^>. ^J^^ ^0^ IMAGE EVALUATION TEST TARGET (MT-3) 1.0 il ■^ ^ 1 2.2 li 2.0 i.e L25 liu 111.6 _ 6" — V] t w '/W Photographic Sciences Corporation 23 WE2T MAIN ST«(6ET WEBSTER, N.Y. 1T580 (716) 872-1503 n.' ^m« ^9> % 5".% % / rf> CIHM/ICMH Microfiche Series. CIHM/ICMH Collection de microfiches. Canadian Institute for Historical Microreproductions / Institut Canadian da microraproductlons hi.torique. Technical and Bibliographic Notes/Notes techniques et bibliographiques The Institute has attempted to obtain the best original copy available for filming. Features of this copy which may be bibliographicaily unique, which may alter any of the images in the reproduction, or which may significantly change the usual method of filming, are checked below. n n D Coloured covers/ Couverture de couleur Covers damaged/ Couverture endommagie Covers restored and/or laminated/ Couverture restaurde et/ou pellicul^e r~~| Cover title missing/ Le titre de couverture manque Coloured maps/ Cartes g^ographiques en couleur Coloured ink (i.e. other than blue or black)/ Encre de couleur (i.e. autre que bleue ou noire) Coloured plates and/or illustrations/ Planches et/ou illustrations i^n couleur Bound with other material/ Relid avec d'autres documents Tight binding may cause shadows or distorticn along interior margin/ Lareliure serr6e paut causer de I'ombre ou de la distortion le long de la marge int^rieure Blank leaves added during restoration may appear within the text. 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Tl to Tl P< o( fll O b^ th si 01 fii si oi Tl s» Tl w M di •r b« "< re m □ Additional comments:/ Commentaires suppl6mentaires; [Printed ephemera] 1 sheet (verse blank) This item is filmed at the reduction ratio checked below/ Ce document est filmd au taux de reduction indiqud ci-dessous. 10X 14X 18X 22X 26X 30X y 12X 16X 20X 24X 28X 32X The copy filmed her* has been reproduced thanks to the generosity of: D. B. Weldon Library University of Western Ontario (Regional History Room) The images appearing here are the best quality possible considering the condition and legibility of the original copy and in Iceeping with the filming contract speciflcationa. Original copies in printed paper covers are filmed beginning with the front cover and ending on the last page with a printed or illustrated impres- sion, or the back cover when appropriate. 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Les diagrammes suivants illuatrent ia m^thode. 1 2 3 1 2 3 4 5 6 f 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 ?