 ^ 9. Given ^ (4 +|a:)-| (2 z-\) = «| to find the value of a. 
 
 V 10. Giver 1 + t=:n 
 X y 
 
 — + — = JW 
 
 to find the values of x and y. 
 
 N 1 1. Given bx-l\ ^y-ir 13^^=22 
 
 Ax+ 6 v/y + 5^^=31 \ ^° ^^^ the value of *, y, and «■. 
 
 -i i= 2 
 
 X— y' + e^ 
 
 vl2. Simplify a-(J-c)- Ja-(6 + a) j _ j _(_ J -(_ j _(-«+{)_ ^j ) J ) J 
 
 13. Find a number such that whether it be divided into two or into three equal parts the continued product of the 
 parts shall be the same. 
 
 15. Divide the number 90 into two such parts that if half the greater be added to double the smaller, the result 
 is the original number 90. 
 
 15. Of two brothers, whose ages differ by 20 year?, one is as much above 25 as the other is below it. "What is the 
 age of each ?