>^^!^ ^^^..^c IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I ■ 50 ™^^ t 1^ 2.5 !L25 1 1.4 I 2.2 2.0 1.6 6" ^ ■7 "# Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 CIHM/ICMH Microfiche Series. CIHM/ICMH Collection de microfiches. Canadian Institute for Historical Microreproductions / Institut Canadian de microreproductions historiques 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 bibliographically unique, which may alter any of the images in the reproduction, or which may significantly change the usual method of filming, are checked below. □ Coloured covers/ Couverture de couleur □ Covers damaged/ Couverture endommagde □ Covers restored and/or laminated/ Couverture restaur6e et/ou pelliculie D D n Cover title missing/ Le titre de couverture manque □ Coloured maps/ Cartes giographiques en couleur □ Coloured inli (i.e. other than blue or b!ack)/ Encre de couleur (i.e. autre que bleue ou noire) □ Coloured plates and/or illustrations/ Planches et/ou illustrations en couleur □ Bound with other material/ Reli6 avec d'autres documents Tight binding may cause shadows or distortion along i iterior margin/ La re liure serrde peut causer de I'ombre ou de la distortion lo long de la marge intdrieure Blank leaves added during restoration may appear within the text. Whenever possible, these have been omitted from filming/ II se peut que certaines pages blanches ajout6es lors d'une restauration apparaissent dans le texte, mais, lorsque cela 6tait possible, ces pages n'ont pas 6t6 filmies. L'institut a microfilm^ le meilleur exemplaire qu'il lui a iti possible de se procurer. Les details de cet exemplaire qui sont r>eut-dtre uniques du point de vue bibliographique, qui peuvent modifier une image reproduite, ou qui peuvent exiger una modification dans la mithode normale de filmage sont indiquAs ci-dessous. Coloured pages/ Pages de couleur □ Pages damaged/ Pages endommagdes □ Pages restored and/or laminated/ Pages restaurdes et/ou peiliculdes n/ Pages discoloured, stained or foxed/ Pages dicolordes, tachet^es ou piqu6es I I Pages detached,' Pages J6tachdes Showthrough/ Transparence Quality of prir Qualitd indgale de I'impression Includes supplementary materia Comprend du materiel supplementaire j I Showthrough/ I I Quality of print varies/ I I Includes supplementary material/ D D Only edition available/ Seule Edition disponible Pages wholly or partially obscured by errata slips, tissues, etc., have been refilmed to ensure the best possible image/ Les pages totalement ou partiellement obscurcies par un feuillet d'errata, une pelure, etc., ont it^ film6es d nouveau de facon d obtenir la meilleure image possible. n to Tl P< o\ fil b< H si o fi si o T si T VI ^ d e b ri ri n S Additional comments:/ Commentaires suppldmentaires: [Printed ephemeral 1 sheet (verso blank) This item is filmed at the reduction ratio checked below/ Ce document est filmd au taux de reduction indiqu6 ci-dessoM« 18X 22X 10X 14X 26X 30X 12X 16X 20X 24X 28X 32X Th« copy filmed her* has been reproduced thanks to the generosity of: D. B. Weldon Library Univeriity 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 iteeping with the filming contract specifications. 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 bacic cover when appropriate. All other original copies are filmed beginning on the first page with a printed or illustrated impres- sion, and ending on the last page with a printed or illustrated impression. The last recorded frame on each microfiche shall contain the symbol •^»> (meaning "CON- TINUED"), or the symbol ▼ (meaning "END"), whichever applies. ly^aps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: L'exemplaire filmA fut reproduit grAce i la gAnirositi dc: D. B. Weldon Library University of Western Ontario (Regional History Room) Las imeges suivantas ont §ti reproduites avec le plua grand soin, compte tenu de la condition at de la nettet* de l'exemplaire filmi, et en conformity avec lee conditions du contrat de fitmage. Lea exemplaires originaux dont la couverture en papier est imprimte sont filmte on commenpant par le premier plat et en terminant soit par la darniAre page qui comporte une empreinte d'impression ou d'illuctration. soit par le second plat, salon le cas. Tous lee autres exemplaires originaux sont filmte en commenqant par ia premiere page qui comporte une empreinte d'impression ou d'illustration et en terminant par la dernlAre page qui comporte une telle empreinte. Un des symboles suivants apparaitra sur la dsrniAre image de cheque microfiche, seion le caa: le symbols — »• signifie "A SUIVRE '. le symbols V signifie "FIN ". Lea cartaa, planches, tableaux, etc., peuvent dtre fiimAs A dee taux de rMuction diff Arents. Lorsque le document est trop grand pour dtre reproduit en un soul cliche, il est filmA A partir de I'angle supArieur gauche, de gauche A droite. et de haut en baa, en prenant le nombre d'images nAcessaire. Lea diagrammes suivants illustrent ia mithode. 1 2 3 1 2 3 4 5 6 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~^'